(k) = -10*k**4 + 26*k**3 - 74*k**2 + 68*k - 17. Let a(g) = 5*h(g) - 7*x(g). Let a(c) = 0. What is c?
1, 8
Suppose 8*v - 5*v = 27. Suppose -6 = -v*d + 6*d. Factor 8/5 - 4/5*s**d - 4/5*s.
-4*(s - 1)*(s + 2)/5
Let j be (-21)/(-12) - (-3)/12 - 0. Let q(g) be the second derivative of 0 - 1/10*g**4 - 2*g + 1/50*g**5 + 1/5*g**3 - 1/5*g**j. What is f in q(f) = 0?
1
Let y(t) be the first derivative of t**4/4 + 2*t**3 + 5*t**2/2 + 79. Factor y(o).
o*(o + 1)*(o + 5)
Find p such that 27/5*p**2 + 768/5 - 288/5*p = 0.
16/3
Let z = -42880/3 + 14294. Determine k, given that -1/6*k**3 + z - 1/2*k**2 + 0*k = 0.
-2, 1
Let x(v) be the third derivative of -5*v**9/3024 + v**7/56 + v**6/36 + 7*v**3/6 + 4*v**2. Let k(m) be the first derivative of x(m). Factor k(o).
-5*o**2*(o - 2)*(o + 1)**2
Let q be ((-8)/(-10))/(2/10). Let x be 200/24 - q/(-6). Factor -2*i + x - 6*i**2 + 4*i**3 - i**3 - i**3 - 3.
2*(i - 3)*(i - 1)*(i + 1)
Suppose 5*b - 18 = -4*r, -r + 8 = -12*b + 15*b. Let s(n) be the second derivative of 1/14*n**4 - 4/21*n**3 + 0 + 6*n - 4/7*n**b. Find t such that s(t) = 0.
-2/3, 2
Let c(o) be the second derivative of -o**6/135 + 7*o**5/90 - 11*o**4/54 + 5*o**3/27 - 300*o. Factor c(n).
-2*n*(n - 5)*(n - 1)**2/9
Let i = 11 + -9. Suppose 3*h**3 + 12 - 3*h + 10*h**i - 7*h**2 - 15*h**2 = 0. What is h?
-1, 1, 4
Factor 1/2*x**2 - 11 - 21/2*x.
(x - 22)*(x + 1)/2
Let d(f) be the first derivative of -375*f**4/16 + 675*f**3/4 - 3645*f**2/8 + 2187*f/4 - 74. Factor d(c).
-3*(5*c - 9)**3/4
Let l(t) = -t**3 + t + 3. Let a be l(0). Suppose -5 = 4*d - 13. Factor -11*n**a + 8*n**3 - n**4 - 5*n**2 + 3*n**d.
-n**2*(n + 1)*(n + 2)
Let z be (-1)/11 + 1360/4675. Let -1/5*y + 1/5 - 1/5*y**2 + z*y**3 = 0. Calculate y.
-1, 1
Let m = -13/183 + 3895/732. Solve -m*c**5 + 0*c - 57/4*c**4 + 3*c**2 + 0 - 6*c**3 = 0.
-2, -1, 0, 2/7
Let z = 20 + -16. Solve -z*u**5 + 0*u**3 + 2*u**5 - 2*u**3 + 4*u**4 = 0.
0, 1
Let g = 909 + -21815/24. Let h(x) be the second derivative of -g*x**3 + 0*x**2 + x - 1/48*x**4 + 0. Factor h(y).
-y*(y + 1)/4
Suppose -20/7*a + 18/7*a**2 + 8/7*a**3 - 6/7 = 0. Calculate a.
-3, -1/4, 1
Let u(c) = -5*c**2 - 320*c + 40. Let b(v) = v - 2. Let z(y) = -20*b(y) - u(y). Solve z(r) = 0.
-60, 0
Let s(d) be the third derivative of 11*d**2 + 0 - 5/8*d**4 + 5/336*d**8 - 1/4*d**6 + 0*d**3 + 0*d + 0*d**7 + 2/3*d**5. Factor s(a).
5*a*(a - 1)**3*(a + 3)
Let f be (3 + 3)*(901 + -1). Factor 2000 - f*b - 1081*b**3 + 4860*b**2 - 475*b**3 + 98*b**3.
-2*(9*b - 10)**3
Let r be (44/6)/(-3 - (-48)/13). Let g = 2/27 + r. Find s, given that -4/3*s**3 + 8*s**2 - 16*s + g = 0.
2
Factor -4*u**3 + 10*u**3 - 8*u - 10594*u**4 + 10592*u**4.
-2*u*(u - 2)**2*(u + 1)
Let h(u) = -345*u - 2067. Let n be h(-6). Let 16/5*z**n - 24/5 + 76/5*z + 76/5*z**2 = 0. Calculate z.
-3, -2, 1/4
Let c be (-2)/(-60)*(-117 - -132). Suppose 1 - 1/2*t**4 - 3/2*t - c*t**2 + 3/2*t**3 = 0. What is t?
-1, 1, 2
Let d(s) = -6*s**3 - 21*s**2 + 11*s + 36. Let w(v) = -v**3 + 2*v**2 + 2*v + 1. Let t(z) = 3*d(z) - 15*w(z). Factor t(x).
-3*(x - 1)*(x + 1)*(x + 31)
Let s(q) = q**2 - 3*q + 3. Let r be s(3). Suppose 1 - 4 = -2*v + r*x, -5*x + 11 = 2*v. Factor -3*j**2 - 3*j**2 - 3*j**v + 0*j**2 + 3*j**4.
3*j**2*(j - 2)*(j + 1)
Let j(t) = -2*t**4 + 2*t**3 + 14*t**2 - 20*t + 6. Let l(g) = -g**3 + 2*g - 1. Let n(x) = -j(x) - 6*l(x). Factor n(o).
2*o*(o - 1)**2*(o + 4)
Let l(d) be the first derivative of 2/5*d**5 - 1/22*d**4 - 6 + 4/11*d - 4/33*d**6 + 5/11*d**2 - 26/33*d**3. Suppose l(n) = 0. Calculate n.
-1, -1/4, 1, 2
Factor -7*m + 3/2*m**4 - 3/2 - 8*m**2 - m**3.
(m - 3)*(m + 1)**2*(3*m + 1)/2
Suppose 0 + 208/7*j**2 - 5406/7*j**3 - 2/7*j**5 - 208/7*j**4 + 5408/7*j = 0. Calculate j.
-52, -1, 0, 1
Let d be (2 - 5)/(-15)*3. Suppose -3*x - 3 + 15 = 0. Factor 2/5*u**2 + 1/5*u**3 - 4/5*u**x + 0*u + 0 - d*u**5.
-u**2*(u + 1)**2*(3*u - 2)/5
Let m(k) be the third derivative of -k**7/630 - 7*k**6/90 - 43*k**5/30 - 209*k**4/18 - 605*k**3/18 - 79*k**2 + 4. Suppose m(w) = 0. What is w?
-11, -5, -1
Let u(w) be the third derivative of w**5/12 - 35*w**4/12 + 2*w**2 + 640. Solve u(a) = 0.
0, 14
Suppose -5*l + 16 = -4*s, -2*l - 22*s = -25*s - 12. Solve -4/3*g**2 - 2/3*g**3 + 0*g + l = 0 for g.
-2, 0
Let h(p) = -7*p**3 - p**2 - 6*p - 2. Suppose 0 = 2*z + k + 12, -z + 5*k + 4 = -1. Let s(o) = -4*o**3 - 3*o - 1. Let i(n) = z*s(n) + 3*h(n). Factor i(v).
-(v + 1)**3
Let w be -6*28/(-72)*3. Let u(i) be the second derivative of -2/285*i**6 + 0*i**5 + 0*i**2 + 0 + 1/57*i**3 + 1/57*i**4 - 6*i - 1/399*i**w. Factor u(q).
-2*q*(q - 1)*(q + 1)**3/19
Let c(a) be the third derivative of -7/240*a**5 + 0 + 7/192*a**4 + 1/24*a**3 + 1/192*a**6 + 0*a - 30*a**2. Determine k so that c(k) = 0.
-1/5, 1, 2
Let h be ((-1904)/(-1344))/((-85)/(-15)). Solve -h + 0*r + 1/4*r**2 = 0 for r.
-1, 1
Let g(o) be the third derivative of -o**5/20 + 85*o**4/8 + 43*o**3 + 396*o**2. Factor g(b).
-3*(b - 86)*(b + 1)
Let i(n) = -3 - n**3 + 9 + 2*n - 5*n**2 + 6*n. Let g(a) = -80*a**2 - a - 1 - 56*a**2 + 137*a**2. Let h(b) = -6*g(b) - i(b). Let h(w) = 0. Calculate w.
-1, 0, 2
Suppose 10*r - 6*r + 84 = 0. Let j be (-15)/(-5) + (54/r - 0). Factor 2/7*s**2 + j*s**3 + 0 - 1/7*s.
s*(s + 1)*(3*s - 1)/7
Factor -3*y**2 - 7/3*y**3 + 4/3 + 4*y.
-(y - 1)*(y + 2)*(7*y + 2)/3
Suppose s - 5*b + 143 = 0, -s + 3*b = -5*s - 457. Let i = 592/5 + s. Solve 1/5*k**4 + i - 1/5*k + 1/5*k**3 - 3/5*k**2 = 0 for k.
-2, -1, 1
Suppose -2*v - v = -6. Suppose v = 3*n - 4. Factor 0 - 1 - 2*d + n + d**2.
(d - 1)**2
Solve -155*v**5 + 150*v**5 - 30*v**3 - 20*v**2 + 6*v**4 + 19*v**4 + 40*v = 0 for v.
-1, 0, 2
Let t(v) be the second derivative of -9/5*v**2 - 8/15*v**4 + 0 + 8/5*v**3 - 12*v. Factor t(z).
-2*(4*z - 3)**2/5
Let a(k) be the first derivative of 2*k**5/45 + 2*k**4/9 + 8*k**3/27 + 81. Let a(p) = 0. Calculate p.
-2, 0
Let n be (101 + -95)*(-8)/(-36). Factor -4/3*t - 10/9 + 2/9*t**4 + 8/9*t**2 + n*t**3.
2*(t - 1)*(t + 1)**2*(t + 5)/9
Suppose -9*v + 78 = 78. Let z(n) be the second derivative of 0*n**2 - 1/48*n**4 + 1/24*n**3 + v + 2*n. Solve z(x) = 0.
0, 1
Solve 1/4*c - 3/4*c**2 - 1/4*c**3 + 1/4*c**4 + 1/2 = 0.
-1, 1, 2
Suppose -10/9*t**2 + 8/9 + 38/9*t = 0. What is t?
-1/5, 4
Factor 45*n**3 - 36*n**4 - 45*n**2 + 45*n**3 - 4*n**5 - 39*n**2 + 7*n**5 + 27*n.
3*n*(n - 9)*(n - 1)**3
Let w = 16397/4 + -4079. Factor -33/4*u**4 - w + 3/4*u**5 - 135/2*u**2 + 243/4*u + 69/2*u**3.
3*(u - 3)**3*(u - 1)**2/4
Let z(q) be the first derivative of q**3/3 + 11*q**2 + 121*q + 8. Suppose z(o) = 0. Calculate o.
-11
Let m(h) be the first derivative of h**5/10 - 5*h**4/6 + 7*h**3/3 - 3*h**2 - 4*h - 29. Let j(y) be the first derivative of m(y). Factor j(t).
2*(t - 3)*(t - 1)**2
Solve -28*d**2 - 4*d**4 + 399*d**3 - 96 - 176*d - 44*d**2 - 48*d**2 - 435*d**3 = 0 for d.
-3, -2
Let j(u) = 4*u**3 + u**2 - 5*u + 9. Let q(o) = 3*o**3 + 4*o**2 + o + 1. Let d(v) = -j(v) + q(v). Factor d(t).
-(t - 4)*(t - 1)*(t + 2)
Suppose -15*z + 24*z = -100*z + 436. Let 0 - 4/5*k**5 - 56/5*k**2 + 4*k - 8/5*k**z + 48/5*k**3 = 0. What is k?
-5, 0, 1
Let d(u) = -u**3 - 9*u**2 - 10*u + 1. Let j be d(-7). Let n be (6/9)/((-6)/j). Factor -8*q**2 + 3*q + 2*q**4 - 6*q**2 - 3*q**n + 5*q**2 + 6 + q**4.
3*(q - 2)*(q - 1)*(q + 1)**2
Let n be 3*((-12)/(-8) + -1). Let y(r) be the first derivative of 1 + n*r**2 + 4*r**3 + 9/4*r**4 + 0*r. Solve y(f) = 0 for f.
-1, -1/3, 0
Suppose -5*j - 10 = -0*j - 4*d, 0 = -3*j + 2*d - 6. Let g be 1/(j/(-10) + 0). Factor -r**3 - g + 2*r**3 - r**2 + 2*r**2 - r + 4.
(r - 1)*(r + 1)**2
Let y = 1296/11 + -15541/132. Suppose -y*v**2 + 1/12*v + 0 = 0. Calculate v.
0, 1
Factor -964*l**4 + 959*l**4 + 23*l**2 + 15*l**3 - 3*l**2.
-5*l**2*(l - 4)*(l + 1)
Let n(r) = 5 + r**3 - 4*r**2 + 0*r**2 - r**2 + 4*r. Let b be n(4). Solve -5*g**4 - g**3 - 6*g**4 - 2*g + 11*g**2 - b*g**3 - g**3 + 9*g**5 = 0 for g.
-1, 0, 2/9, 1
Let o(k) be the first derivative of 2*k**6/3 + 4*k**5/5 - 3*k**4 - 4*k**3/3 + 4*k**2 + 1. Factor o(p).
4*p*(p - 1)**2*(p + 1)*(p + 2)
Let p(f) be the first derivative of -f**7/7560 + f**6/1080 - f**5/540 - 2*f**3/3 + 22. Let r(i) be the third derivative of p(i). Factor r(s).
-s*(s - 2)*(s - 1)/9
Let x(h) be the first derivative of 4*h**5/5 + 2*h**4 - 12*h**3 - 4*h**2 + 32*h - 365. Suppose x(i) = 0. What is i?
-4, -1, 1, 2
Let m(x) be the first derivative of -49*x**