**3. Factor i(b).
(b + 1)*(b + 2)/4
Let n(a) = a**3 - 10*a**2 + 9*a + 5. Let c be n(9). Suppose 3*m**2 - 3*m**4 + 12*m - 10*m - m**3 + 4*m**c - 5*m**5 = 0. What is m?
-2, -1, 0, 1
Let s(u) be the second derivative of -u**8/168 + 2*u**7/105 - u**5/15 + u**4/12 - 3*u**2/2 - 4*u. Let q(f) be the first derivative of s(f). Factor q(w).
-2*w*(w - 1)**3*(w + 1)
Let u(r) be the first derivative of -r**7/63 + r**5/15 - r**3/9 - 2*r - 2. Let w(g) be the first derivative of u(g). Find d, given that w(d) = 0.
-1, 0, 1
Let p(x) be the third derivative of -x**6/120 - 3*x**5/40 + 17*x**4/48 - x**3/2 - 2*x**2 - 44. Factor p(d).
-(d - 1)*(d + 6)*(2*d - 1)/2
Let d(t) = -t + 3. Let f be d(-3). Let r(w) be the second derivative of -2*w - 8/3*w**4 + 14/15*w**f + 2*w**2 - 3/10*w**5 + 0 + w**3. Solve r(l) = 0.
-1, -2/7, 1/2, 1
Let c(k) be the first derivative of -2*k - 2*k**2 - 2/3*k**3 + 3. Factor c(z).
-2*(z + 1)**2
Let r(i) be the second derivative of -i**4/18 - 2*i**3/9 + 14*i. Determine j so that r(j) = 0.
-2, 0
Let p(j) be the third derivative of -j**5/180 - j**4/18 - 2*j**3/9 - 9*j**2. Find r such that p(r) = 0.
-2
Let o be (-1 - 0 - 3)*4/(-24). Suppose -q = -0*q. Factor -1/3*n**3 + 0 - 1/3*n**5 - o*n**4 + q*n**2 + 0*n.
-n**3*(n + 1)**2/3
Factor -1/4*y**4 - 1/4*y**2 + 0 + 1/2*y**3 + 0*y.
-y**2*(y - 1)**2/4
Let z = -5/32 + 163/224. Find a, given that 0*a**2 + z*a**3 + 2/7 - 2/7*a**4 - 4/7*a = 0.
-1, 1
Let t(f) be the second derivative of f**4/12 + f**3 + 9*f**2/2 - f. Solve t(l) = 0 for l.
-3
Let l = -3031/4 + 758. Factor 0*m + 1/2*m**2 + m**4 + 0 - 5/4*m**3 - l*m**5.
-m**2*(m - 2)*(m - 1)**2/4
Find z, given that 2*z**2 - 5 + 12 - z**4 - 8 = 0.
-1, 1
Let l be 16/(-20)*(7/2 - 6). Factor 0*y**3 + 0 - 1/3*y**4 + 0*y + 1/3*y**l.
-y**2*(y - 1)*(y + 1)/3
Let k = 473 + -469. Let 3/4*m**2 - 1/4*m + 1/4*m**k - 3/4*m**3 + 0 = 0. What is m?
0, 1
Let s(l) = l**3 - l**2 - l - 1. Let q(t) = -18*t**5 + 40*t**4 + 3*t**3 - 47*t**2 + 15*t - 15. Let b(i) = -2*q(i) + 22*s(i). Factor b(c).
4*(c - 1)**3*(c + 1)*(9*c - 2)
Let f(w) = -w**3 - 3*w**2 + 5*w - 5. Let i(l) = l + 11. Let m be i(-5). Let b(d) = -d**3 - 4*d**2 + 6*d - 6. Let a(p) = m*f(p) - 5*b(p). Factor a(y).
-y**2*(y - 2)
Suppose 0 = 4*m - 2*z - 4, -m = -0*m - z. Solve 5*u + 2*u - 3*u - 5*u + u**m = 0 for u.
0, 1
Factor 3*w**2 - 6 - 8*w**2 - 10*w + 4*w**2 + 2*w**3 - w**2.
2*(w - 3)*(w + 1)**2
Let z(y) be the first derivative of y**4/28 - 3*y**2/14 - 2*y/7 - 11. Suppose z(s) = 0. What is s?
-1, 2
Let o(w) be the second derivative of w**7/168 - w**6/120 - w**5/40 + w**4/24 + w**3/24 - w**2/8 - 35*w. Factor o(n).
(n - 1)**3*(n + 1)**2/4
Let h(p) be the third derivative of 11*p**8/1512 + 13*p**7/945 + p**6/270 + 14*p**2. Let h(m) = 0. What is m?
-1, -2/11, 0
Let g(u) be the second derivative of -u**6/30 + 3*u**5/20 + 5*u**4/6 + 2*u - 25. Determine c so that g(c) = 0.
-2, 0, 5
Let w(b) be the third derivative of -b**6/720 + b**5/480 - 7*b**3/6 + 3*b**2. Let l(t) be the first derivative of w(t). Solve l(x) = 0.
0, 1/2
Let q(g) = 6*g + 27. Let y be q(-4). Let k(p) be the third derivative of p**2 + 0*p - 1/20*p**5 + 0 + 0*p**y + 1/16*p**4. Factor k(n).
-3*n*(2*n - 1)/2
Suppose 3*f = 3*z - 12, 5*z - z - 16 = -5*f. Suppose -6*l**3 - 2*l**2 - 12*l**4 - l + 20*l**z + l = 0. What is l?
-1/4, 0, 1
Let x(z) be the second derivative of z - 1/2*z**3 + 1/4*z**4 + 0 - 3*z**2. Solve x(j) = 0.
-1, 2
Let c(z) be the third derivative of -z**8/2016 + z**6/360 - z**4/144 + 28*z**2. Factor c(x).
-x*(x - 1)**2*(x + 1)**2/6
Suppose -135 = -4*r - 19. Let y = r - 29. Solve y + 0*g**3 + 0*g - 2/3*g**4 + 2/3*g**5 + 0*g**2 = 0.
0, 1
Let b(a) be the third derivative of 0*a**4 + 1/30*a**6 + 0*a**3 + 0*a + 1/105*a**7 + 0 - 3*a**2 + 1/30*a**5. Factor b(d).
2*d**2*(d + 1)**2
Let v(j) be the third derivative of -j**8/1344 - j**7/840 + j**6/480 + j**5/240 + 3*j**2. Let v(m) = 0. Calculate m.
-1, 0, 1
Let i(v) be the second derivative of v**4/12 - 5*v**3/6 + 3*v**2 + 4*v. Let p be i(4). Factor 5/3*o**4 - 4/3*o - o**3 + 0 - 4*o**p.
o*(o - 2)*(o + 1)*(5*o + 2)/3
Let m(d) be the first derivative of 8*d**5/5 - 3*d**4 + 4*d**3/3 + 6. Factor m(f).
4*f**2*(f - 1)*(2*f - 1)
Let w(y) be the second derivative of y**4/4 + 3*y**3/2 + 3*y**2 + 7*y. Let w(z) = 0. What is z?
-2, -1
Factor 6*y**2 + 6*y**3 - 2*y**5 + 0*y**5 - 3*y**3 - 17*y**3 + 10*y**4.
-2*y**2*(y - 3)*(y - 1)**2
What is n in -2/9 - 2*n**2 - 4/3*n = 0?
-1/3
Suppose k = -5*f - 11, 47*k - 44*k + 4*f = 0. Factor 3/5*b**k - 2/5*b**2 - 1/5*b**5 - 2/5*b**3 - 1/5 + 3/5*b.
-(b - 1)**4*(b + 1)/5
Suppose -4 - 23*g - 42*g**4 - 82*g**3 + 28*g**2 - 20*g - 8*g**5 - 102*g**2 + 13*g = 0. What is g?
-2, -1, -1/4
Let s(x) = -x**3 + 6*x**2 + x + 2. Let u(d) = -2*d**3 + 13*d**2 + 2*d + 5. Let p(i) = 9*s(i) - 4*u(i). Factor p(v).
-(v - 2)*(v - 1)*(v + 1)
Let t = -5 + 11. Let x(w) be the first derivative of -2*w - 2 + 4/3*w**3 - 1/3*w**t - w**2 - 2/5*w**5 + w**4. Solve x(n) = 0.
-1, 1
Let h be (-8)/(-44) - (-144)/176. Find c such that 1/2*c + 1/2*c**2 - h = 0.
-2, 1
Suppose -27*m**4 + 5*m**2 + 14*m**4 + 8*m**4 = 0. What is m?
-1, 0, 1
Let z be -3 - -7 - 8/2. Let o(b) be the third derivative of z*b**3 + 2*b**2 - 1/48*b**4 + 1/120*b**5 + 0*b + 0. Factor o(y).
y*(y - 1)/2
Suppose -24 = -2*o - 20. Let n = 3 + -3. Suppose l**o + n - 2/3*l = 0. What is l?
0, 2/3
Let 24/5*g - 22/5*g**2 - 12*g**3 + 10*g**4 + 8/5 = 0. What is g?
-2/5, 1
Let r(h) be the first derivative of -h**6/3 + 12*h**5/5 + 11. What is a in r(a) = 0?
0, 6
Let z(n) = -n**4 - n**3 - 1. Let q(y) = 18*y**5 - 17*y**4 - 21*y**3 + 12*y**2 - 2*y - 5. Let j(u) = q(u) - 5*z(u). Solve j(h) = 0.
-1, 0, 1/3, 1
Let f = -8 + 2. Let n(v) = v**4 - 4*v**3 - 3*v**2 + 4*v + 4. Let x(h) = h**4. Let q(s) = f*x(s) + 3*n(s). Factor q(o).
-3*(o - 1)*(o + 1)*(o + 2)**2
Let n = -96 + 96. Let k(g) be the third derivative of n*g**3 - 1/336*g**8 + 2*g**2 - 1/60*g**5 + 0 - 1/40*g**6 + 0*g**4 + 0*g - 1/70*g**7. Factor k(i).
-i**2*(i + 1)**3
Let q(f) be the second derivative of -1/3*f**4 - 5/6*f**3 - 1/20*f**5 - f**2 + 3*f + 0. Factor q(m).
-(m + 1)**2*(m + 2)
Let z(f) be the second derivative of f**7/147 - 4*f**6/105 + f**5/70 + 5*f**4/21 - 4*f**3/21 - 8*f**2/7 + 2*f. Factor z(g).
2*(g - 2)**3*(g + 1)**2/7
Suppose b + b = 8. Suppose -3*m**2 + 0 + 1 + m**2 + m**b = 0. Calculate m.
-1, 1
Suppose 0*s = s + 3. Let p be (s/(-1))/(3/2). Determine c so that 2*c**4 + 3*c**2 + 5*c**3 + c**p + c**3 = 0.
-2, -1, 0
Let y = -48 + 53. Factor 1/4*n**y + 0*n - 3/4*n**4 + 3/4*n**3 - 1/4*n**2 + 0.
n**2*(n - 1)**3/4
Let o be ((-6)/4)/((-15)/20). Determine k so that 4/9 - 2/9*k - 10/9*k**3 - 16/9*k**o = 0.
-1, 2/5
Let z(f) be the third derivative of -f**7/630 - f**6/360 + f**5/180 + f**4/72 - 23*f**2. Factor z(l).
-l*(l - 1)*(l + 1)**2/3
Let b(q) be the second derivative of 1/40*q**5 - 1/24*q**6 - q - 1/2*q**2 + 1/6*q**3 + 0 + 5/16*q**4. Solve b(m) = 0.
-1, 2/5, 2
Let x = 25 + -7. Let h be (-1)/x - 10/(-20). Solve -2/9*o - 2/9*o**2 + h = 0 for o.
-2, 1
Find r, given that -20*r**2 + 7*r**2 - 25*r**3 - 92*r**2 - 25 + 10*r**4 - 95*r = 0.
-1, -1/2, 5
Let v(s) be the first derivative of 5 - 1/7*s**4 + 0*s - 8/21*s**3 - 2/7*s**2. Determine q, given that v(q) = 0.
-1, 0
Let z = -2 - -1. Let l be z/4*24/(-15). Let 4/5*n**2 + 2/5*n**3 - l*n - 4/5 = 0. Calculate n.
-2, -1, 1
Suppose -3*d + 9 = 3. Suppose -2*x**2 - x**d - 9*x - x**2 - 6 + x**2 = 0. What is x?
-2, -1
Let q = 957 + -954. Factor -2/9*w**q + 2/9*w**2 + 4/9*w + 0.
-2*w*(w - 2)*(w + 1)/9
Let y(z) be the first derivative of 6*z**5/25 + z**4/5 - 14*z**3/15 + 2*z**2/5 + 7. Suppose y(t) = 0. Calculate t.
-2, 0, 1/3, 1
Let y(j) = 3*j - 15. Let b be y(6). Let w be (-1)/b + 35/42. Factor 1/2*r**3 + 1/2*r**2 - 1/2*r - w.
(r - 1)*(r + 1)**2/2
Let u(f) = 2*f**2 - 14*f + 2. Let t be u(7). Let r(m) be the first derivative of 0*m + 1/2*m**2 - 1/6*m**3 + t. Factor r(h).
-h*(h - 2)/2
Factor -w**3 - 1/4 + 7/4*w**2 - 1/2*w.
-(w - 1)**2*(4*w + 1)/4
Let j(y) be the first derivative of 15*y**4/4 - 35*y**3/3 + 25*y**2/2 - 5*y - 33. Factor j(p).
5*(p - 1)**2*(3*p - 1)
Let j(n) be the first derivative of -n**6/3 + 2*n**5/5 - 6. Factor j(o).
-2*o**4*(o - 1)
Let y(o) be the second derivative of 0 - 1/2*o**4 + 7/40*o**5 + 1/2*o**2 + 1/4*o**3 + 6*o. Factor y(h).
(h - 1)**2*(7*h + 2)/2
Let q(v) b