et c(z) = -z**3 + 31*z**2 + 8*z - 17. Let w(l) = 16*l**2 + 4*l - 8. Let h(x) = k*c(x) - 7*w(x). Factor h(r).
-4*(r - 3)*(r - 1)*(r + 1)
Let h(r) be the third derivative of -r**5/30 + r**4/4 + 6*r**2. What is v in h(v) = 0?
0, 3
Let t be ((-12)/10)/((-9)/30). Find r such that r**4 - 3*r**t + 15*r**2 - 13*r**2 = 0.
-1, 0, 1
Determine b, given that -3/2*b - 1 + 3/2*b**3 + 2*b**2 - b**4 = 0.
-1, -1/2, 1, 2
Let g(r) = -r**3 + 6*r**2 - r + 6. Let y be g(6). Suppose 2*n - 2*q - 20 + 8 = y, -3*q = 12. Factor 0 - 4/9*s**n - 2/9*s**3 + 0*s.
-2*s**2*(s + 2)/9
Let p(x) = -7*x**2 + 13*x + 15. Let w(o) = -4*o**2 + 7*o + 8. Let r(j) = 3*p(j) - 5*w(j). Solve r(s) = 0 for s.
-1, 5
Let g(p) = -p**3 - p**2 + p - 1. Let v(d) = 3*d**3 + 3*d**2 - 2*d + 4. Let s(z) = 4*g(z) + v(z). Factor s(b).
-b*(b - 1)*(b + 2)
Let s be (3*(-3 + 1))/(-3). Determine f so that -40/9*f**4 - 2*f + 8/9*f**s - 4/9 + 6*f**3 = 0.
-2/5, -1/4, 1
Suppose 12/7*g**2 + 12/7*g**4 + 0 + 22/7*g**3 + 2/7*g = 0. What is g?
-1, -1/2, -1/3, 0
Factor 9*c**3 + 4*c**2 + 3*c**2 - 28*c**2 + 6 - 9*c + 15*c**4.
3*(c - 1)*(c + 1)**2*(5*c - 2)
Let v = -5 - -7. Determine t, given that 2*t**2 + 2*t + t**v - t = 0.
-1/3, 0
Let d(r) = -3*r**5 + 3*r**3 + 4*r**2. Suppose g + 2 = -g. Let o(b) be the third derivative of b**5/60 - 2*b**2. Let x(y) = g*d(y) + 4*o(y). Factor x(l).
3*l**3*(l - 1)*(l + 1)
Let z(w) = -w + 7. Let r be z(7). Suppose 3*p - 6*p + 3 = r, -2*n - 4*p = -8. Find x such that 1 - 2 + 3 - 3*x + x**n = 0.
1, 2
Determine g so that -g + 5*g - 8*g**3 + 4*g**2 - g**5 + 5*g**4 - 4*g = 0.
0, 1, 2
Let a(x) = x**3 - 1. Let q(j) = -9*j**3 + 45*j**2 - 36*j - 15. Let c(h) = -3*a(h) + q(h). Determine u so that c(u) = 0.
-1/4, 2
Let m(b) be the first derivative of 3 - 1/165*b**6 - 3*b + 1/33*b**4 + 0*b**2 + 0*b**3 - 1/110*b**5. Let g(a) be the first derivative of m(a). Factor g(t).
-2*t**2*(t - 1)*(t + 2)/11
Let z(w) be the second derivative of -w**8/10080 - w**7/3780 + 5*w**4/12 + w. Let v(b) be the third derivative of z(b). What is a in v(a) = 0?
-1, 0
Determine b, given that -2/11*b**3 + 0*b + 2/11*b**4 + 0 - 2/11*b**2 + 2/11*b**5 = 0.
-1, 0, 1
Let d be ((-6)/27)/(-2*1/3). Factor -d*q**2 + 0 + 1/3*q.
-q*(q - 1)/3
Let a(u) be the second derivative of u**5/170 + u**4/34 + 2*u**3/51 - 3*u. Let a(y) = 0. Calculate y.
-2, -1, 0
Let n(c) be the third derivative of c**5/30 - 8*c**2. Factor n(h).
2*h**2
Let l(q) be the first derivative of q - 2 - 7/12*q**3 + 3/2*q**2. Factor l(y).
-(y - 2)*(7*y + 2)/4
Suppose 3*k - 5*k + 2 = 0. Factor -4*n + n**2 - n**3 + 9*n - k - 4*n.
-(n - 1)**2*(n + 1)
Factor -2 - 3*n**2 - 6*n - 7 + 4*n**2 - 2*n**2.
-(n + 3)**2
Let g(d) be the second derivative of 3*d + 1/165*d**6 + 0 + 0*d**2 - 1/66*d**4 + 1/33*d**3 - 1/110*d**5. Suppose g(c) = 0. Calculate c.
-1, 0, 1
Let t be 5 - (1 + 20/5). Factor t - 3/2*j**3 + 3/4*j**2 + 3/4*j.
-3*j*(j - 1)*(2*j + 1)/4
Let o(i) be the third derivative of 1/48*i**4 + 1/240*i**6 - 4*i**2 + 0*i - 1/60*i**5 + 0 + 0*i**3. Determine z, given that o(z) = 0.
0, 1
Let n be (-24)/(-32) - 19/36. Let k(b) be the first derivative of 1/9*b**4 - n*b**2 + 1 + 2/45*b**5 - 2/9*b + 0*b**3. Factor k(a).
2*(a - 1)*(a + 1)**3/9
Suppose 13*f = 15*f - 4. Let o(b) be the first derivative of -2/3*b - 3 - 7/6*b**f + 4/9*b**3. Solve o(j) = 0.
-1/4, 2
Let k(m) be the third derivative of 0*m**3 + 0*m**4 - 3/80*m**6 + 0 + 0*m - 1/60*m**7 - 1/60*m**5 - 3*m**2. Factor k(i).
-i**2*(i + 1)*(7*i + 2)/2
Let q be -3 - -11*(2 - 20/12). Factor -2/3 - 4*b**2 - 8/3*b**3 - q*b**4 - 8/3*b.
-2*(b + 1)**4/3
Let c(h) be the first derivative of h**6/1440 + h**5/160 + h**4/48 + h**3/3 + 1. Let a(v) be the third derivative of c(v). Factor a(i).
(i + 1)*(i + 2)/4
Solve -2/5*c**2 - 2/5*c + 2/5 + 2/5*c**3 = 0 for c.
-1, 1
Let b(j) be the first derivative of j**4/4 - j**3 + 4*j + 43. Solve b(w) = 0.
-1, 2
Let m(p) be the first derivative of p**6/135 + p**5/45 - p**4/54 - 2*p**3/27 - 8*p - 6. Let y(c) be the first derivative of m(c). Determine j so that y(j) = 0.
-2, -1, 0, 1
Let d(r) be the first derivative of 0*r**2 - 2/5*r**5 - 4/3*r**3 - 1 + 0*r + 3/2*r**4. Let d(p) = 0. Calculate p.
0, 1, 2
Let m(b) be the first derivative of 2/3*b + 2*b**5 + 40/9*b**3 + 25/6*b**4 - 3 + 7/18*b**6 + 5/2*b**2. Factor m(z).
(z + 1)**4*(7*z + 2)/3
Let p(t) = 12*t**2 - 12*t + 4. Let x(z) = z**2. Let r = -6 - -5. Let s(j) = r*p(j) + 3*x(j). Determine l so that s(l) = 0.
2/3
Suppose -2*g + 6*g = 0. Factor -2*x**3 - 6*x**2 - 2*x**4 + 3*x**4 + g*x**3 + 5*x**2 + 2*x.
x*(x - 2)*(x - 1)*(x + 1)
Let i(a) = 7*a + 3. Let q(k) = k**2 + k. Let o(g) = i(g) - 2*q(g). Let r = 4 - 7. Let h(j) = 4*j**2 - 9*j - 5. Let t(p) = r*h(p) - 5*o(p). Factor t(v).
-2*v*(v - 1)
Let s be (-52)/32*-4 - 5. Let 3*r**2 - 3 + s*r - 3/2*r**3 = 0. Calculate r.
-1, 1, 2
Let g(v) = v + 0*v**5 + v**5 + v**3 - 2*v. Let o = 2 + -3. Let q(h) = 3*h**5 + 3*h**4 + 4*h**3 - 5*h. Let l(f) = o*q(f) + 5*g(f). Factor l(y).
y**3*(y - 1)*(2*y - 1)
Let f(a) be the second derivative of -27*a**3 + 0 + 1/20*a**6 + 27/4*a**4 - 9/10*a**5 + 243/4*a**2 - 5*a. Factor f(v).
3*(v - 3)**4/2
Let d(u) = -u**3 - 2*u**2 - u + 2. Let f(y) = y**2 - y - 2. Let h(m) = -5*d(m) + 5*f(m). Let h(s) = 0. Calculate s.
-2, 1
Let b(y) be the second derivative of -y**6/60 + 3*y**5/20 - 13*y**4/24 + y**3 - y**2 + 11*y. What is a in b(a) = 0?
1, 2
Let v(b) be the first derivative of b**7/70 - 2*b**6/25 + 3*b**5/20 - b**4/10 - 3*b + 7. Let o(u) be the first derivative of v(u). Factor o(i).
3*i**2*(i - 2)*(i - 1)**2/5
Let f(l) = -l**3 + l + 1. Let c(p) = -3*p**4 - 15*p**3 + 6*p**2 + 18*p + 18. Let i(m) = c(m) - 18*f(m). What is w in i(w) = 0?
-1, 0, 2
Suppose -5*h + 13 = 4*g, 2*g + h = 5 - 0. Let v(t) be the first derivative of -1/3*t**3 - 3 - t + t**g. Factor v(o).
-(o - 1)**2
Let m(n) = -4*n**2 - 2*n + 2. Let d(u) = -5*u**2 - 2*u + 3. Suppose -3*w + 2 + 10 = 0. Let v(b) = w*m(b) - 3*d(b). Factor v(r).
-(r + 1)**2
Let d = 109 + -215/2. Find o, given that -d*o**2 - o - 1/6 = 0.
-1/3
Let y(f) be the second derivative of 3*f**5/20 + 5*f**4/12 - 2*f**3/3 - 2*f**2 - 16*f. Factor y(h).
(h - 1)*(h + 2)*(3*h + 2)
Suppose 2*s - 8 = 4*u - 3*u, 0 = s + 4*u + 5. Let a(d) = -4*d + 10. Let h be a(2). Factor 3/2*r**s + 0*r - r**h + 0 - 1/2*r**5 + 0*r**4.
-r**2*(r - 1)**2*(r + 2)/2
Suppose 5 = -5*u - 0, 4*q = -4*u + 8. Let d(r) be the second derivative of -1/5*r**2 - 1/3*r**q - 2/15*r**4 - 3*r + 0. Factor d(l).
-2*(l + 1)*(4*l + 1)/5
Factor 0 - 4/9*b**2 + 0*b**4 - 2/9*b**5 + 0*b + 2/3*b**3.
-2*b**2*(b - 1)**2*(b + 2)/9
Let o(b) be the second derivative of b**6/45 - b**5/10 + b**4/9 + b. Factor o(f).
2*f**2*(f - 2)*(f - 1)/3
Let l be 1/(-5) - (1 - (-16)/(-10)). What is p in 6/5*p**2 - l*p + 2/5*p**3 - 6/5*p**4 + 0 = 0?
-1, 0, 1/3, 1
Let l be ((-2)/2)/(9/(-18)). Determine n so that 0*n**3 + 0 - 2/5*n**4 + 0*n**l + 0*n = 0.
0
Let r(j) = 7*j**3 - j**2 - 2*j + 4. Let a(n) = -8*n**3 + 2*n**2 + n - 5. Let o(z) = 4*a(z) + 5*r(z). Factor o(c).
3*c*(c - 1)*(c + 2)
Let h(y) be the first derivative of y**6/15 + 6*y**5/25 + y**4/5 - 7. Factor h(i).
2*i**3*(i + 1)*(i + 2)/5
Let d(o) = 4*o**5 + 8*o**4 + 6*o**2. Let h(g) = -g**4 + 3*g**2 + 8*g**4 + 2*g**2 + 3*g**5. Let p(u) = 5*d(u) - 6*h(u). Factor p(y).
2*y**4*(y - 1)
Let h(z) = 24*z**2 - 9*z**4 + 6*z**3 + 2*z**3 + 6*z**5 + 4 + 4*z**3 - 1. Let c(f) = f**5 + f**4 + f**3 - f. Let s(m) = 18*c(m) - h(m). Solve s(v) = 0 for v.
-1, -1/4, 1
Let o = 2989/8 + -373. Let v = 51/56 - o. Let 2/7*a**4 + 2/7*a**3 + 0 - 2/7*a - v*a**2 = 0. Calculate a.
-1, 0, 1
Let b be (-2)/(-6) + 70/(-156). Let n = b - -8/13. Let 0 + d**2 - 1/2*d**3 - n*d = 0. What is d?
0, 1
Suppose -2*q + 4 = -a - 0*a, q + 5*a = 13. Let -2/3*h - 4/3*h**2 + 0 - 2/3*h**q = 0. What is h?
-1, 0
Suppose -6 - 1/2*y + 1/2*y**2 = 0. Calculate y.
-3, 4
Let y be -3 + 5 - (-594)/(-371). Let t = y + -6/53. Determine n, given that 2/7*n + t*n**2 + 0 - 4/7*n**3 = 0.
-1/2, 0, 1
Let x(c) = c**3 + 14*c**2 + 13*c + 3. Let f be x(-13). Factor -2/3*r**2 + 0 - 6*r**f + 26/3*r**4 - 10/3*r**5 + 4/3*r.
-2*r*(r - 1)**3*(5*r + 2)/3
Let i(n) be the third derivative of n**5/15 - 2*n**3/3 + 22*n**2. Factor i(c).
4*(c - 1)*(c + 1)
Suppose -2*i - 15 = -2*f - 3, -4*f + 27 = -5*i. Let n be 4/(1 + 1 + f). Factor s**2 - 2/5*s**3 - n*s + 1/5.
-(s - 1)**2*(2*s - 1)/5
Le