 + 2)/5
Let f(n) = -9*n**2 + 82*n - 56. Let j(d) = -3*d**2 + 27*d - 18. Let v(i) = -6*f(i) + 17*j(i). What is t in v(t) = 0?
1, 10
Let d = 18 + -48. Let l = -28 - d. Factor 0 + 1/4*y**l + 1/4*y.
y*(y + 1)/4
Factor u**3 + 15*u + 9*u**2 - 7 - 13*u**2 - 5*u**2.
(u - 7)*(u - 1)**2
Let f(g) = -2 + 0 + 1. Suppose 5*u + 5*a = 0, -5*u + 3*a = -4*u + 12. Let p(q) = q**2 + 2*q - 1. Let w(l) = u*p(l) + 6*f(l). Find o such that w(o) = 0.
-1
Suppose -472*l = -477*l. Factor l - 3/2*t + 3/2*t**3 + 3/2*t**4 - 3/2*t**2.
3*t*(t - 1)*(t + 1)**2/2
Factor 4*f**2 - 5*f + 10*f + 0*f**2 + f**2.
5*f*(f + 1)
Let s(w) be the first derivative of w**6/120 + 3*w**5/40 + w**4/4 + 8*w**3/3 + 3. Let t(q) be the third derivative of s(q). Determine p, given that t(p) = 0.
-2, -1
Determine i, given that 5/6*i**2 + 2/3 + 2*i = 0.
-2, -2/5
Let c = -30 + 34. Let d(m) = -m**3 - 7*m**2 - 5*m + 8. Let a be d(-6). Factor -c*n + n**3 + a*n**3 + 10*n - 3*n**2 - 6*n**2.
3*n*(n - 2)*(n - 1)
Let h be 20/6*12/10. Determine y, given that -y**h - 2*y**3 + 0*y**4 + 2*y**2 - 3*y**2 = 0.
-1, 0
Factor 3/2*b**3 + 1 - 3/2*b - 1/2*b**2 - 1/2*b**4.
-(b - 2)*(b - 1)**2*(b + 1)/2
Let x(f) be the first derivative of 18*f**6 - 756*f**5/5 + 414*f**4 - 1192*f**3/3 + 174*f**2 - 36*f + 8. Find h, given that x(h) = 0.
1/3, 3
Suppose 3 = 3*y - 6. Let w(c) = c**3 + 7*c**2 - 8*c + 2. Let m be w(-8). Factor -t + 6*t**m + 7*t**2 + 13*t + t**4 + 4 + 6*t**y + 0*t**3.
(t + 1)**2*(t + 2)**2
Let h(w) = -2*w**3 + 6*w**2 - 5*w + 5. Let i be h(5). Let l be i/(-18) - 2/(-6). What is m in m + 2*m - l*m**2 + 4*m**2 = 0?
0, 1
Let d = -7202/23 - -4734451/15111. Let p = d - -3/73. Factor 0 - p*r - 2/9*r**2.
-2*r*(r + 1)/9
Let k(b) = 4*b**5 + 12*b**4 - b**3 - 44*b**2 - 48*b - 13. Let o(t) = -4*t**5 - 12*t**4 + 44*t**2 + 48*t + 12. Let g(v) = -4*k(v) - 3*o(v). Solve g(s) = 0 for s.
-2, -1, 2
Let t(l) be the first derivative of l**4/18 - l - 5. Let h(d) be the first derivative of t(d). What is b in h(b) = 0?
0
Let u(m) be the second derivative of m**7/105 - m**6/30 + m**5/30 + m**2/2 - 2*m. Let w(q) be the first derivative of u(q). Factor w(c).
2*c**2*(c - 1)**2
Let d(t) be the second derivative of -t**4/27 + 2*t**3/27 + 4*t**2/3 + 30*t. Solve d(s) = 0.
-2, 3
Let i(k) be the first derivative of -3*k**5/10 - 15*k**4/8 - 3*k**3 - 31. Find b such that i(b) = 0.
-3, -2, 0
Let j = 6 + -4. Let t = -49 - -49. Factor y - j*y + t*y - y**2.
-y*(y + 1)
Let h = 33 + -97/3. Let d be ((-7)/(-21))/((-1)/(-2)). Factor h*u + 0 + d*u**2.
2*u*(u + 1)/3
Let a(q) be the second derivative of 49*q**4/6 + 14*q**3/3 + q**2 + 5*q. Factor a(v).
2*(7*v + 1)**2
Let s(o) be the third derivative of o**8/84 + 3*o**7/70 + o**6/60 - 2*o**5/15 - o**4/4 - o**3/6 - 7*o**2. Suppose s(c) = 0. What is c?
-1, -1/4, 1
Let o(u) be the third derivative of -u**7/105 - u**6/20 - u**5/30 + u**4/4 + 2*u**3/3 - 6*u**2. Solve o(j) = 0 for j.
-2, -1, 1
Determine c so that 4/5*c + 2/5*c**4 - 4/5*c**3 + 0*c**2 - 2/5 = 0.
-1, 1
Suppose 3 = -d - 4. Let l = -4 - d. Factor 1/2*j**l + 0 + 1/4*j**2 + 1/4*j**4 + 0*j.
j**2*(j + 1)**2/4
Let f(w) = 2*w**2. Let t be f(1). Factor -4*m - m**3 + 11*m - 6*m + t*m**2 - 2.
-(m - 2)*(m - 1)*(m + 1)
Let w(t) = -t**3 + 2*t**2 - 5*t - 4. Let z(c) = -3*c**3 + 5*c**2 - 11*c - 9. Let v(i) = -5*w(i) + 2*z(i). Factor v(k).
-(k - 2)*(k + 1)**2
Let r be (-4)/(-5)*(-25)/(-10). Factor 3*k + 4 + 0*k**2 + 0*k + r*k**2 + 3*k.
2*(k + 1)*(k + 2)
Suppose j + 30 = 7*j. Let t(p) be the third derivative of -1/420*p**7 + 0*p**6 + 0 + 0*p**4 + 0*p**j + 0*p - p**2 + 0*p**3. Factor t(f).
-f**4/2
Let l = 66 - 64. Let j(t) be the second derivative of 0 - 4*t + 1/9*t**3 + 1/36*t**4 - 1/2*t**l. Factor j(r).
(r - 1)*(r + 3)/3
Factor -16 - 114*p**2 + 48*p**2 + 4*p**3 + 46*p**2 + 32*p.
4*(p - 2)**2*(p - 1)
Suppose -4*x + 0*x = -64. Suppose -2*t = -3*n + 14 - 2, -5*t = 4*n - x. Solve t*j**3 + 2*j**3 - 3*j + j = 0 for j.
-1, 0, 1
Solve 1/2 - 1/4*u - 1/4*u**2 = 0 for u.
-2, 1
Let u = -6 + 11. Let k be 4/12 + (-10)/(-6). What is y in 4*y**2 - y**5 + 3*y**u - k*y + 0*y**2 - 4*y**4 = 0?
-1, 0, 1
Let f(z) be the third derivative of z**8/9240 - z**6/1980 - z**3/3 + 2*z**2. Let s(w) be the first derivative of f(w). Let s(o) = 0. Calculate o.
-1, 0, 1
Let q(l) be the first derivative of -l**5/10 - 2*l**4/3 - 5*l**3/3 - 2*l**2 + l + 3. Let s(t) be the first derivative of q(t). Factor s(o).
-2*(o + 1)**2*(o + 2)
Let u(y) be the second derivative of y**5/360 - y**4/24 + y**3/4 + 3*y**2 + 3*y. Let r(k) be the first derivative of u(k). Factor r(g).
(g - 3)**2/6
Let k(d) = -d**2 - 18*d - 29. Let q be k(-16). Let r(n) be the second derivative of 0 + 1/3*n**3 + 1/2*n**2 + 1/12*n**4 + q*n. Factor r(p).
(p + 1)**2
Let x(p) be the first derivative of -7 + 2/15*p**3 + 2/5*p - 2/5*p**2. Factor x(d).
2*(d - 1)**2/5
Suppose 0 = 3*q - 5*c - 94 + 36, -3*c = -q + 18. Let t be ((-2)/q)/(3/(-9)). Factor 2/7*h**2 - 2/7*h**4 - 2/7*h**3 + 0 + t*h.
-2*h*(h - 1)*(h + 1)**2/7
Let x(k) be the first derivative of 4*k - 3*k**2 + 2/3*k**3 + 2. Factor x(m).
2*(m - 2)*(m - 1)
Let k(o) be the third derivative of o**5/150 - o**4/20 + 2*o**3/15 - 15*o**2. Factor k(d).
2*(d - 2)*(d - 1)/5
Let d be (2/(-3))/((-11)/165). Suppose v = d - 5. Factor 13/4*t**4 + 9/2*t**2 + 1/4 - 11/2*t**3 - 7/4*t - 3/4*t**v.
-(t - 1)**4*(3*t - 1)/4
What is p in -34*p**2 - 22*p - 46*p**2 - 5*p**5 + 20*p**4 + 65*p + 37*p = 0?
-2, 0, 2
Solve -2 + 44*m - 43*m + 2 + m**2 = 0 for m.
-1, 0
Let o(m) = m**2 + 1. Let q be o(2). Let x be (q + -4)*4/14. Factor 2/7*u - 2/7*u**2 - x*u**3 + 2/7.
-2*(u - 1)*(u + 1)**2/7
Let z(n) = 2*n**5 + 2*n**4 + 2. Let b(w) = -10*w**5 - 11*w**4 - w**3 - 11. Let l(v) = -2*b(v) - 11*z(v). Factor l(q).
-2*q**3*(q - 1)*(q + 1)
Let d(w) be the third derivative of -w**7/2100 - w**6/300 - w**5/150 + w**3/6 + w**2. Let b(m) be the first derivative of d(m). Factor b(c).
-2*c*(c + 1)*(c + 2)/5
Factor 0*z**4 + 9/5*z - 12/5*z**3 + 6/5 - 6/5*z**2 + 3/5*z**5.
3*(z - 2)*(z - 1)*(z + 1)**3/5
Let v(b) be the second derivative of 1/18*b**3 + 1/30*b**5 + 1/180*b**6 + 0*b**2 + 0 - 4*b + 5/72*b**4. Factor v(w).
w*(w + 1)**2*(w + 2)/6
Suppose -3*z - 4*d + 32 = 0, -2*z = -0*z - 3*d - 10. Let l be 28/z - 2 - 1. Factor 0 + l*c + 1/2*c**4 - 1/2*c**3 - 1/2*c**2.
c*(c - 1)**2*(c + 1)/2
Let l = -261/5 - -53. Determine z, given that 2/5 + 2/5*z**2 + l*z = 0.
-1
What is p in -2*p**4 - 4 - 12 + 28*p**3 + 4*p**5 - 32*p - 4*p**2 + 22*p**4 + 0*p**5 = 0?
-2, -1, 1
Factor -2/3*j + 2/3*j**2 + 1/6*j**3 + 0 - 1/6*j**4.
-j*(j - 2)*(j - 1)*(j + 2)/6
Let o = 1576/3 + -525. Factor o - 1/3*d**3 - d + d**2.
-(d - 1)**3/3
Let k(o) be the third derivative of o**8/1680 + o**7/840 - o**3/6 - 4*o**2. Let p(h) be the first derivative of k(h). Determine a so that p(a) = 0.
-1, 0
Let i(q) = -5*q - 2. Suppose 2*u + 1 + 3 = 0. Let d be i(u). Factor -g**2 + d + 8*g + 0*g**2 + 3*g**2.
2*(g + 2)**2
Factor -7*q**3 + 11*q**2 - q**3 - 3*q**4 + 3*q**3 - 3*q + 0*q.
-q*(q - 1)*(q + 3)*(3*q - 1)
Let x(s) be the third derivative of -1/840*s**8 + 0*s + 3*s**2 + 0 + 0*s**5 + 0*s**6 + 0*s**4 - 1/525*s**7 + 0*s**3. Factor x(d).
-2*d**4*(d + 1)/5
Let a(m) be the first derivative of m**7/105 + m**6/180 + m**3/3 + 2. Let f(o) be the third derivative of a(o). Factor f(r).
2*r**2*(4*r + 1)
Suppose 3*o + 75 = -5*r, 0*r + 3*r = -5*o - 61. Let i be ((-3)/r)/((-5)/(-8)). Determine f so that 0 + 4/5*f**4 + 2/5*f - i*f**5 + 0*f**3 - 4/5*f**2 = 0.
-1, 0, 1
Let c(q) be the third derivative of -q**6/320 + 7*q**5/160 - 5*q**4/32 + 20*q**2. Factor c(i).
-3*i*(i - 5)*(i - 2)/8
Let m(t) be the first derivative of -t**6/9 + 2*t**5/5 - t**4/3 + 19. Factor m(i).
-2*i**3*(i - 2)*(i - 1)/3
Let p(v) = -6*v**4 - 2*v**3 - 4*v - 4. Let d(f) = 5*f**4 + f**3 + 3*f + 3. Let y(z) = -4*d(z) - 3*p(z). Factor y(n).
-2*n**3*(n - 1)
Let i(t) be the second derivative of 0 + 3*t + 1/4*t**4 - 2*t**3 + 9/2*t**2. Factor i(n).
3*(n - 3)*(n - 1)
Let s(i) = 3*i**3 + 3*i - 6. Let u(r) = 4*r**3 + r**2 + 2*r - 5. Let v(t) = -5*s(t) + 6*u(t). Let v(c) = 0. What is c?
-1, 0, 1/3
Find m, given that 2/7*m**2 - 4/7*m**3 + 0*m + 2/7*m**4 + 0 = 0.
0, 1
Let g(d) be the first derivative of 2*d**6/3 + 4*d**5/5 - 5. Factor g(u).
4*u**4*(u + 1)
Let c(v) be the first derivative of -v**7/147 - v**6/105 + 3*v**5/70 + 5*v**4/42 + 2*v**3/21 - 2*v + 3. Let n