x) = 0. What is x?
1, 23
Let d(y) be the second derivative of -y**5/200 + y**4/30 + y**3/60 - y**2/5 - 2*y + 8. Suppose d(q) = 0. What is q?
-1, 1, 4
Let c = -2/51 + 157/102. Let q(a) = -a**2 + 40*a + 2. Let v be q(0). Find m, given that 1/2*m**3 + c*m**v + 3/2*m + 1/2 = 0.
-1
Determine f, given that 1/8*f**2 - 3/2 + 1/8*f = 0.
-4, 3
Suppose 4*w - 5*t - 43 = 0, 5*t + 10 - 1 = 2*w. Let u = -15 + w. Determine k, given that -2*k**u + 2 + k**5 - 2 + 6*k**3 - 6*k**4 + k**5 = 0.
0, 1
Let m be 18/(18/24 - 1). Let i = 72 + m. Suppose 1/2*g**4 + 1/2*g + 3/2*g**2 + 3/2*g**3 + i = 0. What is g?
-1, 0
Let y(f) = -12*f - 1389. Let h be y(-116). Factor 3/2*q**3 + h*q**2 - 14*q - 1/2*q**4 + 12.
-(q - 2)**3*(q + 3)/2
Let z be 14*((-9)/6)/(-1). Let r = z + -13. Factor -2*d**2 - 7*d**3 + r*d**3 - d**5 + 2*d**3.
-d**2*(d - 1)**2*(d + 2)
Find l, given that 2/5*l**4 + 42*l**2 + 100 - 110*l - 34/5*l**3 = 0.
2, 5
Factor -10615*w**4 - 4*w**3 + w**5 + 3*w**3 + 10614*w**4 + w**2.
w**2*(w - 1)**2*(w + 1)
Suppose 1820 = -3*t + 16*t. Factor 13*m + 131 - t - m - 3*m**2.
-3*(m - 3)*(m - 1)
Factor -2*u - 6*u**2 - 35*u**3 + 4 + 3 - 1 + 37*u**3.
2*(u - 3)*(u - 1)*(u + 1)
Let b(i) be the first derivative of 3/8*i**2 - 1/24*i**6 + 3/20*i**5 - 1/8*i**4 - 1/6*i**3 + 13 - 1/4*i. Factor b(m).
-(m - 1)**4*(m + 1)/4
Let z(b) = 3*b**3 - 324*b**2 - 103*b + 58. Let w(u) = u**3 - 323*u**2 - 103*u + 60. Let x(c) = 6*w(c) - 5*z(c). Find v such that x(v) = 0.
-35, -2/3, 1/3
Let w(f) = f + 1. Let d(p) = -p**2 - 9*p - 12. Let b be -2 - (8/(-36) + (-33)/(-27)). Let m(j) = b*d(j) - 6*w(j). Factor m(r).
3*(r + 2)*(r + 5)
Let n(f) be the first derivative of f**5/240 + f**4/24 - 5*f**3/24 - 10*f**2 + 13. Let y(m) be the second derivative of n(m). Factor y(t).
(t - 1)*(t + 5)/4
Let y be (-27)/(-9) + (-3 - 0). Let m be 1/(-7)*2 - 1846/(-728). Suppose -3/4 - 3/2*f**3 + y*f + m*f**2 = 0. What is f?
-1/2, 1
Suppose -62*j + 162 = 38. Find z, given that 4/7*z + 6/7*z**j - 2/7 = 0.
-1, 1/3
Let k(x) be the third derivative of x**6/252 + 31*x**5/630 + 47*x**4/252 + x**3/3 - 18*x**2 + 3. Factor k(y).
2*(y + 1)**2*(5*y + 21)/21
Let j(v) = -28*v**2 + 212*v + 5613. Let d(n) = -39*n**2 + 318*n + 8420. Let h(l) = -5*d(l) + 7*j(l). Suppose h(o) = 0. Calculate o.
-53
Let f(h) be the second derivative of h**7/14 - 7*h**6/15 - 7*h**5/20 + 5*h**4/6 + 700*h. What is v in f(v) = 0?
-1, 0, 2/3, 5
Factor -96*m**2 - 2*m**3 - 24*m**2 - 2*m**3 + 0*m**3.
-4*m**2*(m + 30)
Suppose 14*v = 9 + 33. Let u(a) be the third derivative of 0 + 1/20*a**5 - 3/4*a**4 + 0*a + 9/2*a**v + 4*a**2. Factor u(d).
3*(d - 3)**2
Factor 0 + 0*c - 2/3*c**3 + 4/3*c**2.
-2*c**2*(c - 2)/3
Let y = 24401/7 + -3485. Factor -10/7*f**2 - 2*f - 2/7*f**3 - y.
-2*(f + 1)**2*(f + 3)/7
Suppose -140*m - 76 + 140*m**3 + 1085*m**4 - 1081*m**4 - 148*m**2 + 220 = 0. Calculate m.
-36, -1, 1
Determine d so that 216 - 40*d + 95*d - 115*d - 4*d**2 = 0.
-18, 3
Factor -88 + 69*i**2 - 358*i + 128 + 43*i + 203 + 3*i**3.
3*(i - 3)*(i - 1)*(i + 27)
Let x(d) be the second derivative of d**7/18 + 2*d**6/15 - d**5/15 - 7*d**4/18 - d**3/6 + d**2/3 + 57*d + 1. Suppose x(t) = 0. What is t?
-1, 2/7, 1
Let h = -3870 - -6529/2. Let d = h - -619. Let 9*x - d - 3/2*x**2 = 0. What is x?
3
Let k(u) = 35*u**4 - 15*u**3 + 40*u**2 + 30*u + 30. Let c(l) = l**4 - l**3 + l**2 + l + 1. Let f(h) = -30*c(h) + k(h). Solve f(b) = 0 for b.
-2, -1, 0
Factor 2/15*g**3 - 14/3*g - 32/15*g**2 - 12/5.
2*(g - 18)*(g + 1)**2/15
Let r(u) = -5*u**5 - 6*u**4 + 3*u**3 + 4*u**2 + 4*u - 4. Let l(d) = -d**5 - 2*d**4 - d**3 + d - 1. Let w(k) = 4*l(k) - r(k). Solve w(p) = 0.
-1, 0, 4
Let k(z) be the first derivative of 2/21*z**3 + 6/7*z + 4/7*z**2 - 9. Solve k(s) = 0.
-3, -1
Find p, given that 15/4*p**3 + 1/2 - 4*p**2 + 3/4*p - p**4 = 0.
-1/4, 1, 2
Let z(d) = d**4 - d**3 + d. Let h(o) = -69*o**2 - 21*o**2 - 103*o - 11*o**3 - 8*o**4 - 40 - 21*o**3. Let b(f) = h(f) + 3*z(f). Let b(x) = 0. Calculate x.
-2, -1
Factor 8 - o - 1/4*o**2.
-(o - 4)*(o + 8)/4
Let n = 40 + -36. Factor 12*r**4 + n*r**3 + 4*r**2 + 0*r**2 - 20*r**3.
4*r**2*(r - 1)*(3*r - 1)
Let y(a) be the third derivative of a**6/180 + a**5/30 + a**4/12 - a**3 + 5*a**2. Let i(z) be the first derivative of y(z). Let i(j) = 0. What is j?
-1
Let x be 255/50*2 - (-2)/(-10). Let y = -8 + x. Factor 0 - 3/2*q**3 - 6*q - 6*q**y.
-3*q*(q + 2)**2/2
Let g(l) be the second derivative of 9*l**5/4 - 625*l**4/12 + 515*l**3/6 + 65*l**2/2 - 5*l - 22. Factor g(z).
5*(z - 13)*(z - 1)*(9*z + 1)
Let 158 + 58*s**2 - 27*s**2 + 32*s + 98 - 30*s**2 = 0. What is s?
-16
Let g(t) be the first derivative of 2*t**3/51 - 14*t**2/17 + 26*t/17 + 71. Factor g(z).
2*(z - 13)*(z - 1)/17
Suppose 0*f - f = -3*y + 10, 0 = -4*f - 4. Let a(d) be the second derivative of 0 + 0*d**2 + d + 3/14*d**y - 1/28*d**4. Factor a(t).
-3*t*(t - 3)/7
Suppose -5*v + 60 = 7*v. Suppose -v*a - f = -8*a + 8, 0 = -5*a + 5*f. Suppose 0*n - 1/2*n**5 - 1/2*n**2 + 1/2*n**a + 0 + 1/2*n**3 = 0. Calculate n.
-1, 0, 1
Factor 49/5*l**3 - 42*l**2 + 57/5*l - 4/5.
(l - 4)*(7*l - 1)**2/5
Factor -76*d**2 - 20/3*d**3 - 88/3*d + 0.
-4*d*(d + 11)*(5*d + 2)/3
Solve 280/3*k**4 + 44/3*k**2 + 200*k**5 - 2/3*k + 0 - 274/3*k**3 = 0.
-1, 0, 1/10, 1/3
Let z(i) be the first derivative of -25/12*i**4 - 15*i + 15 + 5/36*i**6 - 20/9*i**3 + 1/3*i**5 + 55/4*i**2. What is w in z(w) = 0?
-3, 1, 2
Solve 0 + 1/4*w**3 - 83/4*w**2 + 0*w = 0 for w.
0, 83
Let g(x) be the third derivative of -1/360*x**6 - 1/6*x**3 - 1/40*x**5 + 0*x + 7*x**2 + 0 + 0*x**4. Let y(k) be the first derivative of g(k). Factor y(j).
-j*(j + 3)
Find j, given that -1/2*j**3 - 1680*j + 57*j**2 + 3136 = 0.
2, 56
Let v(a) be the third derivative of 0*a + 0*a**3 - 1/540*a**6 + 8*a**2 + 0 + 1/54*a**5 - 1/36*a**4 - 1/945*a**7. Factor v(b).
-2*b*(b - 1)**2*(b + 3)/9
Suppose -7*c + 9*c = 10. Let j(z) = 2*z**2 - 7*z + 5. Let h be j(c). Let f**2 + 42*f - h*f - 21*f = 0. Calculate f.
-1, 0
Let a(w) be the third derivative of -w**6/72 - 2*w**5/9 - 5*w**4/8 + 5*w**3 + 5*w**2 - 2. Determine j, given that a(j) = 0.
-6, -3, 1
Let m(x) be the first derivative of -3*x**2 - 3/5*x**5 + 9/4*x**4 + 0*x + x**3 - 1/2*x**6 + 17. Let m(t) = 0. What is t?
-2, -1, 0, 1
Let o(y) be the second derivative of -19*y - 6/5*y**5 - 1/3*y**4 + 0 - 32*y**2 - 2/15*y**6 + 16*y**3. Factor o(s).
-4*(s - 1)**2*(s + 4)**2
Solve -r**4 + 7*r**3 - 7/2*r - 1 - 7/2*r**5 + 2*r**2 = 0 for r.
-1, -2/7, 1
Let z(v) be the first derivative of -1/16*v**4 + 3 - 1/8*v**2 - 1/6*v**3 + 0*v. Factor z(k).
-k*(k + 1)**2/4
Suppose -22*b + 2 = -20*b. Let s(a) = -2*a**3 - 18*a**2 - 10*a + 2. Let t(j) = j**3 - j**2 + j + 1. Let h(f) = b*s(f) - 2*t(f). Suppose h(w) = 0. Calculate w.
-3, -1, 0
Let b = 1912 + -1909. Factor 0 + 0*i**2 - 3/4*i + 3/4*i**b.
3*i*(i - 1)*(i + 1)/4
Let i(o) be the third derivative of 3/20*o**5 - 9/35*o**7 - 1/6*o**8 + 0*o**3 + 0 + 22*o**2 - 1/12*o**4 + 13/120*o**6 - 2*o. Determine z, given that i(z) = 0.
-1, -1/2, 0, 1/4, 2/7
What is h in 4*h - 4*h**2 - 54406 + 54406 = 0?
0, 1
Let n(q) be the second derivative of -q**7/7560 + q**6/270 - 2*q**5/45 + 13*q**4/6 + 24*q. Let m(b) be the third derivative of n(b). What is i in m(i) = 0?
4
Suppose -14*k - 7*k = 63. Let p be (3 + (-18)/15)*(-1)/k. Solve -p - 6/5*l - 3/5*l**2 = 0.
-1
Let k(u) = -4*u - 30. Let g be k(-8). Factor 7*s**g - 446*s + 20 - 2*s**2 + 426*s.
5*(s - 2)**2
Let r(l) = -2*l**4 + 11*l**3 + 4*l**2 - 11*l + 9. Let v(c) = -c**3 + c - 1. Let d(g) = -2*r(g) - 22*v(g). Factor d(f).
4*(f - 1)**2*(f + 1)**2
Let k be (-3636)/(-2376) + (-6)/4. Let n(o) be the second derivative of 1/33*o**4 + 0 + k*o**3 + 0*o**2 + 6*o. Suppose n(t) = 0. Calculate t.
-1/2, 0
Let z = 293 + -293. Let g(i) be the third derivative of -14*i**2 + 1/84*i**8 + 0*i**5 - 1/15*i**6 + 0*i + z*i**7 + 0*i**3 + 0 + 1/6*i**4. Factor g(y).
4*y*(y - 1)**2*(y + 1)**2
Let h(m) be the second derivative of -23/80*m**5 + 0 - 7/12*m**4 - 1/168*m**7 + 0*m**2 - 1/2*m**3 + 23*m - 1/15*m**6. Find i such that h(i) = 0.
-3, -2, -1, 0
Let c be (-132)/(-99) + (-15)/18. What is l in 2/3 + c*l**2 + 4/3*l = 0?
-2, -2/3
Suppose -5*k - 5*b - 15 = 0, -5*b - 3 = -18. Let d = -1 - k. Solve 1 - 2*l + d*l**2 - 1 + 0*l**2 + 2*l**3 - 5*l**4 = 0 for l.
-1, 0, 2/5, 1
Let w be ((-66)/55)/((-8)/60). Let n be 5 + w/6*-2. Determine d, given that -1