tive of 7*j**6/300 + 9*j**5/200 + j**4/60 - 4*j. Let a(o) = 0. What is o?
-1, -2/7, 0
Let a be 2/(-14) - (-2)/14. Let p(s) be the third derivative of 3*s**2 - 1/96*s**4 + a*s**3 + 0 - 1/240*s**5 + 0*s. Factor p(k).
-k*(k + 1)/4
Let r(h) = -h**3 - h**2 - h - 1. Let x be r(-1). Suppose x = 4*k - 8*k + 8. Factor -6*m + 6*m + 2*m**k - 2.
2*(m - 1)*(m + 1)
Let x be 4/14 - 12/(-7). Let y = 10 + x. Factor -2 - 3*r - 36*r**3 - y*r**4 + 0 - 1 - 15*r - 39*r**2.
-3*(r + 1)**2*(2*r + 1)**2
Let b(k) be the first derivative of 1/20*k**5 + 4 + 0*k + 1/16*k**4 - 1/12*k**3 - 1/8*k**2. Factor b(a).
a*(a - 1)*(a + 1)**2/4
Let q(c) = -c**4 + 3*c**3 - 4*c**2 + 4*c + 4. Suppose 23 = -5*n - 22. Let z(j) = 3*j**4 - 6*j**3 + 9*j**2 - 9*j - 9. Let a(m) = n*q(m) - 4*z(m). Factor a(t).
-3*t**3*(t + 1)
Let p(t) = -8*t**3 + 28*t**2 - 37*t + 17. Let f(o) = 65*o**3 - 225*o**2 + 295*o - 135. Let m(l) = 3*f(l) + 25*p(l). Factor m(b).
-5*(b - 2)**2*(b - 1)
Let f(z) = -z**3 - z**2 + z + 7. Let q be f(0). Let g = q + -2. Find c, given that -3/4*c**4 + 3/2*c**2 + 3/4*c**g - 3/2*c**3 + 3/4*c - 3/4 = 0.
-1, 1
Let j = -11 - -11. Let r be j + -6*1/(-3). Let -4/3*h + 0 + 2*h**4 - 1/3*h**5 - 13/3*h**3 + 4*h**r = 0. What is h?
0, 1, 2
Suppose 9*u - 46 = -19. Find x, given that 8/7 - 10/7*x**4 + 2*x**u - 16/7*x + 2/7*x**5 + 2/7*x**2 = 0.
-1, 1, 2
Let v(n) = 13*n**3 - 23*n**2 + 2*n - 8. Let c(w) = 7*w**3 - 12*w**2 + w - 4. Let q(m) = -11*c(m) + 6*v(m). Let y be q(6). Factor 1/2 - 3/4*j**y - 5/4*j.
-(j + 2)*(3*j - 1)/4
Suppose -5*w - 4*v = -65, w + v - 13 = -0*w. Suppose 2*p - 5*d = 1, -4*p + 2*d + w = 3*d. Factor -2*j**p + 4*j**2 + j - 3*j + 0*j**3.
-2*j*(j - 1)**2
Let h(t) = -2*t**3 - 2*t. Let r(v) = -3*v**3 + v**2 - 3*v. Let i(p) = -20*p**3. Let m be i(-1). Suppose -3*d + m = d. Let s(k) = d*h(k) - 4*r(k). Factor s(o).
2*o*(o - 1)**2
Factor -11*n**3 + 9*n**3 + 2 - 2*n**4 + 10*n + 2 + 6*n**2.
-2*(n - 2)*(n + 1)**3
Let c(u) = -5*u**3 + 2*u**2 - u. Let m(s) = s**3. Let z(g) = -c(g) - 4*m(g). Factor z(r).
r*(r - 1)**2
Let g(x) be the third derivative of x**6/240 - x**5/120 - x**4/48 + x**3/12 - 17*x**2. Factor g(j).
(j - 1)**2*(j + 1)/2
Let k = -1/4 - -3/4. Let y be (-3 - 33/(-9))*3. Factor -1/2*f**3 - k*f**5 + 0 - f**4 + 0*f + 0*f**y.
-f**3*(f + 1)**2/2
Let y(g) be the first derivative of g**6/360 - g**5/60 + 2*g**3/3 - 2. Let d(v) be the third derivative of y(v). Factor d(q).
q*(q - 2)
Factor 5 + 5 - 5*n**2 + 0*n**2 - 5.
-5*(n - 1)*(n + 1)
Suppose -4/3*f**2 + 4*f - 8/3 = 0. What is f?
1, 2
Let a(j) be the second derivative of 0 - 1/60*j**5 - 1/9*j**3 + 0*j**2 - 1/12*j**4 + 2*j. Let a(y) = 0. What is y?
-2, -1, 0
Suppose -2*t - t = -15. Suppose 0 = 5*b - t*a - 5, 0 = -2*b + 3*a + 1. Find h such that 2*h + h**2 + b*h - 3*h**2 = 0.
0, 2
Factor 15*p**4 + 0 - 12/5*p + 72/5*p**2 - 27*p**3.
3*p*(p - 1)*(5*p - 2)**2/5
Let v = 38/279 - 5/62. Let r(o) be the first derivative of 0*o**2 - 1/27*o**6 + 2/27*o**3 + 0*o + v*o**4 - 2/45*o**5 + 2. Let r(y) = 0. What is y?
-1, 0, 1
Let q be (-3)/(-6)*(-5 - -6). Let c(g) be the first derivative of 2/3*g**3 + 0*g**2 + 0*g + q*g**4 - 1/3*g**6 - 2/5*g**5 - 2. What is l in c(l) = 0?
-1, 0, 1
Factor 14/3*v**2 - 2*v - 4/3*v**3 + 0.
-2*v*(v - 3)*(2*v - 1)/3
Let o(i) = -3*i**2 - 11*i - 5. Let y(m) be the third derivative of m**4/24 + m**3/6 + 2*m**2. Let t(w) = -o(w) - 5*y(w). Let t(p) = 0. What is p?
-2, 0
Let a(s) be the third derivative of 2*s**2 + 1/180*s**5 + 0*s**3 + 1/630*s**7 + 1/180*s**6 + 0 + 0*s**4 + 0*s. Solve a(g) = 0 for g.
-1, 0
Let t(h) be the second derivative of -h**4/12 + 4*h**3/3 + 4*h**2 - 3*h. Let a(o) = 8*o + 9. Let b(j) = 4*a(j) - 5*t(j). Find d, given that b(d) = 0.
-2/5, 2
Suppose -2*u - 5*t = -23, -7*u - 2*t + 38 = -3*u. Let j = u - 7. Determine i, given that -2/5 - 2*i - 8/5*i**j = 0.
-1, -1/4
Let d(u) be the second derivative of u**8/252 - u**7/42 + u**6/18 - u**5/18 + u**3/18 - 3*u**2/2 + 2*u. Let t(f) be the first derivative of d(f). Factor t(r).
(r - 1)**4*(4*r + 1)/3
Let q(v) = -v**2 - 14*v - 6. Let z be q(-9). Suppose 3*l - 15 = 0, -4*n - 3*l = -0*l - z. Factor 2*j**3 + n*j**2 + 2*j**3 + 2*j + 2*j**4 + 2*j**3.
2*j*(j + 1)**3
Let z be ((-1)/(-3))/(3/27) - -2. Let l(m) be the first derivative of 18/55*m**z - 1/11*m**2 + 0*m + 14/33*m**3 - 1 - 15/22*m**4. Factor l(t).
2*t*(t - 1)*(3*t - 1)**2/11
Let q(k) be the second derivative of -k**10/30240 + k**8/6720 - k**4/12 + k. Let d(s) be the third derivative of q(s). Factor d(m).
-m**3*(m - 1)*(m + 1)
Let r be 4/12*2/10. Let n(a) be the third derivative of 0*a + 1/30*a**6 + r*a**5 + 0 - 1/105*a**7 - 1/3*a**3 - 1/12*a**4 - 1/168*a**8 - 2*a**2. Factor n(b).
-2*(b - 1)**2*(b + 1)**3
Let i(d) be the second derivative of d**5/25 + 4*d**4/5 + 32*d**3/5 + 128*d**2/5 + 17*d. Factor i(h).
4*(h + 4)**3/5
Let a(r) be the third derivative of 0*r**4 - 1/30*r**6 - 1/30*r**5 + 0*r - 2*r**2 + 0 + 0*r**3 - 1/105*r**7. Determine z so that a(z) = 0.
-1, 0
Let n be (304/(-12))/(-4) + 6. Factor -n*w**2 - 4/3 - 10*w**3 - 20/3*w - 3*w**4.
-(w + 1)**2*(3*w + 2)**2/3
Let k(a) be the second derivative of 5*a**7/28 - 17*a**6/20 + 27*a**5/20 - a**4/4 - 7*a**3/4 + 9*a**2/4 + 9*a. Factor k(t).
3*(t - 1)**4*(5*t + 3)/2
Let d(w) be the third derivative of 1/120*w**6 + 0 + 0*w**4 + 0*w**3 + w**2 + 0*w + 1/60*w**5. Solve d(p) = 0 for p.
-1, 0
Let q = 225 - 221. Factor 0 + 3/2*h**2 - 3/2*h**q + 0*h + 0*h**3.
-3*h**2*(h - 1)*(h + 1)/2
Let u(a) = -a**2 + 1. Suppose -3*d + q - 8 = 0, 0 = -4*d - 2*q + 2 + 4. Let k(n) = 9*n**3 - 10*n**2 - 9*n + 10. Let r(m) = d*k(m) + 4*u(m). Factor r(b).
-3*(b - 1)*(b + 1)*(3*b - 2)
Let m(r) be the third derivative of -13/1155*r**7 + 3*r**2 + 1/330*r**5 + 3/220*r**6 + 0*r + 0*r**3 - 1/66*r**4 + 0 + 5/1848*r**8. Factor m(t).
2*t*(t - 1)**3*(5*t + 2)/11
Let y = 287 + -1431/5. Factor 4/5*w**2 - 4/5*w**4 + 0 - 4/5*w + y*w**3.
-4*w*(w - 1)**2*(w + 1)/5
Let x be (-22)/(-6) + 2/6. Let t = -4 + x. Factor -1/2 + t*o - 1/2*o**4 + o**2 + 0*o**3.
-(o - 1)**2*(o + 1)**2/2
Let g(r) be the first derivative of 0*r - 1/20*r**5 + 0*r**2 + 3 + 1/12*r**3 + 0*r**4. Factor g(n).
-n**2*(n - 1)*(n + 1)/4
Let w(n) be the second derivative of 1/4*n**4 - n**3 - 5*n - 9/2*n**2 + 0. Suppose w(h) = 0. Calculate h.
-1, 3
Let r(v) be the second derivative of -v**5/20 + v**4/36 + v**3/9 + 11*v. Determine o, given that r(o) = 0.
-2/3, 0, 1
Let y(f) = 16*f**4 + 12*f**3 - 4*f**2 + 4*f - 4. Let v(r) = -16*r**4 - 12*r**3 + 4*r**2 - 5*r + 5. Let j(a) = 4*v(a) + 5*y(a). Solve j(g) = 0.
-1, 0, 1/4
Let g = -11/5 + 13/5. Solve -12*u**2 + 18/5*u**5 + 18/5*u - g - 66/5*u**4 + 92/5*u**3 = 0.
1/3, 1
Let n = -20 + 23. Let y(i) be the first derivative of -n + 5/4*i**4 - 2*i - 5/2*i**2 + 2/3*i**3. Factor y(q).
(q - 1)*(q + 1)*(5*q + 2)
Factor 0 + 2/13*r**4 + 2/13*r**3 + 0*r - 4/13*r**2.
2*r**2*(r - 1)*(r + 2)/13
Let p(w) be the second derivative of -w + 1/15*w**5 - 1/15*w**6 + 1/18*w**4 + 0 + 0*w**3 + 0*w**2. Factor p(b).
-2*b**2*(b - 1)*(3*b + 1)/3
Let n(t) = -t**3 + t**2 - t - 1. Let v(o) be the third derivative of 7*o**6/120 - o**5/12 + o**3/3 - o**2. Let u(s) = 2*n(s) + v(s). Let u(m) = 0. What is m?
-2/5, 0, 1
Let g(m) be the first derivative of -m**4/4 + m**3/3 - 3*m**2/2 - m + 3. Let r(j) = -3 + j**3 + 3 + 3*j + 1. Let i(c) = -3*g(c) - 4*r(c). Factor i(u).
-(u + 1)**3
Suppose 0 = -6*s + 3*s. Let l(m) be the third derivative of -m**2 + 0*m**3 + s + 0*m + 1/24*m**4 - 1/30*m**5. Solve l(i) = 0.
0, 1/2
Let h(m) be the third derivative of m**5/20 - m**4/8 - m**3 - 9*m**2. What is i in h(i) = 0?
-1, 2
Suppose 2*q + 3*r = 31 - 11, 20 = 5*r. Factor -3*d**3 - 3*d + q - 2*d**2 - 4 + 8*d**2.
-3*d*(d - 1)**2
Let p(l) be the third derivative of l**7/2100 - l**6/225 + l**5/100 + 3*l**3/2 + 6*l**2. Let d(c) be the first derivative of p(c). Suppose d(g) = 0. What is g?
0, 1, 3
Let r(l) = -11*l**4 - 9*l**3 + 4*l**2 + 15*l + 1. Let d(u) = -10*u**4 - 10*u**3 + 4*u**2 + 14*u + 2. Let p(n) = 3*d(n) - 2*r(n). Let p(i) = 0. Calculate i.
-1, -1/2, 1
Let k(n) be the second derivative of 0*n**2 - 1/90*n**6 - 1/60*n**5 + 0*n**3 + 0 + 3*n + 0*n**4. Factor k(g).
-g**3*(g + 1)/3
Factor 4*r**3 - 2*r + 3*r**5 - 4*r**2 + 2*r**4 + 7*r**5 - 15*r**5 + 2 + 3*r**5.
-2*(r - 1)**3*(r + 1)**2
Let v(m) be the third derivative of -m**8/1120 - m**7/560 + m**6/240 + m**5/80 - 7