*(k + 2)**3
Let y be ((-1)/4)/(-1) + 686/40. Let r = y + -81/5. Find b such that -2/5*b**3 - 8/5*b**2 + 0 - r*b = 0.
-3, -1, 0
Suppose 288 = -0*c + 9*c. Let g = -157/5 + c. Suppose 3/5*n**5 + 0*n + 3/5*n**2 - g*n**4 + 0 - 3/5*n**3 = 0. Calculate n.
-1, 0, 1
Factor -1/4*s**2 + 19/2 + 17/4*s.
-(s - 19)*(s + 2)/4
Suppose o = w - 19, 2*w - 20 = 3*o + 35. Let j = 21 + o. Factor 18 + 2*z**2 - 12*z + j*z**2 - 4*z**2.
2*(z - 3)**2
Let o(a) = -8*a**3 + 60*a**2 - 594*a + 2000. Let h(p) = p**3 - p. Let r(t) = t**2 + 11*t + 24. Let z be r(-6). Let g(w) = z*h(w) - o(w). Factor g(q).
2*(q - 10)**3
Let o(f) = -f**2 + 4*f + 5. Suppose n - 16 = -3*n. Let v be o(n). Let 2*k**2 - 2*k + v*k - 5*k**2 - 6*k**3 = 0. What is k?
-1, 0, 1/2
Let u(y) be the second derivative of -1/110*y**5 - 12*y + 7/66*y**4 - 16/11*y**2 + 0 - 8/33*y**3. Factor u(q).
-2*(q - 4)**2*(q + 1)/11
Suppose -5*y - 3*c = -75, 0*c + 4*c - 75 = -5*y. Solve -y*l**3 + 1 - 6 + 5*l**2 + 32*l - 17*l + 0 = 0.
-1, 1/3, 1
Determine v so that -22 - 3*v**3 - 8*v - 23 + 13*v**2 + 33 = 0.
-2/3, 2, 3
Let m(g) be the first derivative of -g**7/1260 + 13*g**6/540 - 4*g**5/15 + g**4 + 8*g**3/3 + 18. Let v(n) be the third derivative of m(n). Factor v(w).
-2*(w - 6)**2*(w - 1)/3
Let f be (4/(-3))/(4/(-6)). Let j = -144 + 150. What is d in -j + 5 + 2*d**2 + 3*d**3 - d**f + d - 4*d**3 = 0?
-1, 1
Suppose -2*s - 3*z = s - 144, -3*z = -s + 36. Let x = s - 45. Find y, given that -1/5*y**2 + x*y + 1/5 = 0.
-1, 1
Let l(f) = -4*f**3 + 17*f - 8. Let h(i) = -i**2 - 24 + 52*i - 17*i**3 + 5*i**3 + i**2. Let b(t) = -5*h(t) + 16*l(t). Let b(n) = 0. What is n?
-2, 1
Solve -159*q**2 + 74*q**2 + 15*q**3 + 20*q**4 - 46*q - 14*q + 20 = 0 for q.
-2, -1, 1/4, 2
Let h(u) be the second derivative of -u**7/630 - u**6/60 - u**5/15 + u**4/3 - 5*u. Let y(v) be the third derivative of h(v). Factor y(m).
-4*(m + 1)*(m + 2)
Let n be (-9 - -6) + 11/66*21. Factor 0 - 1/4*t**4 + 1/4*t**5 + 1/4*t**2 - 3/4*t**3 + n*t.
t*(t - 2)*(t - 1)*(t + 1)**2/4
Let g = -28491 + 85493/3. Factor 16*j**4 + g*j**5 + 8/3*j**2 + 0 + 0*j + 12*j**3.
4*j**2*(j + 1)**2*(5*j + 2)/3
Let b be 3/(-12)*(-12)/(-9)*-6. Factor -3*u**2 - 86 + u**4 + b*u + 86.
u*(u - 1)**2*(u + 2)
Factor 0 + c**4 - 7/2*c + 13/2*c**3 - 4*c**2.
c*(c - 1)*(c + 7)*(2*c + 1)/2
Let s(z) = z**2 - z + 5. Let j be 8*(-1)/2 - -4. Let u be s(j). Factor -d**4 + d**5 - 8*d**2 + 6*d**3 + d**u - 8*d + 9*d**4.
2*d*(d - 1)*(d + 1)*(d + 2)**2
Let j be (18 + -9)*(12/9 + -1). Factor -j*k**3 + 6*k**2 - k**5 - 2*k**2 - 4*k**4 + 3*k**5 + k**3.
2*k**2*(k - 2)*(k - 1)*(k + 1)
Let t be (-1)/(1/(5/(-4))*60). Let x(q) be the second derivative of 0 - 1/8*q**3 + 0*q**2 - t*q**4 + q. Factor x(r).
-r*(r + 3)/4
Let a(q) be the first derivative of q**3/7 - 69*q**2/14 + 68. Factor a(u).
3*u*(u - 23)/7
Let m(i) be the second derivative of -4/57*i**3 + 0 + 1/114*i**4 + 3/19*i**2 + 17*i. Solve m(u) = 0 for u.
1, 3
Let a(n) be the first derivative of 0*n**4 + 0*n + 1/12*n**3 + n**2 - 1/120*n**5 + 7. Let x(z) be the second derivative of a(z). Let x(w) = 0. What is w?
-1, 1
Let h be -6*(2 - 75/6). Let i be 27/h + 19/(-77). Factor 0*j - i*j**4 + 4/11*j**3 - 2/11*j**2 + 0.
-2*j**2*(j - 1)**2/11
Let j(g) be the first derivative of g**5 + 485/3*g**3 - 660*g**2 + 55/2*g**4 - 10 + 720*g. Factor j(u).
5*(u - 1)**2*(u + 12)**2
Let j = 264 + -261. Suppose -2*q - 16 = -3*x + 2*q, 0 = x - q - 5. Factor -z**x - 2*z**2 - 4*z**j + z**4 - 2*z**4.
-2*z**2*(z + 1)**2
Let c(n) be the second derivative of -n**6/40 + 9*n**5/80 - n**4/8 + 3*n - 9. Determine h so that c(h) = 0.
0, 1, 2
Let g(y) be the second derivative of y**6/105 - 2*y**5/35 - 2*y**4/7 + 64*y**3/21 - 64*y**2/7 + y - 25. Factor g(r).
2*(r - 4)*(r - 2)**2*(r + 4)/7
Let w = -2167/14 - -155. Let l(d) be the first derivative of -1/7*d**2 + 9 - 8/21*d**3 + 4/7*d + w*d**4. Factor l(o).
2*(o - 1)**2*(3*o + 2)/7
Determine c, given that 202 - 280*c - 152 + 71*c**2 + 238 + 2*c**3 + 0*c**2 - 7*c**2 = 0.
-36, 2
Let z(a) = 2*a**4 + 22*a**3 - 2*a**2 - 22*a. Let i(q) = 3*q**4 + 43*q**3 - 3*q**2 - 43*q. Let k(l) = -6*i(l) + 11*z(l). Factor k(j).
4*j*(j - 4)*(j - 1)*(j + 1)
Let t be (-18)/12 - 276/(-8). Let z = 0 + 0. Let -32*d**3 + t*d**3 + z*d**2 - 2*d**2 = 0. What is d?
0, 2
Let s = -3 - -5. Let p be 0 + 0 + 0 - (9 - 11). Factor 6*y**2 - p*y + s*y - 3*y**2 - 3*y**3 - 3*y**4 + 3*y.
-3*y*(y - 1)*(y + 1)**2
Suppose -2*h = -2*t + 12, 3 = -2*h + 1. Let n(i) be the third derivative of 0 + 1/270*i**t + 0*i**4 - 1/945*i**7 + 0*i**3 + 0*i + 0*i**6 + 9*i**2. Factor n(g).
-2*g**2*(g - 1)*(g + 1)/9
Let h(x) be the second derivative of 61/96*x**4 + 1/16*x**2 + 14*x - 7/24*x**3 + 3/20*x**6 + 0 - 21/40*x**5. Solve h(l) = 0 for l.
1/6, 1
Let a = 127 + -114. Suppose -l + 4*j - 19 = -4*l, 2*j = 3*l - a. Find s, given that 26/19*s**4 - 2*s**3 + 0 + 22/19*s**2 - 6/19*s**l - 4/19*s = 0.
0, 1/3, 1, 2
Let z = 32 + -31. Factor -16*t + 4*t + z - 1 - 3*t**2.
-3*t*(t + 4)
Let h(m) be the first derivative of -m**6/10 - 6*m**5/5 - 24*m**4/5 - 38*m**3/5 - 9*m**2/2 - 463. Let h(q) = 0. Calculate q.
-5, -3, -1, 0
Let g(k) be the third derivative of k**10/10080 - k**9/3780 + k**8/6720 - k**4/8 + 22*k**2. Let f(q) be the second derivative of g(q). Factor f(r).
r**3*(r - 1)*(3*r - 1)
Let s(c) be the second derivative of 2*c**7/21 - 8*c**6/15 - 2*c**5/5 + 4*c**4 + 6*c**3 + 6*c + 13. Factor s(j).
4*j*(j - 3)**2*(j + 1)**2
Let x(g) be the first derivative of g**7/21 + 4*g**6/15 + 3*g**5/5 + 2*g**4/3 + g**3/3 - 16*g - 6. Let l(i) be the first derivative of x(i). Factor l(t).
2*t*(t + 1)**4
Let z(h) be the first derivative of 3*h**5/25 - 9*h**4/10 + 12*h**3/5 - 12*h**2/5 - 51. Factor z(w).
3*w*(w - 2)**3/5
Let b(y) be the second derivative of 5*y**4/16 - 595*y**3/12 + 395*y**2/8 - 27*y - 7. Solve b(c) = 0 for c.
1/3, 79
Let h(n) be the second derivative of -n**4/2 - 357*n**3/4 - 267*n**2/4 - 13*n. Factor h(w).
-3*(w + 89)*(4*w + 1)/2
Let h be 18/10*-20*(-4)/136. Factor -h + 12/17*l - 2/17*l**2.
-2*(l - 3)**2/17
Suppose -95*q - 20 = -105*q. Let b(r) be the first derivative of -3/2*r**6 - 1 - 6*r + 33/2*r**q + 6*r**4 + 12/5*r**5 - 18*r**3. What is s in b(s) = 0?
-2, 1/3, 1
Let n(b) be the third derivative of 0*b + 1/9*b**4 - 1/210*b**7 - 1/180*b**6 + 1/15*b**5 + 0*b**3 + 0 - b**2. Factor n(m).
-m*(m - 2)*(m + 2)*(3*m + 2)/3
Let t(c) be the first derivative of 2/15*c**6 + 4*c**2 - 1/5*c**5 + c - c**4 - 8 + 2/3*c**3. Let f(y) be the first derivative of t(y). Factor f(i).
4*(i - 2)*(i - 1)*(i + 1)**2
Let n be (18/48)/(-6*(-225)/12). Let c(h) be the third derivative of -5*h**2 + 1/60*h**4 + 0*h**3 + 0*h**5 + 0*h - n*h**6 + 0. Suppose c(w) = 0. What is w?
-1, 0, 1
Factor 8*a**2 - 2*a**3 + 6*a**4 + 5*a**4 - 2*a**4 - 10*a**4.
-a**2*(a - 2)*(a + 4)
Suppose 73 = 8*s - 7. Let 5*t**3 + s*t**4 + 15*t - 11*t - 4*t + 5*t**5 = 0. What is t?
-1, 0
Solve -14/13*p**3 - 20/13 + 54/13*p + 60/13*p**2 = 0.
-1, 2/7, 5
Let i(o) be the second derivative of o**8/3080 - 3*o**7/1540 + o**6/660 - 2*o**4/3 + 24*o. Let q(m) be the third derivative of i(m). Factor q(v).
6*v*(v - 2)*(4*v - 1)/11
Let a = 10014/695 - 6/695. Factor -16/5 + a*h + 54/5*h**3 - 108/5*h**2.
2*(3*h - 2)**3/5
Suppose -55*j = -57*j + 6. Factor 39*x**j - 6*x - 5*x**4 + 7*x**3 - 11*x**3 - 29*x + 45*x**2 - 40.
-5*(x - 8)*(x - 1)*(x + 1)**2
Let j be ((-2)/4)/((-1429)/(-96) - 15). Determine m, given that 18/11*m**3 - j - 60/11*m**2 - 2/11*m**4 + 8*m = 0.
2, 3
Let o = -207 - -204. Let u be o - (204/20)/(-3). Factor 4/5*s**4 - 4/5*s**2 + 2/5*s**5 + 0*s**3 - u*s + 0.
2*s*(s - 1)*(s + 1)**3/5
Let y(u) be the second derivative of u**7/7560 + u**6/216 - 11*u**5/360 + 25*u**4/12 + 27*u. Let q(t) be the third derivative of y(t). Factor q(m).
(m - 1)*(m + 11)/3
Determine n, given that -20*n**3 - 5/2*n - 3/2*n**5 + 0 - 13*n**2 - 11*n**4 = 0.
-5, -1, -1/3, 0
Let c(a) = 2*a**2 - 78*a. Let q(m) = 5*m**2 - 231*m. Let f(i) = -8*c(i) + 3*q(i). Let f(g) = 0. Calculate g.
-69, 0
Let x(a) = -12*a**3 + 38*a**2 - 72*a + 24. Let c(t) = t + 1. Let o(r) = r**3 - 4*r - 6. Let i(p) = 5*c(p) + o(p). Let h(d) = -6*i(d) - x(d). Factor h(w).
2*(w - 3)**2*(3*w - 1)
Let k(s) be the third derivative of 1/525*s**7 + 4*s**2 + 0*s**4 + 0 + 1/300*s**6 + 0*s**5 + 0*s**3 + 0*s. Solve k(g) = 0 for g.
-1, 0
Suppose -2 - 1 = -3*c - 3*a, 3*c = 4*a - 4.