*z**3 + 4. Let c be r(10). What is h in -2/5*h**2 - 2/5*h**3 + 0*h + 2/5*h**4 + 0 + 2/5*h**c = 0?
-1, 0, 1
Let l(b) = -2*b**2 - 33*b - 16. Let g be l(-16). Let j(k) be the third derivative of g - 1/21*k**3 + 0*k**4 + 0*k + 1/210*k**5 - 2*k**2. Factor j(y).
2*(y - 1)*(y + 1)/7
Let d(h) be the third derivative of -h**5/360 + h**4/144 + h**3/18 - 9*h**2. Suppose d(c) = 0. Calculate c.
-1, 2
Let n(q) = -12*q**3 + 12*q**2 + 12*q - 3. Let v(l) = 13*l**3 - 12*l**2 - 12*l + 4. Let z(w) = 4*n(w) + 3*v(w). Factor z(i).
-3*i*(i - 2)*(3*i + 2)
What is k in -4/9*k**2 - 2/9*k**3 + 2/3*k**5 + 8/9*k**4 + 0 + 0*k = 0?
-1, 0, 2/3
Let w(b) be the second derivative of -b**7/1260 - b**6/360 + 2*b**4/3 - 9*b. Let m(k) be the third derivative of w(k). Determine p so that m(p) = 0.
-1, 0
Let v(j) = j**2 + 6*j - 5. Let y be v(-7). Factor -h + y*h**2 + h + 4 - 4*h - 2.
2*(h - 1)**2
Let o(p) = -p**2 - 4*p + 3. Let h be o(-4). Let v(w) be the first derivative of 1 - 2/21*w**h + 2/7*w + 4/7*w**2 - 2/7*w**4. Factor v(q).
-2*(q - 1)*(q + 1)*(4*q + 1)/7
Let j = -163 + 655/4. Suppose j*g**2 + 3/4 + 3/2*g = 0. What is g?
-1
Let i(f) = -6*f - 6. Let s be i(-1). Let w(t) be the first derivative of s*t**3 - t**4 + 1/3*t**6 - 4 + 0*t + t**2 + 0*t**5. Let w(p) = 0. Calculate p.
-1, 0, 1
Suppose -2*d = d. Suppose 2*b - 4*b + 6 = d. What is u in 1/4*u + 3/4*u**b + u**2 + 0 = 0?
-1, -1/3, 0
Determine a so that 27/2*a**3 + 3*a + 3/2*a**5 + 15/2*a**4 + 21/2*a**2 + 0 = 0.
-2, -1, 0
Let p(v) be the third derivative of -v**8/20160 + v**7/5040 + v**6/360 + v**5/30 + 3*v**2. Let s(d) be the third derivative of p(d). What is x in s(x) = 0?
-1, 2
Let d = 163/2 + -80. Factor 3/4*k + d - 3/4*k**2.
-3*(k - 2)*(k + 1)/4
Find o, given that 12*o**2 + 3 - 5*o**3 - 3*o**2 + 9*o + 3*o**3 + 5*o**3 = 0.
-1
Solve -3*t**4 - 3*t**3 - 3*t - 2*t**2 - 7*t**2 - 6*t**3 = 0.
-1, 0
Factor 24*i**3 + 2*i - 17*i**4 + 3*i - 12*i**2 - 3*i**4 - 3*i + 6*i**5.
2*i*(i - 1)**3*(3*i - 1)
Let p(y) be the second derivative of -y**4/18 - y**3/3 - 2*y**2/3 + 18*y. Factor p(i).
-2*(i + 1)*(i + 2)/3
Let i(f) be the third derivative of f**7/1680 - f**5/240 - 2*f**3/3 - 4*f**2. Let k(s) be the first derivative of i(s). Factor k(x).
x*(x - 1)*(x + 1)/2
Let d(x) be the second derivative of -x**9/7560 + x**8/1120 - x**7/420 + x**6/360 + x**4/12 + 3*x. Let i(z) be the third derivative of d(z). Factor i(t).
-2*t*(t - 1)**3
Find m, given that -3/5*m**2 - 3/5*m + 0 = 0.
-1, 0
Let n(k) be the first derivative of 3 + 0*k - 1/3*k**3 - 1/2*k**2 + 1/5*k**5 + 1/4*k**4. Factor n(q).
q*(q - 1)*(q + 1)**2
Determine n so that -2*n**2 + 4 - 3*n + 1 - n - 7 = 0.
-1
What is c in 12*c + 4*c**3 - c**3 + 24 + 21*c**2 + 27*c + 3*c = 0?
-4, -2, -1
Let s = 11 + -10. Suppose 3*w = -3*z + 24, -w - s = -z - 3. Determine a so that -1/5*a - 1/5 + 1/5*a**2 + 1/5*a**z = 0.
-1, 1
Let y(r) be the second derivative of -r**5/60 - r**4/48 + r**3/12 + r**2/2 - r. Let f(u) be the first derivative of y(u). Find n such that f(n) = 0.
-1, 1/2
Suppose -4*r = 3*t + 7, -5*r = 3*t - t + 14. Factor -8*z**2 - z - 8*z - 2*z**t + 3*z - 4 - 4*z.
-2*(z + 1)**2*(z + 2)
Let t(i) = i**2 - 3*i - 5. Let j be t(4). Let x(u) = 1 - u - 2 + 2. Let p(b) = 4*b**2 + 8. Let f(m) = j*p(m) + 6*x(m). Suppose f(c) = 0. What is c?
-1, -1/2
Let p(m) = -m**3 - 10*m**2 - m - 7. Suppose 53 = -5*r + 2*l + l, 5*l - 15 = r. Let y be p(r). Solve 0 + 1/3*x + 1/3*x**y + 2/3*x**2 = 0.
-1, 0
Let d(h) be the third derivative of -h**7/70 + h**6/20 + 9*h**2. Factor d(g).
-3*g**3*(g - 2)
Factor 16*t**2 + 17*t**3 + 14*t**4 - 2*t**3 - 8*t + 23*t**3.
2*t*(t + 1)*(t + 2)*(7*t - 2)
Let d(n) = 3*n**2 + 87*n - 123. Let q(o) = o**2 + 22*o - 31. Let t(l) = -4*d(l) + 15*q(l). Factor t(m).
3*(m - 3)**2
Let u = 4 - 2. Suppose 0*t = t - 2. Factor h + t*h**2 - h**u + h.
h*(h + 2)
Suppose 4*s - 6 + 2 = 0. Let n(z) = 6*z**2 - 6. Let c(l) = l**2 - 1. Let r(h) = s*n(h) - 8*c(h). Suppose r(y) = 0. Calculate y.
-1, 1
Let q(w) = w**4 - w**2 + w - 1. Let r(u) = 5*u**4 - 4*u**3 - 9*u**2 + 6*u - 6. Let h(x) = 6*q(x) - r(x). Factor h(y).
y**2*(y + 1)*(y + 3)
Let n(y) be the first derivative of 3*y**5/5 + 3*y**4/4 - y**3 - 3*y**2/2 + 5. Suppose n(q) = 0. Calculate q.
-1, 0, 1
Let m(w) be the third derivative of 5*w**6/156 - 5*w**5/78 - w**4/39 + 4*w**3/39 - 12*w**2. Suppose m(u) = 0. What is u?
-2/5, 2/5, 1
Factor 7*w**2 + 16*w**2 - w**4 - w**3 + w - 22*w**2.
-w*(w - 1)*(w + 1)**2
Suppose 0 = -3*t + 3*q, 6*q = -2*t + 7*q. Factor 2/9*m**3 + 0 + 4/9*m**2 + t*m.
2*m**2*(m + 2)/9
Suppose 8*m = 3*m + 15. Solve -10/7*y + 18/7*y**2 + 4/7*y**4 - 2*y**m + 2/7 = 0 for y.
1/2, 1
Let m(y) be the third derivative of y**5/60 + y**4/12 - 2*y**2. Factor m(j).
j*(j + 2)
Factor -1 + 5*n**2 - 4*n**2 + 93*n - 93*n.
(n - 1)*(n + 1)
Let v(o) be the third derivative of o**6/240 - o**5/60 - o**4/48 + o**3/6 - 42*o**2. Determine g so that v(g) = 0.
-1, 1, 2
Let q be (-5 - -1 - -3)*0. Let j(n) be the second derivative of 0*n**3 + 0*n**2 + 3*n + q - 1/6*n**4. What is r in j(r) = 0?
0
Suppose -6*z + 11 + 1 = 0. Let v = 76/7 + -74/7. Determine d, given that 0*d + 0*d**z + 0 - v*d**3 = 0.
0
Let t = -198 + 198. Let z(b) be the third derivative of -4*b**2 + 1/21*b**7 + 7/10*b**5 + 11/12*b**4 + 0*b + 17/60*b**6 + 2/3*b**3 + t. Solve z(g) = 0 for g.
-1, -2/5
Factor 6/13*p**2 + 2/13 - 6/13*p - 2/13*p**3.
-2*(p - 1)**3/13
Let c(y) be the third derivative of -y**5/20 - y**4/8 + y**3 - 9*y**2. What is x in c(x) = 0?
-2, 1
Let j(s) = -7*s**3 - 5*s**2 - s - 3. Let w(i) = -1. Let q(k) = -8*k**3 - 6*k**2 - 2*k. Let d(n) = -q(n) - 4*w(n). Let h(l) = 3*d(l) + 4*j(l). Factor h(g).
-2*g*(g + 1)*(2*g - 1)
What is y in 8/15*y**5 + 20/3*y**2 - 26/15*y**4 - 2/3*y**3 - 88/15*y + 16/15 = 0?
-2, 1/4, 1, 2
Let l(g) be the first derivative of g**4/42 - 4*g**3/21 + 4*g**2/7 - 2*g - 2. Let y(o) be the first derivative of l(o). Factor y(x).
2*(x - 2)**2/7
Suppose -69 = 4*f - 21. Let d be -2 + -7*4/f. Factor 0 - 1/3*u**4 + 0*u**2 + 0*u + d*u**3.
-u**3*(u - 1)/3
Let h(r) be the second derivative of r**6/15 - r**4/6 - 7*r. Factor h(b).
2*b**2*(b - 1)*(b + 1)
Suppose b + 0*b - 4*r + 12 = 0, -12 = 3*b - 4*r. Suppose m**3 + m**2 + 1/3*m + b + 1/3*m**4 = 0. What is m?
-1, 0
Let s = -34 + 21. Let b be -6*(-2 + s/(-7)). Factor b*c**3 + 4/7 - 6/7*c - 4/7*c**2.
2*(c - 1)*(c + 1)*(3*c - 2)/7
Let n(m) be the second derivative of m**5/60 - m**4/24 - 2*m**2 + 3*m. Let v(r) be the first derivative of n(r). Find h, given that v(h) = 0.
0, 1
Let -8/11*m**2 + 0 + 2/11*m + 8/11*m**3 = 0. Calculate m.
0, 1/2
Let a(b) = -b**3 + 6*b**2 - 4*b - 2. Let h be a(5). Suppose -3*z = 2*z - n - h, 9 = -3*z - 3*n. Factor 4/11*k + 0 + 6/11*k**2 - 2/11*k**4 + z*k**3.
-2*k*(k - 2)*(k + 1)**2/11
Let m = -37/2 + 223/12. Let p(c) be the first derivative of 0*c - m*c**4 + 1/6*c**2 + 0*c**3 - 2. Factor p(j).
-j*(j - 1)*(j + 1)/3
Let h(u) = 15*u**2 + 13*u - 15. Let g(l) = 7*l**2 + 6*l - 7. Let q(v) = 13*g(v) - 6*h(v). Solve q(a) = 0 for a.
-1, 1
Let b(a) be the first derivative of -1/4*a**2 - 6 - 1/6*a**3 + 0*a. Find x such that b(x) = 0.
-1, 0
Let z(n) be the first derivative of -n**4/26 - 14*n**3/39 - 16*n**2/13 - 24*n/13 - 2. Factor z(w).
-2*(w + 2)**2*(w + 3)/13
Let z(d) = 3*d**3 - 10*d**2 + 2*d + 3. Let m be z(3). Let v(h) be the first derivative of 1 + m*h**2 + 1/3*h**3 + 0*h. Determine n, given that v(n) = 0.
0
Let d(g) be the third derivative of -g**5/20 + 9*g**4/8 - 4*g**3 + 16*g**2. Factor d(f).
-3*(f - 8)*(f - 1)
Let g(k) = 2 - 1 - k - k + 0*k**2 + 5*k**2. Suppose 0 = -9*h + 4*h + 55. Let y(f) = 14*f**2 - 6*f + 3. Let x(o) = h*g(o) - 4*y(o). Factor x(c).
-(c - 1)**2
Let w(a) be the third derivative of -1/36*a**4 + 5*a**2 + 0*a + 1/180*a**6 - 1/90*a**5 + 0 + 1/9*a**3. Factor w(b).
2*(b - 1)**2*(b + 1)/3
Suppose 3 - 2 = -u, 4*u = 3*o - 10. Let p = -31 - -52. Suppose -k**o + p - 21 + k = 0. What is k?
0, 1
Let n(t) be the third derivative of t**7/420 - t**6/180 - t**5/30 + t**3/3 - 4*t**2. Let x(v) be the first derivative of n(v). Factor x(o).
2*o*(o - 2)*(o + 1)
Let g(c) be the first derivative of 15*c**4/2 + 4*c**3/3 - 15*c**2 - 4*c + 24. Factor g(z).
2*(z - 1)*(z + 1)*(15*z + 2)
Factor -10/11*j**2 - 2/11*j**5 + 0 + 6/11*j**3 + 4/11*j + 2/11*j**4.
-2*j*(j - 1)**3*(j + 2)/11
Suppose -2*j = -196 + 190. Let f(l) be the second der