**4.
-5*t**3*(t - 1)**2
Let d be -4 - (-2 + 40/(-12)). Suppose 2*u = 2*s + s - 5, -4*s + 12 = 0. Factor 1/3*b - d*b**u + 0.
-b*(4*b - 1)/3
Let o(a) be the first derivative of 1/10*a**4 + 2/5*a**2 + 0*a - 2/3*a**3 + 4/25*a**5 + 1. Solve o(z) = 0.
-2, 0, 1/2, 1
Let d = -5849/35 - -1174/7. Solve -3/5*u - 6/5 + d*u**2 = 0.
-1, 2
Let i(h) = h - 6. Let z be i(6). Let p(t) be the first derivative of t**2 + 0*t**3 - 1/2*t**4 + 2 + z*t. Find k, given that p(k) = 0.
-1, 0, 1
Let j(v) be the first derivative of v**6/6 + v**5/15 - 5*v**4/12 - v**3/9 + v**2/3 - 3. Let j(z) = 0. Calculate z.
-1, 0, 2/3, 1
Suppose 4 = 4*s + 20. Let f be (-2)/s - 3/(-2). Factor -6*r**4 + r**4 + 3*r**4 + f*r**5.
2*r**4*(r - 1)
Let j(z) be the second derivative of z**7/3780 - z**6/360 + z**5/90 - z**4/6 - 3*z. Let y(x) be the third derivative of j(x). Let y(n) = 0. What is n?
1, 2
Suppose 2*d + 9 = 5*m, m = -m + 6. Find h, given that -4*h**2 - d*h**3 - 7*h**3 + 8*h**3 = 0.
-2, 0
Let k(a) = -a**2 + a - 1. Let x(l) = 3*l**2 - l + 2. Let q = -9 + 7. Let n(f) = q*x(f) - 4*k(f). Find v such that n(v) = 0.
-1, 0
Let q = 69/140 - 10/21. Let d(z) be the second derivative of q*z**5 + 2/3*z**3 - 4/3*z**2 - z + 0 - 1/6*z**4. Find f such that d(f) = 0.
2
Suppose 6 = -5*p - 4*f, -5*p + 3*f + 10 = -6*p. Factor -2/3*k**3 + 4/3*k**p - 2/3*k + 0.
-2*k*(k - 1)**2/3
Let t(d) be the second derivative of 2*d**4/45 + 11*d**3/45 - d**2/5 + 4*d. What is k in t(k) = 0?
-3, 1/4
Let p(g) be the first derivative of g**8/48 + g**7/105 - 7*g**6/120 - g**5/30 + g**2 - 3. Let f(s) be the second derivative of p(s). Let f(w) = 0. What is w?
-1, -2/7, 0, 1
Let g(r) be the first derivative of -2 + r**2 + 0*r**3 - 4/3*r - 1/6*r**4. Factor g(z).
-2*(z - 1)**2*(z + 2)/3
Let b(l) = 3*l**3 - 6*l**2 + 3*l + 6. Let o = 1 + 5. Let q(d) = 5*d**3 - 12*d**2 + 5*d + 11. Let t be (3/6)/(3/(-66)). Let y(s) = o*q(s) + t*b(s). Factor y(x).
-3*x*(x + 1)**2
Let w = -151 + 153. Factor 1/2*y**w + 0 + y - 1/2*y**3.
-y*(y - 2)*(y + 1)/2
Let v(f) be the first derivative of -3*f**4/4 + 3*f**3 - 12*f - 8. Factor v(x).
-3*(x - 2)**2*(x + 1)
Let y(p) be the third derivative of -1/8*p**4 - 2*p**2 + 0 + 0*p + 1/20*p**5 + 0*p**3. Factor y(w).
3*w*(w - 1)
Let q be ((-2)/3)/(16/24). Let x be q/(-2) + (-7)/(-2). Solve 0*m - x*m**3 + m + 0*m + 9*m**2 - 3*m = 0 for m.
0, 1/4, 2
Let k be 15/9 + 1/3. Find w, given that -4/7*w + 2/7*w**k + 2/7 = 0.
1
Let v = -12 + 15. Factor -j**v + 22*j**2 - 4*j**2 - 10*j - 2*j - 8 - 4*j**3.
-(j - 2)**2*(5*j + 2)
Let m = -24/5401 + 929476/113421. Let z = -32/21 + m. Solve 0 + 25/3*k**5 + 0*k**2 + z*k**4 + 4/3*k**3 + 0*k = 0 for k.
-2/5, 0
Let y = -32 + 34. Determine g so that -g**3 + 1/2*g**4 + 0 + 0*g + 1/2*g**y = 0.
0, 1
Suppose -3*c + 5*c = -2*c. Let i(a) be the first derivative of c*a + 1/12*a**3 - 1 + 1/8*a**2. What is o in i(o) = 0?
-1, 0
Solve -2*o - 2*o + 10*o**2 + 4 - 20 + 8*o + 2*o**3 = 0.
-4, -2, 1
Let o be ((-4)/100)/(18/(-5)). Let u(m) be the third derivative of 0*m**4 + 0*m - 1/9*m**3 + 0 + o*m**5 + m**2. Factor u(l).
2*(l - 1)*(l + 1)/3
Let f(k) be the first derivative of 2*k**3/33 + 2*k**2/11 + 2*k/11 - 3. Factor f(g).
2*(g + 1)**2/11
Let q = 3 + 2. Let u(t) = 3*t**4 - t**3 + 17*t**2 - 11*t + 8. Let f(p) = -2*p**4 + p**3 - 11*p**2 + 7*p - 5. Let b(s) = q*u(s) + 8*f(s). Factor b(z).
-z*(z - 1)**3
Let l be (3 - (-7)/(-2))*0. Suppose -2*h + 11 + 5 = l. Factor -j**5 + 2*j**5 + h*j**4 + j**5 - 4*j**5 + 10*j - 4 - 4*j**2 - 8*j**3.
-2*(j - 2)*(j - 1)**3*(j + 1)
Let w = -23333/12 - -1950. Let l = -17/4 + w. Suppose l*c**2 - 4/3*c**3 - 2/3*c**4 + 2/3*c**5 + 2/3*c - 2/3 = 0. Calculate c.
-1, 1
Let b(s) = 3*s**4 + 13*s**3 + 10*s**2 - 4*s + 4. Let x(r) = -3*r**4 - 12*r**3 - 9*r**2 + 3*r - 3. Let l(v) = -3*b(v) - 4*x(v). Factor l(h).
3*h**2*(h + 1)*(h + 2)
Let o(y) be the third derivative of -y**7/2940 - y**6/315 - y**5/140 - 2*y**3/3 + 6*y**2. Let j(q) be the first derivative of o(q). Factor j(b).
-2*b*(b + 1)*(b + 3)/7
Let x(r) be the first derivative of 0*r + 24/5*r**5 + 2*r**3 - 3/2*r**6 + 0*r**2 + 2 - 21/4*r**4. Factor x(c).
-3*c**2*(c - 1)**2*(3*c - 2)
Let t(z) = 23*z**2 - 12*z. Let w be (-1 + 32 - -3)/2. Let m(x) = 8*x**2 - 4*x. Let q(r) = w*m(r) - 6*t(r). Factor q(o).
-2*o*(o - 2)
Let t = -5 + 9. Suppose -t*p + 6*s = s - 41, 3*p = 4*s + 32. Let -8/5*f**3 + 17/5*f + 2/5 + 37/5*f**2 - 48/5*f**p = 0. Calculate f.
-2/3, -1/4, 1
Factor 0*f**4 - 3/4*f**5 + 3/4*f**3 + 0 + 0*f + 0*f**2.
-3*f**3*(f - 1)*(f + 1)/4
Let z(o) = 4*o**4 - o**3 - o**2 - 2*o. Let g(r) = 3*r**4 - r**3 - r**2 - r. Let h(p) = 3*g(p) - 2*z(p). Factor h(k).
k*(k - 1)**2*(k + 1)
Let u be (-343)/(-840) - (-4)/(-10). Let l(h) be the second derivative of 0 + 0*h**5 + 0*h**4 - 3*h - u*h**6 + 0*h**2 - 1/168*h**7 + 0*h**3. Factor l(q).
-q**4*(q + 1)/4
Let z(l) be the third derivative of 1/60*l**4 + 0 - 1/300*l**5 - 7*l**2 + 0*l - 1/30*l**3. Determine m, given that z(m) = 0.
1
Let k(s) be the first derivative of s**6/15 + 8*s**5/25 + 3*s**4/5 + 8*s**3/15 + s**2/5 + 1. Factor k(c).
2*c*(c + 1)**4/5
Let y be (-27)/(-120) + (-3)/15. Let s(n) be the third derivative of 0 + 2*n**2 + 0*n - y*n**5 - 1/24*n**4 + 1/12*n**3. What is o in s(o) = 0?
-1, 1/3
Let r(h) = -3*h**2 + 3*h - 6. Let n(z) be the first derivative of z**2/2 + z + 5. Let p(a) = -3*n(a) - r(a). Factor p(y).
3*(y - 1)**2
Let u(d) be the second derivative of d**6/6 - 5*d**4/4 + 5*d**3/3 + 5*d. Determine f, given that u(f) = 0.
-2, 0, 1
Suppose -36*a + 37*a + 7 = -5*k, -4*a + 8 = 2*k. Suppose -2/5*y + 8/5*y**a + 1/5 + 2/5*y**5 - 2/5*y**2 - 7/5*y**4 = 0. What is y?
-1/2, 1
Let a(x) be the first derivative of 1/3*x**3 + 0*x**2 - 3 + 0*x. Factor a(f).
f**2
Let c(w) be the first derivative of w**7/2100 + w**6/225 + w**5/75 + w**3 - 1. Let x(n) be the third derivative of c(n). Factor x(u).
2*u*(u + 2)**2/5
Let w(f) = 5*f**4 + 100*f**3 + 365*f**2 + 605*f + 355. Let d(y) = -3*y**4 - 50*y**3 - 183*y**2 - 302*y - 178. Let x(q) = -5*d(q) - 2*w(q). Factor x(k).
5*(k + 2)**2*(k + 3)**2
Suppose 4*y = -5*p + p + 8, 5*p = -4*y + 12. Let a be (4 + y/(-1))*1. Solve 12*t + 3/2*t**2 - 15/2*t**4 - 3/2*t**5 + a - 21/2*t**3 = 0 for t.
-2, -1, 1
Let o(m) = 2*m**2 - 11*m - 11. Let s(g) = g**2 - 6*g - 6. Let y(v) = -6*o(v) + 11*s(v). Find l, given that y(l) = 0.
0
Let h = 341/5 + -68. Let l(y) be the first derivative of -1 + 2/15*y**3 - h*y**2 + 0*y. Factor l(w).
2*w*(w - 1)/5
Suppose -3*t - 45 = -5*g - 8, g - 7 = t. Suppose g = -4*d + 4*l, -2*l - 1 = 3*d - 5. Suppose 4/9*j**2 + 0*j - 2/9 + d*j**3 - 2/9*j**4 = 0. What is j?
-1, 1
Let q(o) be the second derivative of o**8/10080 - o**6/1080 - o**4/3 - 2*o. Let c(m) be the third derivative of q(m). Factor c(t).
2*t*(t - 1)*(t + 1)/3
Let a(d) = -d - 2 + d**2 - 2*d**2 + 0*d**2. Let o(p) be the first derivative of p + 4. Let c(i) = -2*a(i) - 4*o(i). Determine l, given that c(l) = 0.
-1, 0
Let w be (-14)/(-4) - (-86 - -89). Factor w + 1/2*x**2 + x.
(x + 1)**2/2
Suppose 0 = 5*a + 5*a - 5*a. Let g(p) be the third derivative of 1/80*p**5 + 0*p - 1/32*p**4 + 2*p**2 + 0*p**3 + a. Find u, given that g(u) = 0.
0, 1
Let x(m) = -m**2 + 2*m. Let n be x(2). Let y be (3 + -5)*-1 - n. Factor -1/2*s - 9/2*s**3 + 0 - 3*s**y.
-s*(3*s + 1)**2/2
Let h(x) be the first derivative of 2*x**3/3 + 4*x**2 + 8*x + 17. Find s, given that h(s) = 0.
-2
What is y in 7*y - y - y**4 + y**2 - 14*y**3 + 4 - 5*y**4 - 7*y**2 = 0?
-1, 2/3
Suppose -4*d + 9 = 5*d. Suppose 0 = i - d - 3. Factor 0*z**3 + 0*z + 0*z**2 - 2/3*z**i + 0 - 2/3*z**5.
-2*z**4*(z + 1)/3
Let c(y) be the second derivative of y**7/12 - 9*y**6/10 + 19*y**5/5 - 22*y**4/3 + 4*y**3 + 8*y**2 + 20*y. Factor c(q).
(q - 2)**4*(7*q + 2)/2
Let k(y) = 5*y**2 - 4*y - 9. Let q(v) = -14*v**2 + 12*v + 26. Let h(j) = 17*k(j) + 6*q(j). Let h(c) = 0. What is c?
-3, -1
Let b(p) be the second derivative of 1/12*p**4 - 2*p + 1/20*p**5 + 0 + 0*p**3 + 0*p**2. Solve b(y) = 0 for y.
-1, 0
Let k(n) be the first derivative of -2*n**3/9 + 4*n**2/3 - 8*n/3 + 4. Factor k(y).
-2*(y - 2)**2/3
What is k in 3/7*k**5 - 9/7*k - 9/7*k**4 + 6/7*k**3 + 3/7 + 6/7*k**2 = 0?
-1, 1
Let i = 14066 - 70619/5. Let k = i + 58. Factor -1/5*m**3 - k*m**2 + 1/5*m**4 + 0 + 0*m + 1/5*m**5.
m**2*(m - 1)*(m + 1)**2/5
Let j = 232 + -232. Let j + 0*v - 3/4*v**2 = 0. What is v?
0
Let k = -10 + 12. 