4*n**2. Let u(p) be the second derivative of a(p). Factor u(b).
-b*(b - 1)**2*(b + 1)
Let l(n) = n**5 - n**3 + n + 1. Let w(h) = -h - 9. Let d be w(-7). Let f(o) = -4*o**5 + 4*o**3 - 3*o - 3. Let x(b) = d*f(b) - 6*l(b). What is y in x(y) = 0?
-1, 0, 1
Find r, given that 1/7*r**3 + 64/7*r + 16/7*r**2 + 0 = 0.
-8, 0
Suppose -5*h = -7*h. Let a(m) be the third derivative of 0*m + 1/30*m**5 + 1/12*m**4 + h + m**2 - 1/60*m**6 - 1/3*m**3. Factor a(o).
-2*(o - 1)**2*(o + 1)
Let l(j) be the first derivative of j**3 - 3/4*j**4 + 1/5*j**5 - 1/2*j**2 - 1 + 0*j. Factor l(c).
c*(c - 1)**3
Suppose -x + 54 = 52. Find v such that -2/3*v**x + 0*v - v**3 + v**5 + 0 + 2/3*v**4 = 0.
-1, -2/3, 0, 1
Find v, given that -4/5 - 5*v**2 + 16/5*v + 19/5*v**3 + 1/5*v**5 - 7/5*v**4 = 0.
1, 2
Let v(x) be the second derivative of -1/120*x**6 + 0*x**3 + 0*x**4 - 1/80*x**5 + 0*x**2 - x + 0. Factor v(i).
-i**3*(i + 1)/4
Let q = -10 - -12. Let p(f) be the second derivative of f**q + 1/6*f**4 + 0 + f - 2/3*f**3. Factor p(k).
2*(k - 1)**2
Let w(t) be the third derivative of t**4/24 - 2*t**3/3 + 7*t**2. Let y be w(4). Factor 0*u**2 + 1/2*u**3 + 1/2*u**5 + u**4 + y + 0*u.
u**3*(u + 1)**2/2
Let r(g) be the first derivative of -g**2 + 3*g**3 + 2 - 9/5*g**5 + 7/6*g**6 - 5/4*g**4 + 0*g. Factor r(x).
x*(x - 1)**2*(x + 1)*(7*x - 2)
Suppose -20 = -h - 4*r - 7, 3*h - r - 13 = 0. Suppose 4*o = h*y + 12, -2*y + 6 = 2*o - 0*y. Let -1/6*b**o - 1/6*b - 1/3*b**2 + 0 = 0. What is b?
-1, 0
Let j(p) = -2*p**3 + 2*p**2 - 3*p - 7. Suppose 10 = 3*z + 25. Let m(h) = -h**3 + h**2 - 2*h - 4. Let l(r) = z*m(r) + 3*j(r). Factor l(i).
-(i - 1)**2*(i + 1)
Let 5*i + 12*i**2 - 3*i**3 + 4*i**3 - 5*i**3 - 13*i = 0. Calculate i.
0, 1, 2
Factor -3*n**4 + 20*n**3 - 32*n - n**4 + 3*n**4 - 4*n**5 + 5*n**4 - 4*n**2 - 16.
-4*(n - 2)**2*(n + 1)**3
Suppose 0 = -5*k + 10 - 0. Determine a so that 0*a**k - 2/3*a**3 + 0*a + 0 = 0.
0
Let h = 1 - -19. Solve 0*j + h*j**2 - 19*j**2 - j = 0.
0, 1
Factor -1/11*x**2 + 1/11*x**4 - 1/11*x**5 + 1/11*x**3 + 0 + 0*x.
-x**2*(x - 1)**2*(x + 1)/11
Let q(y) be the third derivative of -y**7/35 - 2*y**6/15 - 2*y**5/15 + 17*y**2. Solve q(k) = 0.
-2, -2/3, 0
Find n such that 86*n**5 - 6*n + 2*n**3 - 5*n**2 + 14*n**4 - 9*n**2 - 82*n**5 = 0.
-3, -1, -1/2, 0, 1
Let k(h) = -9*h**3 + 27*h**2 - 9*h + 3. Let w = -15 + 11. Let s(u) = -8*u**3 + 27*u**2 - 10*u + 4. Let q(o) = w*k(o) + 3*s(o). Solve q(f) = 0.
0, 1/4, 2
Let a = -1/39 + -37/78. Let n = 1 + a. Let 0 + 1/2*t**2 + 0*t - n*t**3 = 0. Calculate t.
0, 1
Let x = 110 - 548/5. Let j(k) be the first derivative of 1/2*k**2 + 2/3*k**3 - 1/6*k**6 + 0*k + 2 + 0*k**4 - x*k**5. Let j(y) = 0. Calculate y.
-1, 0, 1
Let f be (-17)/5 - 3/5. Let q be 1 + f - 10/(-3). Find t such that -1/3*t**2 - q + 2/3*t = 0.
1
Let u(g) be the first derivative of -1 + 0*g + 0*g**2 + 2/3*g**3. Factor u(t).
2*t**2
Let h(w) be the first derivative of w**3/27 + 2*w**2/9 + 4*w/9 + 7. Find d, given that h(d) = 0.
-2
Let o(y) = -y**3 - 5*y**2 + 5. Let g be o(-5). Let q(k) be the third derivative of 0 + 0*k + k**2 - 1/60*k**g + 1/12*k**4 - 1/6*k**3. Factor q(l).
-(l - 1)**2
Let o(q) be the second derivative of -2/105*q**6 - 2/7*q**2 + 2/21*q**3 - 2/35*q**5 + 2/21*q**4 + 0 + 2/147*q**7 + 6*q. Factor o(b).
4*(b - 1)**3*(b + 1)**2/7
Let j = -42 - -42. Determine q so that 0*q + j + 1/5*q**2 + 1/5*q**3 = 0.
-1, 0
Let s = 17 + -12. Suppose -4*b = -8*b - 12, s*n + b = 352. Factor 588*x**2 + 16 + 179*x + 60*x + 686*x**3 - n*x.
2*(7*x + 2)**3
Let c(w) be the second derivative of 0*w**3 + 0*w**2 - 1/40*w**5 + 0 + 0*w**4 - 1/15*w**6 - 3*w. Solve c(n) = 0 for n.
-1/4, 0
Factor -4/3*q**2 - 7*q**4 - 49/3*q**5 + 8*q**3 + 0*q + 0.
-q**2*(q + 1)*(7*q - 2)**2/3
Let y = 10 + -7. Factor -5 - 12*b - 12*b**2 + 0*b**y - 7 - 4*b**3 + 8.
-4*(b + 1)**3
Let i(o) be the first derivative of o**4 - 6*o**2 - 8*o - 5. Factor i(m).
4*(m - 2)*(m + 1)**2
Let m = 117 - 112. Let t(h) be the second derivative of 3*h - 1/30*h**6 - 1/20*h**m + 0 + 5/6*h**3 + h**2 + 1/4*h**4. Suppose t(s) = 0. What is s?
-1, 2
Solve -2/3*b**2 + 2/9*b - 2/9*b**4 + 0 + 2/3*b**3 = 0 for b.
0, 1
Factor -3 - 5*b**2 + b**4 + 2*b**2 + 4 + b**2.
(b - 1)**2*(b + 1)**2
Let i = 188 - 188. Suppose 1/4*h**2 + 0 + i*h = 0. Calculate h.
0
Let p = 8 + -29. Let a = p - -24. Suppose 1/2 + 1/2*k**4 - 2*k**3 + a*k**2 - 2*k = 0. Calculate k.
1
Factor -6*k**2 + 16*k - 3 + 8*k**2 - 14*k**2 - 4*k**2.
-(4*k - 3)*(4*k - 1)
Find l such that 2/5*l - 1/5*l**2 + 3/5 = 0.
-1, 3
Suppose -294*k - 12 = -300*k. Let -2/9*c**k + 4/9 + 2/9*c = 0. Calculate c.
-1, 2
Let s = -2 - -4. Let y be ((-10)/5)/s*-3. Suppose 1/3*l**5 + 0*l**2 + 0*l**4 + 1/3*l + 0 - 2/3*l**y = 0. What is l?
-1, 0, 1
Let v be (35/(-70))/(3/(-92)). Determine k so that 56/9*k + 140/9*k**3 + 8/9 + 50/9*k**4 + v*k**2 = 0.
-1, -2/5
Let m = 37 + -17. Let o be (12/m)/(2/70). Factor 5*s + 4*s + o*s**3 + 16*s**2 - 5*s + 9*s**4.
s*(s + 1)*(3*s + 2)**2
Let c(k) = k**5 - 28*k**4 - 44*k**3 - 15*k**2. Let w(q) = 14*q**4 + 22*q**3 + 8*q**2. Let t(u) = -2*c(u) - 5*w(u). Let t(p) = 0. What is p?
-5, -1, 0
Suppose 23 + 9 = 8*r. Let p(d) be the first derivative of -2/15*d**5 + 2/3*d**2 - 2 + 0*d**3 - 1/3*d**r + 2/3*d. Let p(m) = 0. What is m?
-1, 1
Let t(g) = g + 1. Let f(d) = -3*d**2 - 12*d - 21. Let w(r) = f(r) - 6*t(r). Find y, given that w(y) = 0.
-3
Let j(y) be the third derivative of y**6/120 - 3*y**5/20 + y**4 - 8*y**3/3 - 2*y**2. Factor j(z).
(z - 4)**2*(z - 1)
Let c = 1301/10 - 130. Let i(o) be the second derivative of o**2 + 2*o - c*o**5 + 0 + 1/3*o**3 - 1/6*o**4. Solve i(y) = 0.
-1, 1
Let f(p) = p**2 - 8*p - 1. Let a be f(9). Let k(n) = -n**3 + 8*n**2 + n - 6. Let c be k(a). What is s in -4*s**3 - 11 + 11 + c*s**4 = 0?
0, 2
Let r(j) be the first derivative of -j**4 - 4*j**3/3 + 4*j**2 - 4. Let r(g) = 0. Calculate g.
-2, 0, 1
Factor -15 + 8*q**2 + 3*q**2 - 23*q**2 + 7*q**2 - 20*q.
-5*(q + 1)*(q + 3)
Suppose -2*s + 2 = -10. Solve 0*t**2 + 4*t**4 - t**2 + s*t**3 + 3*t**2 = 0.
-1, -1/2, 0
Let u be 2/(-7) - 242/(-14). Suppose -a + 0*i = i - 6, 2*a = -3*i + u. Factor 5*r - 3*r + 2 - a + r**2.
(r + 1)**2
Let i(p) be the second derivative of -p**8/840 - p**7/840 - p**6/2880 - p**3 + 7*p. Let w(a) be the second derivative of i(a). Factor w(o).
-o**2*(4*o + 1)**2/8
Suppose 15 - 9 - h**4 - 15*h**4 + 45*h**3 - 33*h - 11*h**4 + 33*h**2 = 0. Calculate h.
-1, 1/3, 2
Let 0 - g**2 - 1/2*g**3 + 3/2*g = 0. What is g?
-3, 0, 1
Suppose -9*y = -4*y - 2*l - 6, -4*y - 4*l + 16 = 0. Factor 7/3*z - 2/3 - 5/3*z**y.
-(z - 1)*(5*z - 2)/3
Let j(c) = 2*c**2 + 3*c - 1. Let y be j(2). Suppose -5*o + 28 = 2*u, 0 = 3*u + 4*o - 41 + y. Determine a so that 3 - u + a**2 + a**2 - a**2 = 0.
-1, 1
Let s = 8 - 6. Factor -5*h + 0*h**2 + 2*h**3 - s*h + 2*h**2 + 3*h.
2*h*(h - 1)*(h + 2)
Let t(l) = l**2 + 6 + 3*l - 2*l + 4*l. Let i be t(-4). Find g, given that 6*g**i + g - 2*g**2 - 3*g**3 - 2 - 2*g**2 + 2*g**3 = 0.
-1, 1, 2
Let t(m) be the second derivative of -3*m**5/40 + m**4/8 + m**3/4 - 3*m**2/4 - 2*m - 2. Suppose t(f) = 0. What is f?
-1, 1
Let 12*w - 7*w**4 - w**4 + 52*w**2 + 12*w**3 - 20*w**2 = 0. What is w?
-1, -1/2, 0, 3
Suppose 0 = -3*s + 9 - 3. Let u(h) be the third derivative of 1/60*h**6 + 0 + 3*h**s + 0*h**3 + 0*h**4 - 1/60*h**5 - 1/210*h**7 + 0*h. Factor u(f).
-f**2*(f - 1)**2
Let o(p) be the third derivative of p**5/240 - p**4/48 + p**3/24 - 3*p**2. Factor o(w).
(w - 1)**2/4
Let o(a) = -a**2 + 3*a + 4. Let w(t) = t**2 + t. Let y(f) = o(f) + 5*w(f). Factor y(z).
4*(z + 1)**2
Let m be ((-3)/(-5))/(2/10). Factor -h**3 - 3*h**m - 14*h**4 - 2 - 2*h**5 + 10*h**5 + 16*h**2 - 4*h.
2*(h - 1)**3*(h + 1)*(4*h + 1)
Let q(z) = z**2 + 82*z - 507. Let w(s) = -2*s**2 - 245*s + 1521. Let o(p) = -11*q(p) - 4*w(p). Factor o(m).
-3*(m - 13)**2
Let t(f) = -27*f**4 + f**3 + 27*f**2 - f + 7. Let p(i) = -18*i**4 + i**3 + 18*i**2 - i + 5. Let o(j) = -7*p(j) + 5*t(j). Factor o(a).
-a*(a - 1)*(a + 1)*(9*a + 2)
Let l = 118 - 471/4. Factor 1/4*n + 1/2 - l*n**2.
-(n - 2)*(n + 1)/4
Let b(k) be the second derivative of k**6/45 + k**5/6 + 7*k**4/18 + k**3/3 - 27*k. Let b(g) = 0. Calculate g.
-3, -1, 0
Let j(b) be the first derivative of 6*b**3/5 - 6*b**2/5 + 2*b/5 + 26. Factor j(m).
2*(3*m - 1)**2/5
Let t be 2/6*(-5 + 11). Find j such that 3*j**t - 68 + 68 + 0*j**2 = 0.
0
Let 