e of x(p). Factor h(v).
2*(v - 1)**2*(v + 1)**2/5
Factor -8/3*x - 1/3*x**5 + 5/3*x**3 + 4/3 - 1/3*x**4 + 1/3*x**2.
-(x - 1)**3*(x + 2)**2/3
Suppose 5*u = 3*u. Let k(m) be the first derivative of 0*m - 2/25*m**5 + 1 + 1/15*m**6 + u*m**4 + 0*m**3 + 0*m**2. Solve k(b) = 0 for b.
0, 1
Let h = 615 - 6755/11. Factor 8/11*a + 24/11*a**2 + h*a**3 + 0.
2*a*(a + 2)*(5*a + 2)/11
Let f(n) be the second derivative of 4*n + 0 - 2/9*n**3 + n**2 + 5/36*n**4 - 1/30*n**5. Let g(h) be the first derivative of f(h). What is y in g(y) = 0?
2/3, 1
Let t = 3 + -1. Factor 0 + 2 + t*i**3 - 2 - 2*i**2.
2*i**2*(i - 1)
Suppose 2*l = 7*l. Let q = -123 - -125. Find b, given that l*b + 1/5*b**3 - 1/5*b**5 + 0*b**q + 0*b**4 + 0 = 0.
-1, 0, 1
Let m(r) = 5*r**3 - 5*r**2. Let s(y) = -y**3 + y**2. Let z(h) = m(h) + 2*s(h). Factor z(v).
3*v**2*(v - 1)
Let v(h) be the first derivative of -5*h**6/3 + 4*h**5/5 + 5*h**4/2 - 4*h**3/3 - 1. Let v(u) = 0. What is u?
-1, 0, 2/5, 1
Let q(p) be the third derivative of p**8/672 + p**7/140 - p**5/30 + 43*p**2. Factor q(n).
n**2*(n - 1)*(n + 2)**2/2
Let t(r) be the third derivative of r**8/420 + r**7/126 + r**6/180 - r**4/6 + 5*r**2. Let j(v) be the second derivative of t(v). Let j(s) = 0. Calculate s.
-1, -1/4, 0
Let z(u) = -13*u + 5*u + 8*u**4 - 3*u**2 + 3*u**3 - 5*u**3. Let w(a) = -7*a**4 + a**3 + 3*a**2 + 7*a. Let h(f) = -5*w(f) - 4*z(f). Factor h(m).
3*m*(m - 1)*(m + 1)**2
Let o(y) = -6*y**3 + 2*y**2 - 5*y. Let z(t) = 6*t**3 - t**2 + 4*t. Let a be 42/(-8) + (-10)/(-40). Let h(x) = a*z(x) - 4*o(x). Factor h(n).
-3*n**2*(2*n + 1)
Let p(g) = 7*g**2 - 8*g + 5. Let x be p(8). Let l = x - 3497/9. Solve -2/9*i**4 - 4/9*i**3 + 2/9*i**5 - 2/9 + l*i**2 + 2/9*i = 0.
-1, 1
Let a be 2/6*(-2 + 2). Suppose -6*q + 8*q = a. Find o, given that -1/3*o**2 + 1/3 + q*o = 0.
-1, 1
Let f(y) be the second derivative of -y**6/120 + y**5/80 + y**4/48 - y**3/24 - 18*y. Factor f(l).
-l*(l - 1)**2*(l + 1)/4
Let x be 0 + (-22)/2 + 3. Let v(p) = 3*p**2 - 3*p. Let l(g) = g**3 + 10*g**2 - 8*g. Let t(f) = x*v(f) + 3*l(f). Factor t(r).
3*r**2*(r + 2)
Suppose 4*s = -u + 23, -4*u - 12*s = -9*s - 27. Factor -2/7*w**u + 0 - 2/7*w**4 + 2/7*w**2 + 2/7*w.
-2*w*(w - 1)*(w + 1)**2/7
Let -1/3*m**3 - 1/3*m**2 + 1/3 + 1/3*m = 0. What is m?
-1, 1
Suppose 2*j - 12 = -2*j. Suppose 6 = -i - 3*y, i - 4 = 2*y + 5. Solve -2 - i*g**3 - 4*g**4 - 2 + 3 + j*g + 0 + 5*g**2 = 0.
-1, 1/4, 1
Let j(k) be the second derivative of k**3/6 - 2*k. Let l be j(3). Solve 1/5*h + 1/5*h**4 + 0 - 1/5*h**2 - 1/5*h**l = 0.
-1, 0, 1
Let x(l) be the second derivative of -2*l**7/35 + 2*l**6/15 - 2*l**5/25 + 18*l. Factor x(b).
-4*b**3*(b - 1)*(3*b - 2)/5
Let b(z) be the second derivative of z**6/80 - z**2/2 - 4*z. Let w(t) be the first derivative of b(t). Solve w(m) = 0 for m.
0
Let d = 15 + -13. Suppose 0 = 2*g - v - d + 1, 4*g + 2*v - 14 = 0. Suppose 0*o - 2/5 + 2/5*o**g = 0. What is o?
-1, 1
Let l(r) be the first derivative of -1/420*r**6 - r**2 - 2/21*r**3 + 1/28*r**4 + 0*r + 2 + 0*r**5. Let p(u) be the second derivative of l(u). Factor p(j).
-2*(j - 1)**2*(j + 2)/7
Let q(f) be the first derivative of f**7/210 - 7*f**6/120 + f**5/4 - 3*f**4/8 + 3*f**2 + 5. Let d(z) be the second derivative of q(z). Solve d(v) = 0 for v.
0, 1, 3
Let t(j) be the third derivative of 0 + 0*j**3 - j**2 + 1/12*j**4 + 0*j + 1/60*j**5. Solve t(h) = 0.
-2, 0
Let 3/4*q**2 + 1/4*q + 1/4*q**4 + 3/4*q**3 + 0 = 0. What is q?
-1, 0
Suppose 0 + 3 = 4*u + 5*i, -4 = 4*i. Let z = -16/9 + 116/45. Let -z + 4/5*g - 1/5*g**u = 0. What is g?
2
Let t(u) be the second derivative of -u**5/10 + u**4/3 - u**3/3 + 13*u. Factor t(i).
-2*i*(i - 1)**2
Let f(a) be the third derivative of -a**6/720 + a**5/120 - 27*a**2. Factor f(v).
-v**2*(v - 3)/6
Let z(a) be the third derivative of a**8/20160 - a**7/2520 - a**6/240 + a**5/60 + 3*a**2. Let v(p) be the third derivative of z(p). Factor v(w).
(w - 3)*(w + 1)
Let m(q) = 11*q**4 - 89*q**3 - 49*q**2 + 249*q + 189. Let c(w) = -3*w**4 + 22*w**3 + 12*w**2 - 62*w - 47. Let o(x) = 9*c(x) + 2*m(x). Factor o(z).
-5*(z - 3)**2*(z + 1)**2
Let d = 28 - 13. Suppose -r + 5*k = 15, 4*k + 3 - d = 2*r. Factor -2/11*y**5 + 0*y + 0*y**4 + r + 0*y**2 + 0*y**3.
-2*y**5/11
Factor -6/7*r + 2/7*r**2 + 4/7.
2*(r - 2)*(r - 1)/7
Let a(u) be the third derivative of -u**8/224 - 11*u**7/420 - u**6/16 - 3*u**5/40 - u**4/24 - u**2. Find k, given that a(k) = 0.
-1, -2/3, 0
Suppose -5*l = 4*n - 40, 2*l + 0*n - 16 = -4*n. Suppose l + 50*g + 13*g**2 - 18*g + 29*g**2 + 18*g**3 = 0. Calculate g.
-1, -2/3
Let z(g) be the second derivative of g**5/4 + 5*g**4/6 - 5*g**3/6 - 5*g**2 + 8*g. Factor z(a).
5*(a - 1)*(a + 1)*(a + 2)
Let m be 20/(-70)*21/(-12). Find n such that -5/2*n - m - 2*n**2 = 0.
-1, -1/4
Suppose 4*i + 12 = 0, 3*j + 9 = -2*i + i. Let o be ((-13)/(-65))/(j/(-5)). Factor 0 + 1/2*z**3 - o*z + 0*z**2.
z*(z - 1)*(z + 1)/2
Let n = -1 + 5. Factor 0*w**4 - n*w**3 - 6 + 8 + 4*w - 2*w**4.
-2*(w - 1)*(w + 1)**3
Let o(z) = z**2 - z. Let u be o(0). Let l be u/1 - 12/(-3). Factor 4 + l*j**2 - 4 - 2*j**3.
-2*j**2*(j - 2)
Suppose -v - v = -88. Let w = 133/3 - v. Factor w*p**2 + 1/3 - 2/3*p.
(p - 1)**2/3
Suppose 0 = -2*w + 5*a + 29, 4*w + 0*w = -2*a - 2. Determine i so that 7*i**3 + 8*i + 5*i**3 - 2*i**4 - 3*i - 26*i**w - 8 + 19*i = 0.
1, 2
Let h(k) be the first derivative of -2/5*k**5 - 4*k**2 + 0*k + 3/2*k**4 + 8 + 0*k**3. Factor h(y).
-2*y*(y - 2)**2*(y + 1)
Let h be 4/20 + 48/10. Suppose -h*w = -5 - 5. Find n such that -2 + 2*n**3 - 4*n**3 - 3*n + 2*n**w - 3*n + 8*n = 0.
-1, 1
Let a(y) be the first derivative of -1/36*y**4 + 1/18*y**3 + 0*y**2 + 1 - y. Let k(v) be the first derivative of a(v). Factor k(j).
-j*(j - 1)/3
Let a(v) = -8*v**2 - 28*v - 32. Let o(z) = -9*z**2 - 29*z - 32. Let n(y) = 5*a(y) - 4*o(y). Let n(r) = 0. What is r?
-4, -2
Let m(g) = -3*g**2 + 2. Let v(l) = l. Let d(z) = -16*z**2 + 4*z + 11. Let h(t) = -d(t) + 4*v(t). Let b(n) = -4*h(n) - 22*m(n). Factor b(r).
2*r**2
Let j(m) be the second derivative of m**8/84 - m**6/15 + m**4/6 + 2*m**2 - 3*m. Let o(p) be the first derivative of j(p). Suppose o(d) = 0. What is d?
-1, 0, 1
Let f(c) be the second derivative of -c**6/6 + 7*c**5/4 - 25*c**4/4 + 15*c**3/2 + 41*c. Factor f(o).
-5*o*(o - 3)**2*(o - 1)
Let u(m) = -11*m**2 + m**3 - 9*m**2 + 14*m**2. Let n be u(6). Factor n*r**2 - 1/4*r**3 + 0*r + 0.
-r**3/4
Let u(v) be the first derivative of 16/3*v**3 + 3*v**4 - 16*v**5 + 25/3*v**6 - 4 + 0*v + v**2. Determine n, given that u(n) = 0.
-1/5, 0, 1
Let g = -22 - -21. Let i(a) = -a**3 + 1. Let z(x) = 9*x**3 + 3*x**2 - 12*x - 18. Let w(p) = g*z(p) - 6*i(p). Factor w(q).
-3*(q - 2)*(q + 1)*(q + 2)
Factor 0 + 0*p**3 + 0*p**2 + 0*p + 2/7*p**5 + 4/7*p**4.
2*p**4*(p + 2)/7
Let l(y) be the second derivative of y**6/15 + 3*y**5/10 + y**4/3 - 7*y. Determine p, given that l(p) = 0.
-2, -1, 0
Let h(u) = u**4 - u**3 + u**2 + u + 1. Let n(b) = 0*b**5 - b**5 + 3*b**3 - b**4 - 3*b + 0 - 3*b**4 - 3 - 3*b**2. Let g(i) = 3*h(i) + n(i). Solve g(l) = 0 for l.
-1, 0
What is w in -8/7 + 36/7*w - 40/7*w**2 = 0?
2/5, 1/2
Let j be (-5)/(-20) - 13/4. Let o = 0 - j. Determine z so that -10*z**2 + 7*z**3 + 11*z**o - 4 + 14*z**4 - 3*z - 15*z = 0.
-1, -2/7, 1
Let v(l) be the second derivative of -l**7/14 + 7*l**6/30 + l**5/20 - 7*l**4/12 + l**3/3 + 8*l. What is i in v(i) = 0?
-1, 0, 1/3, 1, 2
Suppose -3*x + 2*p + 8 = 0, -6*x + 3*p + 9 = -2*x. Let b be (-12)/3*(-3)/x. Solve 2/7 - 4/7*k + 2/7*k**b = 0 for k.
1
Let r = -4 + 8. Suppose 4 = -0*c - c - 5*o, -7 = -4*c + 3*o. Factor -r*g + c - g**3 - g + 6*g - g**2.
-(g - 1)*(g + 1)**2
Let d(w) be the first derivative of 4*w**3/3 + 14*w**2 - 32*w - 20. Solve d(u) = 0.
-8, 1
Suppose 8*p - 11*p = 0. Let d(m) be the second derivative of 1/36*m**4 + 0*m**5 - 1/90*m**6 - 2*m - 1/252*m**7 + p + 0*m**2 + 1/36*m**3. Factor d(s).
-s*(s - 1)*(s + 1)**3/6
Suppose 5*o - 1 = 19. Let f(s) be the first derivative of 1/12*s**6 + 5/4*s**o - 1/2*s**5 - 1/2*s - 2 - 5/3*s**3 + 5/4*s**2. Factor f(m).
(m - 1)**5/2
Let o(j) be the third derivative of j**5/60 + j**4/24 + 4*j**2. Let t be o(1). Factor 8/5*z**3 + 2/5*z + 0 - t*z**2.
2*z*(z - 1)*(4*z - 1)/5
Let c = 5 + -5. Factor -4*v**4 - 2*v**5 + c*v**4 + 4*v - 2*v + 4*v**2.
-2*v*(v - 1)*(v + 1)**3
Let b = 30 - 18. Suppose -2*i + 2 = 2*c, b = 4*c + c - 2*i. 