r o(s).
-2*s*(s - 1)**2*(s + 1)/5
Suppose -11*k + 19*k = 13*k. Solve 1/2*n + 1/4*n**2 + k = 0 for n.
-2, 0
Factor 12*y**4 + 57*y**2 + 12 - 75/2*y**3 - 42*y - 3/2*y**5.
-3*(y - 2)**3*(y - 1)**2/2
Suppose -2*j + 4 = -0*j. Let w = j - 2. Determine p, given that 2/3*p**3 + 0*p**2 + w*p + 0 - 2/3*p**5 + 0*p**4 = 0.
-1, 0, 1
Let p = -68 - -68. Let n(b) be the third derivative of 0*b**4 + 0*b**5 + 0*b + 0 - b**2 - 1/525*b**7 + 0*b**3 + p*b**6. Factor n(f).
-2*f**4/5
Let o(w) be the second derivative of -22*w**7/21 - 92*w**6/15 - 41*w**5/5 + 38*w**4/3 + 104*w**3/3 + 16*w**2 + 4*w. Let o(g) = 0. What is g?
-2, -1, -2/11, 1
Let q(x) be the third derivative of 0 - 1/75*x**5 - 1/120*x**4 + 9*x**2 + 0*x**3 + 0*x. Factor q(b).
-b*(4*b + 1)/5
Let a = 3 - 3. Let n(w) be the third derivative of 1/9*w**3 + a + 1/180*w**6 + 0*w - 3*w**2 + 1/12*w**4 + 1/30*w**5. Factor n(r).
2*(r + 1)**3/3
Suppose -c - 8 = -4*d - 28, -44 = 4*d + 5*c. Let b be 0 + (2/d)/(-1). Factor -1/3*z**3 - b*z**4 + 0 + 1/3*z + 1/3*z**2.
-z*(z - 1)*(z + 1)**2/3
Let a be 2/6 - 3/9. Let x(q) be the third derivative of a*q**3 + 1/90*q**5 - 1/72*q**4 - 1/360*q**6 + 0 + 0*q + 2*q**2. Factor x(u).
-u*(u - 1)**2/3
Let d(k) be the third derivative of -1/240*k**5 + 0 + 0*k - k**2 + 1/96*k**4 + 1/24*k**3 - 1/480*k**6. Factor d(f).
-(f - 1)*(f + 1)**2/4
Let 1/9*c**3 + 0 + 5/9*c**2 + 4/9*c = 0. What is c?
-4, -1, 0
Suppose -1 = -4*t + 31. Find w such that t*w - 3*w**5 + 5*w**4 - 4*w**4 - 4*w**2 + 3*w**4 + 7*w**5 - 12*w**3 = 0.
-2, -1, 0, 1
Let a(t) be the second derivative of t**4/42 - 2*t**3/21 + t**2/7 - 2*t. Find n such that a(n) = 0.
1
Let s = 7 - 7. Let j(g) be the third derivative of -1/12*g**4 + s*g + 0 + 1/30*g**5 - g**2 - 1/3*g**3 + 1/60*g**6. Factor j(r).
2*(r - 1)*(r + 1)**2
Let x be (-2)/(3/(6/4)). Let a be 2 + -2 + (x - -3). Factor a*b**2 - 7*b + 8 - 5*b + 4*b.
2*(b - 2)**2
Let n(g) = 8*g**2 - 8*g + 6. Let x(i) = -i. Let l = 20 + -26. Let m(t) = l*x(t) - n(t). Solve m(o) = 0 for o.
3/4, 1
Let o(t) be the third derivative of t**7/735 - t**5/70 + t**4/42 - 2*t**2. Determine n so that o(n) = 0.
-2, 0, 1
Suppose 0 = -10*a + 15*a. Let l(s) be the second derivative of a + 0*s**3 + 0*s**2 + 1/36*s**4 - 2*s. Factor l(w).
w**2/3
Suppose 0 = -q - 3, -4*j + 4*q + 21 = 9. Let j - 1/3*v**4 + 1/3*v**3 - 1/3*v + 1/3*v**2 = 0. Calculate v.
-1, 0, 1
Let l(h) be the second derivative of -h**7/210 - h**6/40 - h**5/20 - h**4/24 + 3*h**2/2 - h. Let m(y) be the first derivative of l(y). Factor m(f).
-f*(f + 1)**3
Let l(c) be the third derivative of -7*c**6/60 + 3*c**5/10 - c**4/6 + 28*c**2. Factor l(d).
-2*d*(d - 1)*(7*d - 2)
Let a(b) be the third derivative of -b**8/448 + b**6/40 - 43*b**2. What is y in a(y) = 0?
-2, 0, 2
Let q(c) be the first derivative of -3*c**4/4 + 6*c**3 - 18*c**2 + 24*c + 7. Solve q(h) = 0.
2
Let i = 3 - -1. Factor i*r**2 - 3 - 2*r + 4 - 3*r**2.
(r - 1)**2
Let w(c) be the first derivative of -3/8*c**2 + 1/2*c - 10 + 1/12*c**3. Factor w(x).
(x - 2)*(x - 1)/4
Let s(g) = g + 7. Let y be s(-5). Determine i so that -9*i**y + 0*i**4 + 2*i**4 + 7*i**2 = 0.
-1, 0, 1
What is o in 2/9*o**2 - 2/9*o - 4/9 = 0?
-1, 2
Let t(h) = h**3 + 14*h**2 - 33*h - 16. Let d be t(-16). Let 3/2*x**3 - 1/2*x**5 + d - 1/2*x**2 - x + 1/2*x**4 = 0. What is x?
-1, 0, 1, 2
Let p(f) be the second derivative of 9*f**5/20 - f**4/2 - 7*f**3/2 - 3*f**2 + f. What is l in p(l) = 0?
-1, -1/3, 2
Let b(v) = v**2 - v + 3. Suppose 17 = 4*j - 7. Let c(d) = -4*d**2 - 3*d**2 + 6*d**2 + d - 4. Let l(p) = j*b(p) + 5*c(p). Factor l(x).
(x - 2)*(x + 1)
Let y(a) = -a - 2. Let q be y(-5). Let z(m) = m. Let r be z(q). Factor -4/3*d**4 + 2/3*d + 4/3*d**2 - 2/3*d**5 + 0*d**r + 0.
-2*d*(d - 1)*(d + 1)**3/3
Let z(d) be the second derivative of -5*d**7/126 - d**6/18 - 21*d. Factor z(i).
-5*i**4*(i + 1)/3
Let t = 1/69 + 15/23. Let t*x**2 - 4/3*x + 2/3 = 0. Calculate x.
1
Let t(q) = -6*q**5 + 6*q**4 - 2*q**3 - 2*q. Let x(z) = 13*z**5 - 11*z**4 + 3*z**3 + 5*z. Let j(a) = 5*t(a) + 2*x(a). Let j(y) = 0. Calculate y.
0, 1
Let u(q) be the first derivative of q**3/12 + q**2/4 - 1. Suppose u(y) = 0. What is y?
-2, 0
Suppose 0 = -3*t - h + 12, 0 = 3*t - 4*h - 3 - 9. Let -g**2 + 5*g**2 - g**t + g**2 - 4*g**2 = 0. What is g?
-1, 0, 1
Let d = 157/4 - 39. Let v = -1/8 - -3/8. Solve v + 0*q - d*q**2 = 0 for q.
-1, 1
Let v(k) = k**3 - 6*k**2 + 2. Suppose 0 = -3*a - 3*y, -3*y - 6 = -a + 2*a. Let b(p) = 6*p**2 - 3. Let o(m) = a*v(m) + 2*b(m). Factor o(u).
3*u**2*(u - 2)
Let r(q) be the second derivative of q**5/25 - 8*q**4/15 + 26*q**3/15 - 12*q**2/5 + 36*q. Find k such that r(k) = 0.
1, 6
Factor 0 - 1/9*j**4 - 2/9*j**3 + 4/9*j**2 + 8/9*j.
-j*(j - 2)*(j + 2)**2/9
Let z = 677/5 - 135. What is t in 0 - z*t + 2/5*t**3 + 2/5*t**4 - 2/5*t**2 = 0?
-1, 0, 1
Factor -1/10*i**2 - 1/10*i + 1/10*i**3 + 0 + 1/10*i**4.
i*(i - 1)*(i + 1)**2/10
Suppose 44*s - 5*s**4 - 14*s**4 + 19*s**3 - 8 + 49*s**3 - 84*s**2 - s**4 = 0. What is s?
2/5, 1
Let b(k) = -k**5 - 4*k**4 - 5*k**3 + k**2 - 3*k + 3. Let i(r) = -r**5 - 4*r**4 - 5*r**3 + 2*r**2 - 4*r + 4. Let g(z) = 4*b(z) - 3*i(z). Factor g(a).
-a**2*(a + 1)**2*(a + 2)
Let p(u) = -3*u + 24. Let x be p(7). Let o(q) be the first derivative of -1/2*q**x + 2 - 1/10*q**5 - 3/8*q**4 + 0*q - 1/4*q**2. Let o(z) = 0. What is z?
-1, 0
Let d = -339/5 - -2041/30. Let c(z) be the second derivative of 2*z + d*z**4 + 0 + 2/15*z**3 + 0*z**2. Factor c(y).
2*y*(7*y + 2)/5
Let w = -5 + 7. Let m(k) = -10*k - 50. Let f be m(-5). Determine s so that w*s**3 + 4/9*s**2 + 0 + f*s + 14/9*s**4 = 0.
-1, -2/7, 0
Let d(p) be the first derivative of 4*p**3/3 + 10*p**2 - 24*p - 54. Factor d(i).
4*(i - 1)*(i + 6)
Let r(f) be the third derivative of -f**6/600 - f**5/150 - f**4/120 + 4*f**2. Factor r(l).
-l*(l + 1)**2/5
Let d(j) be the second derivative of j**5/40 + j**4/12 + j**3/12 + 4*j. Suppose d(o) = 0. Calculate o.
-1, 0
Suppose -w + 4*n - 7*n + 11 = 0, 2*w - 5*n = -11. Let r(k) be the second derivative of 1/20*k**4 - k + 0 + 1/5*k**3 + 3/10*k**w. Suppose r(a) = 0. What is a?
-1
Factor 2/5*j + 2/5*j**5 - 2/5*j**4 - 2/5 - 4/5*j**3 + 4/5*j**2.
2*(j - 1)**3*(j + 1)**2/5
Let p(b) = -3*b**3 - 2*b**2 + b - 2. Let l(y) = 6*y - 16*y**3 + 4*y - 10*y**2 - 3*y - y - 11. Let x(d) = 2*l(d) - 11*p(d). Find s, given that x(s) = 0.
-1, 0
Suppose -3*l - 4*x = 21, -7 = -l + 4*x + 2. Let o = 2 - l. Factor 3*t**2 - 2*t + 2*t**4 + 0*t + 2*t**3 - o*t**2.
2*t*(t - 1)*(t + 1)**2
Let x be -1 + (-22)/(-6) + -2. Factor 2/3 - x*c**2 + 2/3*c - 2/3*c**3.
-2*(c - 1)*(c + 1)**2/3
Let a(p) = p**2 + 4*p. Let y(u) = 2*u**2 + 9*u. Suppose -5*v + h = -3*h + 18, 9 = -2*v + h. Let d(b) = v*y(b) + 13*a(b). Solve d(o) = 0 for o.
0, 2
Let z(d) be the third derivative of -2/3*d**3 + 0*d - 2/15*d**5 + d**2 + 3/4*d**4 + 0. Factor z(f).
-2*(f - 2)*(4*f - 1)
Let c = 1 - -3. What is x in -6*x + 23*x**c - 21*x**2 - 4*x**5 - 9*x**3 - 2*x**4 + 5*x**5 + 14*x**5 = 0?
-1, -2/5, 0, 1
Let q(k) be the first derivative of k**6/30 - k**5/25 - k**4/10 + 2*k**3/15 + k**2/10 - k/5 + 5. Factor q(a).
(a - 1)**3*(a + 1)**2/5
Let w be (-4)/(-12)*6/1. Factor -4*u + 3 - 3 - 2*u**w.
-2*u*(u + 2)
Factor 3*d**2 - 8*d**3 + 5*d**3 - 3*d**2.
-3*d**3
Determine v so that 28/3*v**3 + 16/3 + 80/3*v + 92/3*v**2 = 0.
-2, -1, -2/7
Let w be 6*(2 - (-5)/(-3)). Let t be (1 - 6)/(w + -3). Factor -1/5*h**3 + 1/5*h**t - 1/5*h**2 + 1/5*h**4 + 0*h + 0.
h**2*(h - 1)*(h + 1)**2/5
What is v in 0 - 4/7*v - 2/7*v**3 - 6/7*v**2 = 0?
-2, -1, 0
Let m(q) = -q - 1. Let b be m(5). Let y(h) = -9*h**3 - 9*h**2 - 9*h - 3. Let n(f) = f**3. Let i(v) = b*n(v) - y(v). Suppose i(p) = 0. What is p?
-1
Let v(g) = 3*g - 24. Let n be v(8). Suppose n - 1/2*l**3 + l**2 - 1/2*l = 0. What is l?
0, 1
Let v be 2/4*2 + 65. Let t = 135/2 - v. Determine u, given that t*u + 0*u**2 - 1/2*u**3 + 1 = 0.
-1, 2
Solve 4/11*l + 2/11*l**2 + 2/11 = 0 for l.
-1
Find m such that -2*m**3 + 37*m**2 + 2*m - 35*m**2 - 4 + 2 = 0.
-1, 1
Let p(y) be the second derivative of 1/21*y**7 - 1/6*y**4 + 0*y**2 - 1/5*y**6 + 0*y**3 + 0 + 3/10*y**5 + 2*y. Factor p(t).
2*t**2*(t - 1)**3
Let r(k) = k**3 - 5*k**2 + 5*k - 2. Let o be r(4). Let i be (18/(-4))/(-3)*o. Factor -2*a - 3*a - a + 2*a**i - 4.
2*(a - 2)*(a + 1)**2
Let n(z) = -3*z**2 + 3. Let t(i) = -4*i**2 - i + 3. Let o(k) = -5*n(k) + 4*t(k). Factor o(f).
-(f