question stringlengths 33 165 | answer stringlengths 6 35 |
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b'Let k(d) = d**2 + 2*d + 17. Let n be k(6). Let a = -63 + n. Suppose -2/5*y**4 + 6/5*y**a - 4/5*y + 0 + 0*y**3 = 0. What is y?\n' | b'-2, 0, 1\n' |
b'Let g = 59861/4 + -14959. Factor -15*y**2 + 0 - 3*y**4 - 1/4*y**5 - g*y - 23/2*y**3.\n' | b'-y*(y + 1)**2*(y + 5)**2/4\n' |
b'Suppose -5*z = 4*m - 214, 6*z - m - 125 = 3*z. Determine u, given that -z*u**3 - 9*u**4 + 7*u + 6*u**2 + 27*u**3 - 7*u = 0.\n' | b'-2, 0, 1/3\n' |
b'Let l = -299 + 294. Let q(v) = 2*v**3 + 9*v**2 - 4*v + 7. Let s be q(l). Factor s*w + 4/3*w**2 + 2/3.\n' | b'2*(w + 1)*(2*w + 1)/3\n' |
b'Suppose -578*z + 572*z + 18 = 0. Find s, given that -6/5*s + 21/5*s**3 + 0 - z*s**2 = 0.\n' | b'-2/7, 0, 1\n' |
b'Suppose -5*g - 4*h = -18, 0*h - 3*h = -2*g - 2. Factor 0*d - 1/3 + 1/3*d**g.\n' | b'(d - 1)*(d + 1)/3\n' |
b'Let k = -10 - -12. Let -11*p**2 - p**3 + 21*p**2 - 9*p**k = 0. Calculate p.\n' | b'0, 1\n' |
b'Let p be -4*5/((-20)/4). Suppose 3*n - 2*o = 10 + 5, -p*n + o = -15. Let -11*h**n - 3*h**4 + 3*h**2 + 11*h**3 = 0. What is h?\n' | b'-1, 0, 1\n' |
b'Let o(u) = -u**3 - 2*u**2 - u. Let i be o(-2). Let d = i + 0. Factor -2*p**2 + 2*p - d*p**2 + p**2 - 6 + 7*p.\n' | b'-3*(p - 2)*(p - 1)\n' |
b'Let d(y) be the first derivative of 5/12*y**3 + 18 + y**2 + y + 1/16*y**4. Let d(n) = 0. Calculate n.\n' | b'-2, -1\n' |
b'Let i(d) be the third derivative of -d**6/40 + 9*d**5/5 - 54*d**4 + 864*d**3 + 261*d**2. Factor i(q).\n' | b'-3*(q - 12)**3\n' |
b'Suppose 143*q - 1 - 11 + 56*q + 69*q + 117*q**2 - 40*q = 0. Calculate q.\n' | b'-2, 2/39\n' |
b'Let s = 17 + -15. Let l be s/10*(1 - 6/(-6)). Solve l*j**2 + 0*j + 0 = 0.\n' | b'0\n' |
b'Suppose -17 = -3682*m + 3700*m - 53. Factor -3 - 3/2*y**3 - 6*y**m - 15/2*y.\n' | b'-3*(y + 1)**2*(y + 2)/2\n' |
b'Let z(i) = 5*i**4 - 24*i**3 - 30*i**2 + 16*i + 25. Let w(c) = -5*c**4 + 23*c**3 + 30*c**2 - 17*c - 25. Let g(u) = -4*w(u) - 3*z(u). Factor g(p).\n' | b'5*(p - 5)*(p - 1)*(p + 1)**2\n' |
b'Let c(u) = u**3 + 3*u**2 + u - 2. Let v be c(-2). Factor 2/7*o - 1/7*o**2 + v.\n' | b'-o*(o - 2)/7\n' |
b'Let k(j) be the third derivative of j**7/140 + 7*j**6/40 + 3*j**5/2 + 25*j**4/8 - 125*j**3/4 - 3*j**2 - 3. Find z such that k(z) = 0.\n' | b'-5, 1\n' |
b'Let w be (-270)/(-48)*124/155. Find l, given that -3 - w*l + 0*l**2 + 3/2*l**3 = 0.\n' | b'-1, 2\n' |
b'Let n(l) = -l**2 + 5*l + 10. Let i be n(6). Factor -i*a - 4 - 3*a**2 + a**2 + 1 + 1.\n' | b'-2*(a + 1)**2\n' |
b'Let y(h) be the first derivative of 5/14*h**2 - 33 + 2/7*h + 1/28*h**4 + 4/21*h**3. Factor y(b).\n' | b'(b + 1)**2*(b + 2)/7\n' |
b'Let t(n) be the first derivative of n**4/6 + 10*n**3/9 + 7*n**2/3 + 2*n + 91. Factor t(a).\n' | b'2*(a + 1)**2*(a + 3)/3\n' |
b'Let d(t) be the second derivative of 1/30*t**5 + 13 + 1/45*t**6 + 0*t**2 + 0*t**3 - 1/9*t**4 + 2*t. Suppose d(g) = 0. What is g?\n' | b'-2, 0, 1\n' |
b'Let y(m) be the first derivative of 3*m + 0*m**3 + 2 + 1/12*m**2 - 1/72*m**4. Let n(d) be the first derivative of y(d). Solve n(r) = 0 for r.\n' | b'-1, 1\n' |
b'Let c(p) be the second derivative of -3*p**5/40 + p**4/8 + p**3/2 + 7*p + 4. Find f, given that c(f) = 0.\n' | b'-1, 0, 2\n' |
b'Let z(p) be the second derivative of -p**6/120 - 3*p**5/40 + 17*p**3/6 - 20*p. Let t(i) be the second derivative of z(i). Factor t(n).\n' | b'-3*n*(n + 3)\n' |
b'Factor -1/8*q + 1/2 + 1/8*q**3 - 1/2*q**2.\n' | b'(q - 4)*(q - 1)*(q + 1)/8\n' |
b'Let z be (1 - (-156)/60)/(21/28). Factor 12/5*v - 3/5*v**4 + 0 + 3*v**3 - z*v**2.\n' | b'-3*v*(v - 2)**2*(v - 1)/5\n' |
b'Let c(y) be the second derivative of -1/14*y**7 - 2*y**3 - 22*y + 3/4*y**5 + 5/6*y**4 - 4*y**2 + 0 - 1/15*y**6. Solve c(q) = 0 for q.\n' | b'-2, -1, -2/3, 1, 2\n' |
b'Let p be 1 - (4 + -9 + 83). Let c = -305/4 - p. Let 3/4*d + c*d**2 - 3/2 = 0. What is d?\n' | b'-2, 1\n' |
b'Suppose -14*r - 504 + 504 = r. Factor 4/5*f**4 - 2/5*f**3 + r*f + 0 + 0*f**2 - 2/5*f**5.\n' | b'-2*f**3*(f - 1)**2/5\n' |
b'Let k(p) be the first derivative of p**5 - 5*p**4 - 35*p**3/3 + 25*p**2 - 110. Suppose k(c) = 0. What is c?\n' | b'-2, 0, 1, 5\n' |
b'Let q be (-14)/(-6) + 13/(-39). Factor 3*r - 94*r**2 + 2 + 94*r**q - r**3.\n' | b'-(r - 2)*(r + 1)**2\n' |
b'Let w be 18/(-12)*2 - -8. Let z(u) be the second derivative of 1/21*u**7 + 0 + 0*u**2 - 1/3*u**3 + 0*u**w + 2/15*u**6 - 1/3*u**4 + 2*u. Factor z(c).\n' | b'2*c*(c - 1)*(c + 1)**3\n' |
b'Factor 242/9*s + 0 - 7/9*s**4 - 99*s**2 + 52/3*s**3.\n' | b'-s*(s - 11)**2*(7*s - 2)/9\n' |
b'Let f(u) be the second derivative of 4*u**7/15 - u**6/5 - 13*u**5/25 + u**4/2 - 2*u**3/15 + 3*u. Solve f(c) = 0.\n' | b'-1, 0, 1/4, 2/7, 1\n' |
b'Let u(c) = -c**2 - 18*c - 5. Let z(g) = -4*g**2 - 72*g - 19. Let t(l) = 9*u(l) - 2*z(l). Let h(w) = 9*w + 3. Let o(y) = 5*h(y) + 3*t(y). Factor o(q).\n' | b'-3*(q + 1)*(q + 2)\n' |
b'Let u(b) = 10*b**4 - 10*b**2 + 10. Let k(x) be the second derivative of -x**6/30 - x**2/2 + 18*x. Let p(m) = -5*k(m) - u(m). Factor p(s).\n' | b'-5*(s - 1)**2*(s + 1)**2\n' |
b'Let g(s) be the first derivative of 1/10*s**2 + 4*s + 1/60*s**4 - 1/15*s**3 + 2. Let t(c) be the first derivative of g(c). Solve t(o) = 0.\n' | b'1\n' |
b'Let x(g) = 3*g - 15. Let p be x(6). Factor 7*r**3 - 2*r**4 - 3*r**3 + 2*r**2 - 6*r**p + 2*r**5.\n' | b'2*r**2*(r - 1)**2*(r + 1)\n' |
b'Let x(y) be the second derivative of -5*y**6/24 - 3*y**5/2 + 5*y**4/3 + 14*y**2 + 38*y. Let g(z) be the first derivative of x(z). Let g(d) = 0. Calculate d.\n' | b'-4, 0, 2/5\n' |
b'Factor 6*d**2 - 10*d**5 + 116*d**4 + 484*d**4 - 6*d**2 + 285*d**3 + 315*d**5 - 10*d**2.\n' | b'5*d**2*(d + 1)**2*(61*d - 2)\n' |
b'Let v(b) be the third derivative of 0 - 47*b**2 - 9/16*b**4 + 1/80*b**6 + 0*b + 27/8*b**3 + 0*b**5 - 1/840*b**7. Solve v(k) = 0 for k.\n' | b'-3, 3\n' |
b'Suppose -3 = -h + 2*w - 9, 0 = -5*h + 2*w + 10. Let x = -55596 - -55598. Find r, given that 1/5*r**h + 0 + 0*r - 1/5*r**x + 0*r**3 = 0.\n' | b'-1, 0, 1\n' |
b'Let t = 472 - 470. Determine u so that 2/3*u + 4/3 - 2/3*u**t = 0.\n' | b'-1, 2\n' |
b'Factor -14*q + 17 + 9 - 11 + 0 - q**2.\n' | b'-(q - 1)*(q + 15)\n' |
b'Let n(x) be the third derivative of x**6/1080 - x**5/180 + 5*x**3/2 - 7*x**2. Let l(m) be the first derivative of n(m). Factor l(r).\n' | b'r*(r - 2)/3\n' |
b'Determine z, given that -327/11*z**3 + 730/11*z**2 + 9/11*z**4 + 136/11 - 548/11*z = 0.\n' | b'2/3, 1, 34\n' |
b'Suppose -22604 + 22616 + 33*j**3 + 129*j**2 + 144*j + 6*j**2 = 0. Calculate j.\n' | b'-2, -1/11\n' |
b'Let c = -81 - -79. Let w be ((-4)/(-7))/(c - (-51)/21). Let -4/3*a**2 + 0*a - 1/3*a**4 + 0 + w*a**3 = 0. What is a?\n' | b'0, 2\n' |
b'Let z(s) be the second derivative of 9*s + 0 + 2/21*s**3 - 1/35*s**5 + 4/7*s**2 - 2/21*s**4. Factor z(y).\n' | b'-4*(y - 1)*(y + 1)*(y + 2)/7\n' |
b'Let s = 52226 + -52222. Factor 8/5*v**s + 4/5*v**2 + 0*v + 0 - 2*v**3 - 2/5*v**5.\n' | b'-2*v**2*(v - 2)*(v - 1)**2/5\n' |
b'Suppose -47 = -3*t + 2*t - n, 3*n + 223 = 4*t. Let s be 6/39 + 148/t. Factor 2/9*g + 0 - 2/9*g**2 + 2/9*g**4 - 2/9*g**s.\n' | b'2*g*(g - 1)**2*(g + 1)/9\n' |
b'Solve 2/3*n**3 + 10 - 58/3*n + 26/3*n**2 = 0 for n.\n' | b'-15, 1\n' |
b'Let v(l) be the first derivative of -3*l**5/5 - 39*l**4/4 - 22*l**3 - 95. Find d, given that v(d) = 0.\n' | b'-11, -2, 0\n' |
b'Let k(m) = -66*m**2 + 117*m - 51. Let o(v) be the first derivative of -5*v**3/3 + 9*v**2/2 - 4*v + 4. Let z(h) = 2*k(h) - 27*o(h). Factor z(w).\n' | b'3*(w - 2)*(w - 1)\n' |
b'Let g(s) = -5*s**2 - 212*s - 76. Let u be g(-42). Let b(p) be the first derivative of -p + p**2 + u - 1/3*p**3. Factor b(y).\n' | b'-(y - 1)**2\n' |
b'Let k(d) be the second derivative of 0*d**2 - 3*d - 2/21*d**3 + 1/70*d**5 + 0 + 1/42*d**4. Factor k(p).\n' | b'2*p*(p - 1)*(p + 2)/7\n' |
b'Let t(u) be the first derivative of 1/16*u**4 + 1/4*u + 28 - 1/12*u**3 - 1/8*u**2. Factor t(l).\n' | b'(l - 1)**2*(l + 1)/4\n' |
b'Let t(v) be the second derivative of -v**4/4 + 9*v**3/7 - 12*v**2/7 + 103*v. Factor t(u).\n' | b'-3*(u - 2)*(7*u - 4)/7\n' |
b'Let r(t) = -t**4 - t**3 + t**2 + t + 1. Let n(o) = -7*o**5 + 13*o**4 + 2*o**3 - 4*o**2 - 4*o - 4. Let p(z) = n(z) + 4*r(z). Determine l, given that p(l) = 0.\n' | b'0, 2/7, 1\n' |
b'Let l(t) = -6*t**4 + 6*t**3 - 15*t + 3. Let o be (-2)/14 - 1/(21/(-24)). Let p(s) = s**4 + s**3 + s - 1. Let b(n) = o*l(n) + 3*p(n). Factor b(z).\n' | b'-3*z*(z - 2)**2*(z + 1)\n' |
b'Let q = 5122 + -10217/2. Factor q*t**5 + 8 + 225/2*t**3 - 189/2*t**4 + 68*t + 361/2*t**2.\n' | b'(t - 4)**2*(3*t + 1)**3/2\n' |
b'Let r(o) be the second derivative of 25*o**7/42 - 13*o**6/6 + 3*o**5/2 + o - 7. Factor r(k).\n' | b'5*k**3*(k - 2)*(5*k - 3)\n' |
b'Let m be (-1 - 0)/(1883/(-2646) - (-10)/(-135)). What is b in -24/11 - 32/11*b - m*b**2 - 2/11*b**3 = 0?\n' | b'-3, -2\n' |
b'Determine o, given that 4*o**4 + 17*o**3 + 23*o**3 + 122*o - 2639 - 124*o**2 + 2599 - 2*o**5 = 0.\n' | b'-5, 1, 4\n' |
b'Let a(u) be the first derivative of -u**6/4 - 39*u**5/10 - 15*u**4 - 18*u**3 + 96. What is w in a(w) = 0?\n' | b'-9, -2, 0\n' |
b'Let k(l) be the third derivative of l**8/168 - l**7/210 - l**6/20 + 7*l**5/60 - l**4/12 - 61*l**2. Factor k(m).\n' | b'm*(m - 1)**2*(m + 2)*(2*m - 1)\n' |
b'Let f(r) be the second derivative of r**6/15 + r**5/5 - r**4/6 - 2*r**3/3 + 3*r - 11. Factor f(y).\n' | b'2*y*(y - 1)*(y + 1)*(y + 2)\n' |
b'Let w = -791 - -110741/140. Let k(z) be the third derivative of 0*z**3 + 1/120*z**5 - 1/80*z**6 - 2*z**2 + w*z**7 + 0*z**4 + 0 - 1/672*z**8 + 0*z. Factor k(t).\n' | b'-t**2*(t - 1)**3/2\n' |
b'Let h be 1*(6 + (-1)/1). Find f, given that -11 - f**3 + 5*f**3 - 16*f + 4*f**2 - h = 0.\n' | b'-2, -1, 2\n' |
b'Let a(f) be the third derivative of 2*f**7/735 + 17*f**6/210 + 31*f**5/105 + 5*f**4/14 + 32*f**2 - 3. Solve a(u) = 0.\n' | b'-15, -1, 0\n' |
b'Factor -211*l**2 + 227*l + 172 + 160*l**3 - 7*l**4 + 354*l**2 + 3*l**4 + 285*l + 361*l**2.\n' | b'-4*(l - 43)*(l + 1)**3\n' |
b'Factor 3/2*h**2 + 27/2*h + 27.\n' | b'3*(h + 3)*(h + 6)/2\n' |
b'Let d(u) = 4*u**2 + 132*u + 1804. Let g(c) = 21*c**2 + 666*c + 9022. Let b(s) = 11*d(s) - 2*g(s). Determine q, given that b(q) = 0.\n' | b'-30\n' |
b'Let c(x) be the first derivative of 7*x**3 - 7 + 9*x**2 + 3*x**4 + 27/40*x**5 + 1/16*x**6 + 6*x. Factor c(h).\n' | b'3*(h + 1)*(h + 2)**4/8\n' |
b'Let p(w) = -9*w + 82. Let d(a) = 3*a - 27. Let f(n) = -8*d(n) - 3*p(n). Let i be f(11). Let 12/5*u - 4*u**i - 26/5*u**2 + 5*u**4 + 9/5 = 0. What is u?\n' | b'-3/5, 1\n' |
b'Let s(q) be the second derivative of -q**5/20 - q**4/6 + q**3/6 + q**2/2 - 7*q. Let w be s(-3). Factor 4*x**4 - 6*x**2 + 12*x**3 + 7*x**2 + w*x**2.\n' | b'4*x**2*(x + 1)*(x + 2)\n' |
b'Suppose -2*u - 3*u - 40 = 0. Let r be ((-15)/(-20))/((-2)/u). Factor 3*q**2 - 7*q - 2*q + 6*q**2 - 3*q**3 + r.\n' | b'-3*(q - 1)**3\n' |
b'Let s(k) be the third derivative of k**7/1365 + k**6/390 + k**5/390 + 16*k**2 - 16. Factor s(c).\n' | b'2*c**2*(c + 1)**2/13\n' |
b'Let r be 5/(-15) - 22/(-3). What is k in 17*k**2 + 55*k**5 - 3 - 6*k**5 - 21*k**4 + 24*k + 0 - 73*k**3 + r = 0?\n' | b'-1, -2/7, 1\n' |
b'Let t(n) = -n + 13. Let q be t(9). Suppose 0*a**4 + a**q + 2*a**2 + 2*a - 5*a**2 - 4*a = 0. What is a?\n' | b'-1, 0, 2\n' |
b'Let x be 4/(-84)*35 - (-62)/21. Determine s so that -3/7*s**4 + 3/7*s - 9/7*s**2 + 0 + x*s**3 = 0.\n' | b'0, 1\n' |
b'Let j be ((0 - -7) + -7)/(-4). Let q(r) = 11*r + 2. Let v be q(j). Factor 0 + 1/2*s**3 - 1/2*s + 1/4*s**4 - 1/4*s**v.\n' | b's*(s - 1)*(s + 1)*(s + 2)/4\n' |
b'Let b(f) = -5*f**2 - 120*f + 3719. Let q(u) = 18*u**2 + 359*u - 11156. Let j(v) = 7*b(v) + 2*q(v). Factor j(y).\n' | b'(y - 61)**2\n' |
b'Suppose 10*o = 8*o + 40. Suppose 2*m - o = -2*m. Let -16/7*l**4 - 76/7*l**2 + 2/7*l**m - 16/7 + 8*l + 50/7*l**3 = 0. Calculate l.\n' | b'1, 2\n' |
b'Let a(f) be the first derivative of -4*f**5/5 - 14*f**4 + 4*f**3 + 80*f**2 - 112*f - 120. Factor a(h).\n' | b'-4*(h - 1)**2*(h + 2)*(h + 14)\n' |
b'Let n(v) be the first derivative of v**8/1680 + 2*v**7/525 + v**6/200 + 11*v**2/2 + 11. Let u(l) be the second derivative of n(l). What is p in u(p) = 0?\n' | b'-3, -1, 0\n' |
b'Let z(x) be the first derivative of -4*x**3/21 + 568*x**2/7 - 80656*x/7 + 51. Find a such that z(a) = 0.\n' | b'142\n' |
b'Let s(r) be the third derivative of 3*r**8/112 + 11*r**7/35 + 47*r**6/40 + 3*r**5/5 - 9*r**4/2 - 286*r**2. Suppose s(d) = 0. Calculate d.\n' | b'-3, -2, 0, 2/3\n' |
b'Let u = 3357/2 + -1678. Solve 1/3*p + u*p**2 - 3/2*p**3 + 1/2*p**5 + 1/6*p**4 + 0 = 0 for p.\n' | b'-2, -1/3, 0, 1\n' |
b'Let p(z) be the third derivative of -z**8/1848 - 19*z**7/1155 - 12*z**6/55 - 272*z**5/165 - 256*z**4/33 - 256*z**3/11 + 82*z**2. Factor p(w).\n' | b'-2*(w + 3)*(w + 4)**4/11\n' |
b'Let d(j) be the first derivative of -j**5/5 - 157*j**4/4 + 347. Find x, given that d(x) = 0.\n' | b'-157, 0\n' |
b'Let t(b) be the first derivative of b**6/2 - 3*b**4/2 + 3*b**2/2 + 63. Factor t(h).\n' | b'3*h*(h - 1)**2*(h + 1)**2\n' |
b'Suppose -7*b = -3*b + z - 11, -2*z + 14 = 4*b. Let u = 257/6 - 127/3. What is w in 0 + 5/6*w**b + u*w**3 - 1/3*w = 0?\n' | b'-2, 0, 1/3\n' |
b'Let h(b) be the third derivative of -b**7/273 + b**6/390 + 2*b**5/13 + 14*b**4/39 - 32*b**3/39 + 16*b**2. What is a in h(a) = 0?\n' | b'-2, 2/5, 4\n' |
b'Suppose 25*t**3 - 39*t**2 - 3*t**4 + 129150*t - 129132*t - t**3 = 0. What is t?\n' | b'0, 1, 6\n' |
b'Let u be -4*(21/(-4))/(6/(-4)). Let x be u/70 + 7/10. What is j in x*j**2 + 0*j + 0 = 0?\n' | b'0\n' |
b'Let n(x) = -2*x + 5. Let w(c) = 3*c - 7. Let g(k) = 7*n(k) + 5*w(k). Suppose 9*z - 12*z = 3. Let p(u) = u**2 - u + 1. Let d(l) = z*p(l) + g(l). Factor d(r).\n' | b'-(r - 1)**2\n' |
b'Factor 34/9*i + 10/9*i**2 + 4/3.\n' | b'2*(i + 3)*(5*i + 2)/9\n' |
b'Let n(v) be the third derivative of 1/5*v**5 + 2/15*v**6 - 5*v**2 + 0*v + 0 - 8/3*v**3 - 2/3*v**4 + 2/105*v**7. Determine w so that n(w) = 0.\n' | b'-2, -1, 1\n' |
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