i(d) = d**4 - 3*d**3 + d**2 + 1. Let u(y) = -2*i(y) + 6*w(y). Factor u(p).
4*(p - 1)**2*(p + 1)**2
Let l(b) be the first derivative of -2*b**5/5 + 4*b**4 - 46*b**3/3 + 28*b**2 - 24*b - 29. What is k in l(k) = 0?
1, 2, 3
Let w = -131/7 - -19. Factor 2/7*t**5 + 0 + 4/7*t**4 - 4/7*t**2 - w*t + 0*t**3.
2*t*(t - 1)*(t + 1)**3/7
Let m(x) be the second derivative of -x**6/900 - x**3/2 - 4*x. Let g(o) be the second derivative of m(o). Factor g(b).
-2*b**2/5
Let a(z) = 2*z**3 + 2*z**2 - 2*z + 1. Let t be a(1). Determine q so that -2*q**5 + 3*q**4 + 4*q**3 - t*q**4 - 2*q + 0*q**4 = 0.
-1, 0, 1
Let r(d) = 3*d**3 + 2*d**2 + 5*d + 2. Let o(v) = -13*v**3 - 7*v**2 - 20*v - 8. Let g(s) = 2*o(s) + 9*r(s). Factor g(n).
(n + 1)**2*(n + 2)
Let y be (-1)/(-3)*(-4887)/36. Let t = 46 + y. Factor 0 + t*v**4 - 1/4*v + 1/4*v**2 + 5/4*v**3.
v*(v + 1)**2*(3*v - 1)/4
Let t(j) = -5*j**4 + 6*j**3 + 3*j**2. Let h(z) = z**4 + z**2. Let m(g) = -6*h(g) - t(g). Factor m(d).
-d**2*(d + 3)**2
Factor 3*v**3 - 20*v**5 - 18*v**5 - 16*v**5 + 51*v**5.
-3*v**3*(v - 1)*(v + 1)
Factor 2/3*y**2 - 2/3 + 0*y.
2*(y - 1)*(y + 1)/3
Find k, given that -3/4 - k - 1/4*k**2 = 0.
-3, -1
Factor 2/9*i**2 + 0 - 2/9*i.
2*i*(i - 1)/9
Let g(c) = c + 10. Let x be g(-8). Let u be 4/(-3)*(-3)/x. Factor -8*y**2 - 3*y**3 - 12*y + 2 - 6 - 3*y**u.
-(y + 1)*(y + 2)*(3*y + 2)
Solve -1/5*z**2 + 1/5*z**4 - 1/5*z**3 + 1/5*z**5 + 0*z + 0 = 0.
-1, 0, 1
Let d(i) = -i**3 - 8*i**2 - i - 10. Let t be d(-8). Let h be (-1)/t*(-11 + 11). Suppose 2/5*o + 4/5*o**4 + 0 + h*o**3 - 2/5*o**5 - 4/5*o**2 = 0. What is o?
-1, 0, 1
Let c(s) be the third derivative of s**10/75600 + s**9/15120 + s**8/10080 - s**5/15 - 4*s**2. Let l(i) be the third derivative of c(i). Factor l(a).
2*a**2*(a + 1)**2
Let o(p) be the second derivative of 0 - 3/7*p**2 - 9*p + 1/14*p**3 + 1/28*p**4. Factor o(k).
3*(k - 1)*(k + 2)/7
Let r(c) be the second derivative of 1/15*c**4 + 1/15*c**3 + 0*c**2 + c + 0 + 1/50*c**5. Solve r(b) = 0.
-1, 0
Let j(b) be the second derivative of b**6/480 + b**5/240 - b**2/2 + 3*b. Let y(p) be the first derivative of j(p). Factor y(n).
n**2*(n + 1)/4
Let j be (-4)/(-2*1/((-6)/(-54))). Find p such that -j - 2/3*p - 4/9*p**2 = 0.
-1, -1/2
Suppose 12 = 3*r - 0. Suppose -h - 1 + r = 0. Factor 4/7*s**h - 4/7*s + 2/7 - 2/7*s**2.
2*(s - 1)*(s + 1)*(2*s - 1)/7
Let z(j) = 5*j**3 - j. Let w be z(1). Let n = 48 + -26. Suppose 0 - 8/7*b - 14*b**w - 64/7*b**2 - n*b**3 = 0. Calculate b.
-1, -2/7, 0
Suppose -2*g + 0 = -6. Factor 2*j**3 - 13*j + 7*j + g*j**2 - 3*j**4 + 4*j**3.
-3*j*(j - 2)*(j - 1)*(j + 1)
Suppose -3*r + 5*x - 2 = -1, -3*x = -2*r. Suppose c = -r*c + 16. What is l in 3*l**c - 3 + 4*l**3 - 6*l + 3*l**3 + 0*l**4 - l**3 = 0?
-1, 1
Let h(i) be the first derivative of -3*i**6/2 + 3*i**5/5 + 6*i**4 + 4*i**3 + 9. Let h(y) = 0. What is y?
-1, -2/3, 0, 2
Let p = -1 + 5. Suppose -p*o + 11 = 3. Factor -1 - t - 1 + 0 + t**o.
(t - 2)*(t + 1)
Find j, given that -3*j**5 + 3*j**4 + 82*j**3 - 82*j**3 = 0.
0, 1
Let t(k) be the second derivative of 0*k**3 - 3/4*k**5 - 1/2*k**4 + 0*k**2 - 3*k - 3/10*k**6 + 0. Determine d so that t(d) = 0.
-1, -2/3, 0
Let f = -1/836 + 439/17556. Let h(l) be the second derivative of 0*l**2 + 7/48*l**4 - 2*l + 0 + 13/120*l**6 + 1/24*l**3 + 3/16*l**5 + f*l**7. Factor h(a).
a*(a + 1)**3*(4*a + 1)/4
Let m(g) be the first derivative of 5*g**3/3 + 30*g**2 + 180*g + 31. Factor m(w).
5*(w + 6)**2
Let k = 5/13 - 7/52. Solve -1/2 - 1/4*s + k*s**2 = 0 for s.
-1, 2
Let w(g) be the first derivative of -2*g**5/35 + 3*g**4/14 - 4*g**3/21 - 7. Let w(y) = 0. What is y?
0, 1, 2
Suppose -4*y + 10 = -0*y - 5*j, 5*y - 2*j - 4 = 0. Let a(i) be the first derivative of -1/4*i**2 - 1/8*i**4 + 1/3*i**3 + 2 + y*i. Factor a(u).
-u*(u - 1)**2/2
Let a(t) be the first derivative of t**3/7 + 3*t**2/14 + 3. Find g, given that a(g) = 0.
-1, 0
Let i(v) = -2*v**3 - v**2 + 2*v + 1. Let x be i(-2). Let a be (x/(-6))/((-35)/20). What is n in 4/7 + a*n**2 - 2/7*n**3 - 2/7*n**4 + 10/7*n = 0?
-1, 2
Let r(h) = 9*h**5 - 25*h**4 - 43*h**3 - 27*h**2 + 21*h + 32. Let o(y) = -y**5 + y**4 + y**3 + y**2 + y. Let a(n) = -22*o(n) - 2*r(n). Factor a(d).
4*(d - 1)*(d + 2)**4
Factor -2/3 + 5/6*k**3 + 13/6*k**2 + 2/3*k.
(k + 1)*(k + 2)*(5*k - 2)/6
Let g(s) be the third derivative of s**7/210 - s**6/24 + 3*s**5/20 - 7*s**4/24 + s**3/3 - 4*s**2. Factor g(i).
(i - 2)*(i - 1)**3
Solve -6/5*b**4 + 3*b - 42/5*b**2 - 3/5*b**5 + 0 + 36/5*b**3 = 0 for b.
-5, 0, 1
Let t(u) be the first derivative of -u**5/35 - u**4/28 + 3*u**3/7 - 11*u**2/14 + 4*u/7 - 9. Factor t(j).
-(j - 1)**3*(j + 4)/7
Let k(s) be the third derivative of -s**9/9450 + s**8/3360 - s**7/6300 - s**4/12 + s**2. Let x(y) be the second derivative of k(y). Factor x(q).
-2*q**2*(q - 1)*(4*q - 1)/5
Suppose 3*r + 3*x + 8 = -2*x, 3*x + 16 = r. Let i(m) be the first derivative of 4/3*m**3 + 1/2*m**2 + 0*m - 3 + 1/6*m**6 + 4/5*m**5 + 3/2*m**r. Factor i(s).
s*(s + 1)**4
Suppose 5*d = -2*s + 7, -3*d - 5*s = -5 + 16. Factor 2 - 4*o**3 + 7*o**4 + o - 9*o**4 + d*o.
-2*(o - 1)*(o + 1)**3
Let y(f) = -2*f - 4. Let a be y(-4). Let g(p) be the first derivative of 6*p - 1/2*p**a + 10/3*p**3 - 1 - 7*p**2. Suppose g(i) = 0. What is i?
1, 3
Let d = -7/114 - -53/38. Factor -4/3*g + 1/3*g**2 + d.
(g - 2)**2/3
Let h be (2/8 - 0) + 16/64. Let -1/2*b - h + b**2 = 0. Calculate b.
-1/2, 1
Suppose 3*a + 1 = 10. Let c(u) be the first derivative of 2 + 0*u + 1/12*u**a + 0*u**2 + 1/16*u**4. Factor c(y).
y**2*(y + 1)/4
Let s be 133/(-95)*5/(-2). Let s*g - 1 - 2*g**3 + 4*g**4 - 3*g**2 - 3/2*g**5 = 0. Calculate g.
-1, 2/3, 1
Let v(c) = 2*c**2 - 12*c + 11. Let z be v(5). Let i(h) be the first derivative of 0*h**2 + 1/30*h**6 + 0*h**5 + z + 0*h + 0*h**3 + 0*h**4. Factor i(g).
g**5/5
Let h(b) = b**2 + 29*b + 18. Let z(o) = -o**2 - 44*o - 27. Let d(f) = -8*h(f) - 5*z(f). Factor d(v).
-3*(v + 1)*(v + 3)
Let l = 15 + -12. Let y(w) be the third derivative of 0*w - 1/10*w**5 + 13/240*w**6 + 11/96*w**4 - 1/12*w**l + 0 - 1/60*w**7 - 2*w**2 + 1/448*w**8. Factor y(i).
(i - 1)**4*(3*i - 2)/4
Let c(x) be the third derivative of 0 + 0*x**3 - 1/18*x**4 + 0*x - 1/30*x**5 + 0*x**6 - 4*x**2 + 1/315*x**7. Factor c(r).
2*r*(r - 2)*(r + 1)**2/3
Let q(f) be the second derivative of 2/21*f**4 - 1/7*f**2 + 5/294*f**7 - 6*f + 11/70*f**5 - 1/14*f**3 + 3/35*f**6 + 0. What is h in q(h) = 0?
-1, 2/5
Factor 0 + 2/17*n + 0*n**2 - 2/17*n**3.
-2*n*(n - 1)*(n + 1)/17
Suppose -s = -4*m - m - 13, -5 = -s + m. Suppose 0 = i + 1 - s. Solve 0*v + 0*v**3 + 2/3*v**4 - 4/3*v**i + 2/3 = 0 for v.
-1, 1
Let v(t) be the first derivative of -t**6/3 + 6*t**5/5 - t**4 - 24. What is p in v(p) = 0?
0, 1, 2
Let j(v) = -5*v**3 - v - 2. Let c(m) = 6*m**3 + 2*m + 3. Let t be 12 + -16 - 0/1. Let g(w) = t*c(w) - 5*j(w). Factor g(r).
(r - 2)*(r + 1)**2
Let n(s) be the first derivative of s**7/1260 - s**6/270 + s**5/180 - 2*s**3/3 - 2. Let w(i) be the third derivative of n(i). Factor w(y).
2*y*(y - 1)**2/3
Determine r, given that -2/11 + 4/11*r**3 - 4/11*r**2 - 6/11*r + 6/11*r**4 + 2/11*r**5 = 0.
-1, 1
Let y be (-4)/12 + (-1)/(-3). Let i be (-1 + y)/(3/(-9)). Suppose 2*q**3 + 0*q**i - q**3 = 0. Calculate q.
0
Suppose 4*r + 2*k - 8 = 0, r - 3*k - 4 + 16 = 0. Determine o, given that 2/5*o + 2/5*o**2 + r = 0.
-1, 0
Let s(v) be the second derivative of v**6/120 - v**5/60 - v**4/24 + v**3/6 + v**2/2 - 3*v. Let m(u) be the first derivative of s(u). Solve m(y) = 0 for y.
-1, 1
Suppose -9*w = -14*w + 10. Factor -t**3 - 1/2*t**w + 0*t + 0.
-t**2*(2*t + 1)/2
Suppose -3*i + i - 3*u = 5, 5*u = 5*i - 25. Suppose -2*w - i - 1/2*w**2 = 0. What is w?
-2
Let o = 10 - 6. Let r(a) be the second derivative of a**4/6 + a**2 + 20*a. Let u(k) = -k**2 - k - 1. Let y(s) = o*u(s) + 3*r(s). What is f in y(f) = 0?
1
Suppose 6*j - 2 - 16 = 0. Let k(w) be the second derivative of 0 - w + 0*w**2 - 1/10*w**5 + 0*w**j + 0*w**4 + 1/15*w**6. Solve k(n) = 0.
0, 1
Let b(u) be the second derivative of u**7/420 + u**6/180 - u**5/30 - 7*u**3/6 + 7*u. Let c(k) be the second derivative of b(k). Solve c(a) = 0 for a.
-2, 0, 1
Factor -18*q**2 - 10*q**2 - 15*q + 10 + 12*q**2 - 9*q**2.
-5*(q + 1)*(5*q - 2)
Factor 2/7*g**3 - 4/7*g**2 + 0*g + 0.
2*g**2*(g - 2)/7
Let w = -5 - -3. Let l(u) = -4*u**3 + 4*u + 2. Let b be 6 + 1 - (5 - 3). Let k(a) = -9*a**3 + a*