**5.
-2*x**3*(x - 1)**2
Factor -w**2 - w**2 + 3*w**3 - w**3.
2*w**2*(w - 1)
Let n(c) be the second derivative of 2/147*c**7 + 0*c**2 + 1/42*c**4 + 2/35*c**5 + 5*c + 0 + 1/21*c**6 + 0*c**3. Suppose n(i) = 0. What is i?
-1, -1/2, 0
Let t(f) = -2*f - 12. Let z be t(-6). Let d = 155/164 + -8/41. Factor d*m**2 - 1/4*m + z.
m*(3*m - 1)/4
Let g(d) be the second derivative of 7*d**6/120 - 3*d**5/10 - d**4/2 + d**3/6 - d. Let t(o) be the second derivative of g(o). Let t(u) = 0. Calculate u.
-2/7, 2
Let o(c) be the second derivative of 0*c**5 + 0*c**3 + 0 + 1/30*c**6 + 3*c - 1/6*c**4 + 1/2*c**2. Find x, given that o(x) = 0.
-1, 1
Let n(g) = g**3 - 8*g**2 + 6*g - 5. Let x be n(7). Let c be 0*(-2)/x*3. Factor c + 3/2*l**2 - 3/2*l.
3*l*(l - 1)/2
Let k(h) be the second derivative of h**7/63 - h**5/30 + 5*h. Factor k(c).
2*c**3*(c - 1)*(c + 1)/3
Let c(k) be the first derivative of k**3 + 0*k + 9/2*k**2 - 2. What is u in c(u) = 0?
-3, 0
Let w be (-2 - 3/3)*(-14)/378. Let j(c) be the second derivative of 1/54*c**4 - 2/27*c**3 + w*c**2 + 0 - c. Factor j(u).
2*(u - 1)**2/9
Let t(l) = l**3 + 2*l**2 - l + 1. Let q be t(-2). Let u = 49 + -47. Factor 12*i**u + 10*i**q + 16/5 - 72/5*i.
2*(i + 2)*(5*i - 2)**2/5
Let f(l) = -11 + 33*l**2 + 5*l**2 - l**3 - l - 7*l**2. Let v(b) = 6*b**2 - 2. Let h(y) = 2*f(y) - 11*v(y). Determine c, given that h(c) = 0.
-1, 0
Let y be (-77)/22*2/(-14). Let 1/2*x**2 + y - x = 0. Calculate x.
1
Let c be (-2)/(-12)*((-56)/8 - -9). Determine w so that 0*w - c*w**2 + 1/3 = 0.
-1, 1
Let s(o) be the second derivative of -o**7/441 + 4*o**6/315 - o**5/70 - 6*o. Factor s(f).
-2*f**3*(f - 3)*(f - 1)/21
Let w(j) be the second derivative of 1/6*j**4 - j + 1/10*j**5 + 1/9*j**3 + 0*j**2 + 0 + 1/45*j**6. Find x, given that w(x) = 0.
-1, 0
Let x(g) be the second derivative of 7/60*g**4 + 0 - 3/100*g**5 + 1/10*g**3 - 1/30*g**6 - 5*g - 1/5*g**2. Determine w so that x(w) = 0.
-1, 2/5, 1
Let c(i) = -i**2 - 9*i. Let m(t) = -t**2 - 10*t. Let q(o) = 3*c(o) - 2*m(o). Factor q(g).
-g*(g + 7)
Let k(m) be the second derivative of -4/45*m**6 - 1/3*m**2 + 5/18*m**4 - 5/12*m**5 + 10/63*m**7 + m + 5/18*m**3 + 0. Determine s so that k(s) = 0.
-1, -1/2, 2/5, 1/2, 1
Let a(n) be the first derivative of -n**6/18 + n**5/15 + n**4/6 - 2*n**3/9 - n**2/6 + n/3 + 2. Solve a(p) = 0 for p.
-1, 1
Let i(g) be the third derivative of 0 + 4*g**2 + 0*g**4 + 0*g - 1/45*g**3 + 1/450*g**5. Find w, given that i(w) = 0.
-1, 1
Let p(v) be the first derivative of -1/2*v**3 + 1/20*v**5 + 0*v + v**2 + 0*v**4 - 3. Let k(y) be the second derivative of p(y). Factor k(i).
3*(i - 1)*(i + 1)
Factor 0 - 50/3*q - 5/3*q**2.
-5*q*(q + 10)/3
Let j be 2/3 - 220/(-165). Factor 0 + 0*o + 2/9*o**j.
2*o**2/9
Suppose 5*a - n - 3*n = -29, 5*n - 25 = 4*a. Let w = 9 + a. Let h**5 - 3*h**5 + 2*h**3 + w*h**4 - 2*h**4 - 2*h**2 = 0. Calculate h.
-1, 0, 1
Let d(w) = w**2 - 9*w + 17. Let n be d(7). Suppose 31 = 3*u + 5*p, 2*p - 7 - n = 0. Factor -2/5*m**u + 2/5 + 0*m.
-2*(m - 1)*(m + 1)/5
Let p(b) be the first derivative of 2*b**3/15 - 2*b**2/5 + 2*b/5 - 8. Let p(r) = 0. Calculate r.
1
Find j such that 3*j**3 - 2*j**5 + j**4 + 5*j**5 + 4*j**4 + j**4 = 0.
-1, 0
Suppose 2*w = -5*b - 20, 12 = -4*w + 6*w - 3*b. Suppose w - 98/9*s**3 - 56/9*s**2 - 8/9*s = 0. What is s?
-2/7, 0
Let u(x) = 3*x**3 - 21*x**2 + x - 21. Let m(b) = -b**3. Let q(g) = 2*m(g) + u(g). Let r be q(21). Solve r + 2/5*o + 2/5*o**2 = 0 for o.
-1, 0
Let g(u) be the second derivative of u + 0*u**2 + 0*u**4 + 0 + 1/27*u**3 - 1/90*u**5. Factor g(z).
-2*z*(z - 1)*(z + 1)/9
Factor -3/4*q**2 - 3/4*q**3 + 3/4*q + 3/4.
-3*(q - 1)*(q + 1)**2/4
Let k(z) be the third derivative of z**5/90 - z**4/12 + 6*z**2. Factor k(h).
2*h*(h - 3)/3
Let g(u) be the second derivative of 0 + 0*u**4 + 0*u**2 + 2/15*u**6 + 0*u**5 + 0*u**3 - u. Factor g(p).
4*p**4
Solve 0 + 0*g + 1/2*g**4 + 0*g**3 - 1/4*g**5 + 0*g**2 = 0.
0, 2
Let m(q) = -10*q**3 + 19*q**3 - 4 + 5*q**2 + 6*q - 14*q**3. Let v(t) = 9*t**3 - 9*t**2 - 11*t + 7. Let o(a) = 7*m(a) + 4*v(a). Factor o(z).
z*(z - 2)*(z + 1)
Let d(y) = y**2 + 8*y + 5. Let q be d(-8). Factor 1 + i**2 + 9*i + 2 - 8*i - q.
(i - 1)*(i + 2)
Let b(t) = -4*t**3 + 4*t**2 - 6*t. Let j(n) = 13*n**3 - 11*n**2 + 18*n + 1. Let l(k) = 7*b(k) + 2*j(k). Determine f so that l(f) = 0.
1
Let c(n) be the second derivative of n**5/60 - n**4/8 + 5*n**2/2 + 4*n. Let r(d) be the first derivative of c(d). Factor r(v).
v*(v - 3)
Suppose 4*b + 69 = b. Let c = b - -27. Factor 1/2*p**3 + 0 + 1/2*p**5 + p**c + 0*p + 0*p**2.
p**3*(p + 1)**2/2
Factor 0*o**2 + 0*o**2 + 2*o - 8*o**3 + 6*o**3.
-2*o*(o - 1)*(o + 1)
Let q(n) be the third derivative of 1/80*n**6 + 1/60*n**5 + 0*n + 0*n**3 + 0 + 1/144*n**4 - 3*n**2 + 1/315*n**7. Factor q(r).
r*(r + 1)**2*(4*r + 1)/6
Let g(a) = 1. Let o(w) = -7*w**2 + 9*w - 5. Let y(r) = 6*g(r) + 2*o(r). Factor y(x).
-2*(x - 1)*(7*x - 2)
Let a(u) be the second derivative of -u**7/70 - 7*u**6/120 - u**5/30 - u**2/2 + u. Let r(q) be the first derivative of a(q). Factor r(t).
-t**2*(t + 2)*(3*t + 1)
Let t = -35 + 49. Suppose -1 = h - t. Suppose 2 - g - 20 + h*g - 2*g**2 + 0*g = 0. Calculate g.
3
Determine r, given that -36*r**2 - 4/3*r**3 - 972 - 324*r = 0.
-9
Let s(n) = 5*n**4 - n**3 + 5*n**2 + 9*n + 9. Let v(k) = k**4 + k**2 + 2*k + 2. Let d(x) = -2*s(x) + 9*v(x). Suppose d(y) = 0. Calculate y.
0, 1
Let z(r) = r**2 + 12*r - 15. Let t(i) = 12*i - 16. Let a(q) = -3*t(q) + 2*z(q). Let a(h) = 0. What is h?
3
Solve 0 - 2/9*v**2 - 4/9*v = 0 for v.
-2, 0
Let o(g) be the first derivative of -1/6*g**4 - 7/15*g**5 - 2 + 7/9*g**3 + 0*g + 1/3*g**2. Factor o(n).
-n*(n - 1)*(n + 1)*(7*n + 2)/3
Let q(x) be the second derivative of -x**5/240 + x**4/48 - x**3/24 + x**2/2 + 3*x. Let g(c) be the first derivative of q(c). Factor g(r).
-(r - 1)**2/4
Let u(l) = -2*l + 2. Let b be u(0). Let g(o) be the first derivative of 0*o**2 - 3 + b*o - 2/3*o**3. Find y, given that g(y) = 0.
-1, 1
Suppose 8*h = -1 + 25. Let u(z) be the third derivative of z**2 + 0*z**h + 0*z + 0 + 1/240*z**5 - 1/96*z**4. Determine r so that u(r) = 0.
0, 1
Factor 4/5*z**2 + 2/5*z**3 - 4/5 - 2/5*z.
2*(z - 1)*(z + 1)*(z + 2)/5
Determine f so that -3/5*f**3 + 0*f + 0 + 6/5*f**2 - 3/5*f**4 = 0.
-2, 0, 1
Factor -1/4*z + 1/4*z**3 + 1/4*z**2 - 1/4.
(z - 1)*(z + 1)**2/4
Let q(o) = o**2 + 3*o + 4. Suppose m = -1 - 2. Let l be q(m). Solve 2*h**2 - 2*h**2 + h**2 - 2*h**2 + h**l = 0.
-1, 0, 1
Let s = -27832050/161 + 172869. Let w = -7/23 - s. Determine a so that w*a**2 + 2/7 - 6/7*a = 0.
1/2, 1
Let z(n) be the third derivative of -n**6/60 - n**5/15 - n**4/12 + n**2. Factor z(i).
-2*i*(i + 1)**2
Let p = 16/13 + 1954/39. Suppose 26 = 2*y + 3*y - 4*a, -4*y = -2*a - 16. Solve 0 - 24*x**y + 8/3*x + p*x**3 - 54*x**5 + 24*x**4 = 0 for x.
-1, 0, 2/9, 1
Let t(d) be the second derivative of 289*d**4/48 - 17*d**3/6 + d**2/2 + 6*d. Factor t(r).
(17*r - 2)**2/4
Suppose -8 = 1036*y - 1040*y. Let 64/5 - 668/5*n**4 + 112/5*n**5 - 128/5*n + 1312/5*n**3 - 160*n**y = 0. Calculate n.
-2/7, 1/4, 2
Let k(o) = -o**3 - 5*o**2 + 3. Let u be k(-5). Suppose -7*y + a = -3*y - 10, -3*y + 4 = a. Factor 2*w**u + 10*w + 6*w**y - 4*w + 0*w**2 + 2.
2*(w + 1)**3
Suppose 4*k - 20 = 3*a + 2*a, a = 5*k - 4. Factor -2/7 + k*t - 2/7*t**4 + 0*t**3 + 4/7*t**2.
-2*(t - 1)**2*(t + 1)**2/7
Let a(b) be the first derivative of b**6/15 + 2*b**5/5 + 5*b**4/6 + 2*b**3/3 - 4*b + 4. Let u(h) be the first derivative of a(h). Factor u(k).
2*k*(k + 1)**2*(k + 2)
Let z be 4/(-14)*7/(-4). Suppose 0*i - 2*i + 2 = g, i = 4*g + 19. Find j such that j**2 + 0 + 1/2*j + z*j**i = 0.
-1, 0
Let a(p) be the second derivative of -p**5/360 + p**4/48 - p**3/18 + 5*p**2/2 + p. Let h(j) be the first derivative of a(j). Suppose h(d) = 0. Calculate d.
1, 2
Suppose 17*f + 35 = 103. Factor 0 - 88/9*b**3 - 140/9*b**f + 0*b - 16/9*b**2 - 50/9*b**5.
-2*b**2*(b + 2)*(5*b + 2)**2/9
Let t(q) be the third derivative of q**7/525 + q**6/100 - q**4/15 + 4*q**2. Factor t(r).
2*r*(r - 1)*(r + 2)**2/5
Let s(i) = 5*i - 1. Let r be s(1). Suppose -20 = -r*p - p. Factor 0*h**4 + p*h - h**2 - 2*h**3 - h**4 - 4*h.
-h**2*(h + 1)**2
Let r(q) = -q + 1. Let f be r(1). Let k(c) be the second derivative of 0*c**2 + f + 0*c**4 - 1/168*c**7 + 1/80*c**5 - 2*c + 0*c**6 + 0*c**3. Factor k(o).
-o**3*(o - 1)*(o + 1)/4
Let