*x**3 + 3*x**2 - 20*x**2.
4*x**2*(x - 2)
Suppose 0 = 5*s + 3 - 18. Find n such that -s*n**2 - 12*n**3 + 14*n**3 - n**2 = 0.
0, 2
Suppose -17*m - 35*m = -37*m. Factor m + 1/6*o**2 + 1/6*o.
o*(o + 1)/6
Determine u so that 0 + 1/2*u**2 - 3/4*u + 1/4*u**3 = 0.
-3, 0, 1
Let a(h) be the first derivative of h**8/8400 + h**7/600 + h**6/120 + 3*h**5/200 + 3*h**3 + 24. Let v(n) be the third derivative of a(n). Factor v(g).
g*(g + 1)*(g + 3)**2/5
Let x = -14986 - -14986. Factor 16/7*u - 4/7*u**2 + x.
-4*u*(u - 4)/7
Let x(w) = 17*w + 206. Let z be x(-12). Let j(p) be the first derivative of -3/4*p**4 + 0*p**3 + 2 + 0*p + 3/2*p**z. Factor j(a).
-3*a*(a - 1)*(a + 1)
Let m(x) be the third derivative of 0*x**6 + 0*x**5 + 1/112*x**8 + 0*x**3 + 0*x**4 + 0*x + 0 - 14*x**2 + 1/210*x**7. Let m(l) = 0. Calculate l.
-1/3, 0
Let q(x) = 11*x**3 - 52*x**2 + 71*x + 16. Let m = -30 - -24. Let h(v) = 56*v**3 - 260*v**2 + 356*v + 79. Let o(c) = m*h(c) + 33*q(c). Factor o(a).
3*(a - 3)**2*(9*a + 2)
What is r in 15*r**2 - 12*r**3 - 65*r**2 - 5*r**3 - 3*r + 2*r**3 + 30 - 2*r = 0?
-3, -1, 2/3
Let t = 19176 - 38351/2. Factor 0 + 0*x + 1/2*x**5 + 3/2*x**3 + 3/2*x**4 + t*x**2.
x**2*(x + 1)**3/2
Let i be (-1 - -2)*(5 - 3). Let h(k) be the third derivative of 0*k**3 - i*k**2 + 0*k + 1/5*k**5 + 2/105*k**7 + 0 + 1/6*k**4 + 1/10*k**6. Factor h(f).
4*f*(f + 1)**3
Factor 2/7*n**3 + 20/7*n**2 + 18/7*n + 0.
2*n*(n + 1)*(n + 9)/7
Let c be 15/10*(-13 - -14). Factor c*i**2 + 1 - 5/2*i.
(i - 1)*(3*i - 2)/2
Let g = 849 + -843. Let r(a) be the third derivative of 3/140*a**5 + 1/140*a**g - 4*a**2 + 0*a - 3/56*a**4 + 0 - 1/7*a**3. Factor r(q).
3*(q - 1)*(q + 2)*(2*q + 1)/7
Let m(s) = -88*s**3 - 1176*s**2 - 1636*s + 476. Let t(h) = 10*h**3 + 131*h**2 + 182*h - 53. Let a(i) = -3*m(i) - 28*t(i). Let a(d) = 0. Calculate d.
-7, -2, 1/4
Let g be (-2)/13 - 1642/(-26). Let n be (-2)/2 - (-77)/g. Factor 4/9*x**2 + 2/9*x - 4/9 - n*x**3.
-2*(x - 2)*(x - 1)*(x + 1)/9
Let h(x) = -x**2 - 2*x - 6. Let w = -5 + 10. Let c(k) = w*k - k**2 - 5 - 2*k - 5*k. Let z(r) = -5*c(r) + 4*h(r). Suppose z(d) = 0. Calculate d.
-1
Let t(q) = -q**5 + q**4 - 1. Let n(r) = 9*r**5 + 33*r**4 + 39*r**3 - 25*r**2 - 44*r - 8. Let m(f) = -n(f) - 4*t(f). Find s such that m(s) = 0.
-6, -1, -2/5, 1
Suppose -6*k**3 + 2296*k**4 - 2299*k**4 + 78*k**3 + 36*k**3 = 0. Calculate k.
0, 36
Suppose 0 = 2*o + 2*o. Suppose -3*d - 5*x = -19, d + 1 = 4*x - 4. Factor 2/3*c + o - 2/3*c**d + 0*c**2.
-2*c*(c - 1)*(c + 1)/3
Let g(w) be the second derivative of -w**6/150 + w**5/50 - w**3/15 + w**2/10 - 2*w - 11. Let g(v) = 0. What is v?
-1, 1
Let c(g) be the second derivative of -8/15*g**6 + 0 + 29/3*g**4 + 4*g**2 - 2*g - 22/5*g**5 - 26/3*g**3 + 16/21*g**7. Suppose c(u) = 0. Calculate u.
-2, 1/2, 1
Let f be (36/(-12) - -15) + -10. Find d, given that 0 + 1/2*d**4 + 1/2*d**3 + 1/6*d**5 + 1/6*d**f + 0*d = 0.
-1, 0
Factor -99/5 + 20*f - 1/5*f**2.
-(f - 99)*(f - 1)/5
Suppose 5*j - 4 = -14. Let t = 4 + j. Factor -q**t + 2 + 8*q - 9*q + 2*q.
-(q - 2)*(q + 1)
Let o(b) be the third derivative of -b**7/1260 + b**5/180 - 2*b**3/3 + b**2. Let s(d) be the first derivative of o(d). Factor s(v).
-2*v*(v - 1)*(v + 1)/3
Factor 25*v**3 - 128*v - 17*v**3 - 512 - 18*v**4 + 100*v**2 + 2*v**5 + 64*v**2 + 2*v**4 - 4*v**2.
2*(v - 4)**3*(v + 2)**2
Find t, given that t**3 + 6*t + 70*t**2 + 6*t + 47*t + 4*t**3 + 6*t = 0.
-13, -1, 0
Let y = -2263 - -2267. Factor 2/9*f**2 + 18 - y*f.
2*(f - 9)**2/9
Let d(s) = -s**3 + s + 12. Let y be d(0). Suppose -4*x - 3*t - y = 0, 5*t = 5*x - 18 - 2. Solve -4*i + x*i**2 - 5*i - 6 - i**2 - 2*i**2 = 0 for i.
-2, -1
Suppose 115*m**2 - 73*m**5 + 63*m**5 + 222*m**4 + 293*m**3 - 7*m**4 + 47*m**3 = 0. What is m?
-1, -1/2, 0, 23
Suppose -68 = 24*w - 58*w. Factor 4/5*f**3 + 0*f**w - 4/5*f + 0.
4*f*(f - 1)*(f + 1)/5
Let j(u) be the first derivative of u**4/44 + 5*u**3/11 + 63*u**2/22 + 49*u/11 + 61. Factor j(g).
(g + 1)*(g + 7)**2/11
Let w = -2 + 7. Let a be w - 6/(2 - 0). Factor g**3 - g + g**a - g**4 + 2*g**3 - 2*g**3.
-g*(g - 1)**2*(g + 1)
Let i(j) = 38*j**3 - 60*j**2 + 12*j. Let x(z) = z**3 - 2*z**2 - z. Let s(l) = i(l) - 6*x(l). Let s(q) = 0. What is q?
0, 3/4
Factor 3/5*h**4 + 0 - 21/5*h**2 + 0*h**3 + 18/5*h.
3*h*(h - 2)*(h - 1)*(h + 3)/5
Let a(f) = -f**2 + 10*f - 20. Let o be a(4). Find b, given that -28*b**o + 8*b**4 - 6*b - 27*b**3 + 5*b**4 - 7*b**2 - 3*b**5 - 14*b**2 = 0.
-2, -1, 0
Let u(z) = -4 + 7*z**2 - 3*z**2 + 2*z + 4 + 2. Let w be u(-1). Find a, given that 6*a - 2*a**w + 3*a**5 - a**4 + 0*a + 36*a**3 + 3*a**2 - 45*a**3 = 0.
-1, 0, 1, 2
Let -12/11*j - 14/11 + 2/11*j**2 = 0. Calculate j.
-1, 7
Let s be (-156)/(-13)*(-1 - 4). Let z be (-15)/(-4) - 15/s. Factor -20*q**z - 10*q - 25*q**2 + 19*q**3 + q**3 + 25*q**2 + 4 + 6*q**5.
2*(q - 1)**4*(3*q + 2)
Let f(u) = 2*u**3 + 73*u**2 + 636*u - 41. Let o be f(-22). Suppose 0 - 1/6*m**4 + 0*m + 1/3*m**2 + 1/6*m**o = 0. Calculate m.
-1, 0, 2
Let m(v) be the second derivative of 3*v**5/40 - 7*v**4/8 + 5*v**3/2 - 237*v. What is f in m(f) = 0?
0, 2, 5
Let f = 580/7 + -2313/28. Factor b - 1 + 3/4*b**2 - f*b**4 - 1/2*b**3.
-(b - 1)**2*(b + 2)**2/4
Suppose 6/5*d**3 - 2/3*d**4 + 34/15*d**2 + 0 + 2/5*d = 0. Calculate d.
-1, -1/5, 0, 3
Let z(v) = -31*v - 5. Let y be z(-1). Let d be 15/6 - y/20. Factor 9/5*c + 0*c**2 - 3/5*c**3 - d.
-3*(c - 1)**2*(c + 2)/5
Let u(d) be the first derivative of d**5/150 - d**4/20 - 5*d**2 + 14. Let b(k) be the second derivative of u(k). Factor b(o).
2*o*(o - 3)/5
Let w(b) be the third derivative of -11*b**2 + 1/4*b**3 + 1/240*b**6 - 5/48*b**4 + 1/120*b**5 + 0*b + 0. Find x such that w(x) = 0.
-3, 1
Let r be (-2)/(-3)*(-153)/(-2652)*4. Find z, given that r*z**3 - 20/13*z**2 - 46/13*z - 24/13 = 0.
-1, 12
Let x(m) be the third derivative of m**8/112 - m**6/20 + m**4/8 - 251*m**2. Factor x(h).
3*h*(h - 1)**2*(h + 1)**2
Find f, given that 13*f**4 - 12*f**4 - 2*f**2 + 2 - 1 = 0.
-1, 1
Let a(z) = 12*z**2 + 114*z - 1078. Let u(v) = 15*v**2 + 114*v - 1077. Let f(p) = 6*a(p) - 5*u(p). Determine r so that f(r) = 0.
19
Let z(x) be the second derivative of 5*x**4/3 + 26*x**3 - 16*x**2 - 53*x. Factor z(h).
4*(h + 8)*(5*h - 1)
Suppose -r + 21 = -5*k, r = -2*r + k - 7. Let s be 36/(-30)*2/r. Find d, given that 0 + 3/5*d**3 - s*d + 0*d**2 = 0.
-1, 0, 1
Let m = 464/4113 - -50/457. Let -16/9*t - m*t**2 - 14/9 = 0. Calculate t.
-7, -1
Let k = -21738 + 21743. Find x such that 1/3*x**k + 25/3*x**2 + 4/3 + 19/3*x**3 + 7/3*x**4 + 16/3*x = 0.
-2, -1
Factor 13778/3 + 2/3*q**2 + 332/3*q.
2*(q + 83)**2/3
Let k(z) = -3*z**4 - 8*z**3 + 3*z**2 + 8*z. Let v(f) = 80*f**4 + 215*f**3 - 80*f**2 - 215*f. Let s(y) = 55*k(y) + 2*v(y). Factor s(h).
-5*h*(h - 1)*(h + 1)*(h + 2)
Let x = -116 + 116. Suppose -2*p - 3*h = 2, -3*p - 2*h - h = x. Factor 2/3*i + 1/6*i**p + 2/3.
(i + 2)**2/6
Let i(u) be the third derivative of -u**5/120 - u**4/48 + u**3/2 - 172*u**2 - 3*u. Solve i(h) = 0.
-3, 2
Let h(l) be the third derivative of -l**8/504 - 22*l**7/315 - 46*l**6/45 - 8*l**5 - 36*l**4 - 96*l**3 - 13*l**2 - 1. Solve h(i) = 0.
-6, -2
Let x(h) = 3*h**2 - 9*h + 12. Let b(t) = -4*t**2 + 10*t - 15. Let g(q) = 8*b(q) + 10*x(q). Factor g(u).
-2*u*(u + 5)
Let m(f) be the second derivative of -f**8/2240 - f**7/210 + f**6/240 + f**5/10 - 3*f**4/4 - 38*f. Let q(b) be the third derivative of m(b). Factor q(x).
-3*(x - 1)*(x + 1)*(x + 4)
Let z(m) be the third derivative of -m**7/1890 - m**6/1080 + 7*m**5/540 + m**4/216 - m**3/9 + 159*m**2. What is h in z(h) = 0?
-3, -1, 1, 2
Let y = 2482 + -2480. Let o(x) be the first derivative of 1/9*x**y + 1/6*x**4 + 9 + 0*x - 2/45*x**5 - 2/9*x**3. Factor o(t).
-2*t*(t - 1)**3/9
Let b(h) = 3485*h**3 - 42630*h**2 - 25200*h - 3695. Let i(v) = -249*v**3 + 3045*v**2 + 1800*v + 264. Let p(x) = -4*b(x) - 55*i(x). Find g, given that p(g) = 0.
-2/7, 13
Suppose 5/2*k**2 + 3125/2 + 125*k = 0. Calculate k.
-25
Let v(n) be the third derivative of n**5/135 + n**4/108 - n**3/27 + 8*n**2. Determine u so that v(u) = 0.
-1, 1/2
Let c(m) be the first derivative of -m**8/14280 + 10*m**3 - 10. Let i(y) be the third derivative of c(y). Solve i(o) = 0.
0
Let z be (2 + 1)*(171/27 + 1 + -6). Factor -1/2*y**3 + 1/10*y**z + 7/10*y**2 + 0 - 3/10*y.
y*(y - 3)*(y - 1)**2/10
Suppose -2*b - 21 = -5*b. Let d = b - 4. Determine v so that 8*v