 - 9)**2/5
Let x(w) = -w**3 - w**2 + w. Let k(g) = g. Let b(l) = 2*l**3 + 11*l**2 + 22*l + 6. Let d(j) = -b(j) + 6*k(j). Let z(t) = d(t) + x(t). Factor z(f).
-3*(f + 1)**2*(f + 2)
Factor 2*n**4 - 145*n + 145*n - 14*n**3 + 24*n**2.
2*n**2*(n - 4)*(n - 3)
Let x(j) be the third derivative of 0*j**7 + 1/1848*j**8 + 1/132*j**4 - 1/330*j**6 + 0 - 21*j**2 + 0*j**5 + 0*j**3 + 0*j. Let x(o) = 0. What is o?
-1, 0, 1
Let s(j) be the second derivative of -j**4/6 - 77*j**3/3 - 218*j + 1. Find o such that s(o) = 0.
-77, 0
Let z be 0 - (1 + -3 - (17 - 15)). Let v(f) = 4*f**2 + 45*f + 55. Let t(s) = 2*s**2 + 22*s + 28. Let m(g) = z*v(g) - 7*t(g). Factor m(r).
2*(r + 1)*(r + 12)
Let o(q) be the first derivative of -q**5/240 - q**4/48 - q**3/24 - 11*q**2/2 - 9. Let w(p) be the second derivative of o(p). Factor w(f).
-(f + 1)**2/4
Let g(a) = -2*a**2 - 2*a - 15. Let d(p) = 2*p**2 + 6*p + 29. Let x(y) = -3*d(y) - 5*g(y). Determine w, given that x(w) = 0.
-1, 3
Let s(w) = -w**3 - 8*w**2 - 19*w - 40. Let l be s(-6). Suppose 0*u + 0 - 1/5*u**l = 0. What is u?
0
Let r(c) be the first derivative of 40*c - 5/3*c**3 + 5*c**2 - 48. Determine s so that r(s) = 0.
-2, 4
Suppose 4*m - 4 = 2*m. Find c such that -11 + 8*c**2 + m*c**3 + 6*c + 4*c + 15 = 0.
-2, -1
Let d(h) = h**3 + 12*h**2 + 5*h - 148. Let f be d(-10). Solve 4/3*m + 0 - m**3 + 0*m**f - 1/3*m**4 = 0 for m.
-2, 0, 1
Let a be (-2*1)/((4 - 3) + -2). Factor 4*y**4 - 7*y**a - 7 - y**4 + 10 + y**2.
3*(y - 1)**2*(y + 1)**2
Determine u, given that 0*u**2 + 0*u + 0 + 3/2*u**5 + 3*u**4 - 9/2*u**3 = 0.
-3, 0, 1
Let q(v) be the first derivative of 2*v**5 + 26*v**4 + 160*v**3/3 - 336*v**2 - 288*v + 45. Let q(r) = 0. What is r?
-6, -2/5, 2
Factor 4/5*z**3 - 12*z + 32/5 + 24/5*z**2.
4*(z - 1)**2*(z + 8)/5
Let x(o) be the second derivative of o**7/525 - o**6/150 + o**5/120 - o**4/240 + 11*o**2/2 + 25*o. Let k(v) be the first derivative of x(v). Solve k(t) = 0.
0, 1/2, 1
Let d be 1/(1 + (-75)/76). Solve -189*k**3 + 46*k - d + 74 - 240*k**2 - 99*k**3 = 0.
-1, 1/12
Let c(d) be the third derivative of -2 + 1/420*d**6 + 0*d + 20*d**2 + 125/21*d**3 + 1/14*d**5 + 25/28*d**4. Factor c(t).
2*(t + 5)**3/7
Let y(f) = -f**3 - 15*f**2 - 13*f - 20. Let b be y(-14). Let i be 6/27 + b/(-9). Factor 24*h**2 + 7 + 9 + 31*h + 5*h + i*h**3.
4*(h + 1)**2*(h + 4)
What is i in -256*i**2 - 784*i - 4*i**4 + 1372 - 248*i**2 + 1067*i**3 - 1147*i**3 = 0?
-7, 1
Determine l, given that 0 - 2*l**5 + 7/2*l**3 - l**2 + 5/2*l**4 + 0*l = 0.
-1, 0, 1/4, 2
Let j(z) = z**3 - 3*z**2 - 2*z - 2. Let d be j(4). Suppose 10 = d*p - p. Factor 12*f + 2*f**2 - 3*f**p - 3*f**2 - 8.
-4*(f - 2)*(f - 1)
Let z = -5/11 + 37/33. Let l be (13/26)/(9/30). Find t such that 2/3 + 5/3*t - l*t**3 - z*t**2 = 0.
-1, -2/5, 1
Let a(t) be the third derivative of -t**5/420 + 5*t**4/56 + 17*t**3/21 + 112*t**2. Determine h, given that a(h) = 0.
-2, 17
Let w(p) be the third derivative of -p**5/150 + 4*p**4/15 - 64*p**3/15 + p**2 + 27*p. Factor w(n).
-2*(n - 8)**2/5
Let l = -232 + 9281/40. Let u(z) be the third derivative of -12*z**2 + l*z**5 + 1/8*z**4 + 0*z**3 + 0*z + 0. Determine y so that u(y) = 0.
-2, 0
Suppose -54 = 4*f - 7*f - k, 4*f - 72 = k. Let p = 20 - f. Suppose 0*d**p + 0 + 2/11*d - 2/11*d**3 = 0. What is d?
-1, 0, 1
Let a be 1/2*150/(-15). Let s(q) = 3*q**3 - 5*q**2 + q + 1. Let i(d) = -3*d**3 + 5*d**2 - d - 1. Let u(c) = a*s(c) - 4*i(c). Factor u(x).
-(x - 1)**2*(3*x + 1)
Let i(p) = p**3 + 5*p**2 + 17*p + 20. Let c be i(-6). Let t = c - -120. Factor 2/9*s - 10/9*s**3 - 2/3*s**4 + 0 - 2/9*s**t.
-2*s*(s + 1)**2*(3*s - 1)/9
Let d be (319/63 - 5)*(-3)/(-8). Let f(u) be the second derivative of d*u**4 - 1/70*u**5 + 0*u**2 - 1/105*u**6 + 0 - 2*u + 1/21*u**3. Factor f(l).
-2*l*(l - 1)*(l + 1)**2/7
Suppose -3*d + 10 = -u, -10*d = -13*d + 4*u + 22. Determine b so that 2/7*b**4 - 4/7*b + 0 - 6/7*b**d + 0*b**3 = 0.
-1, 0, 2
Suppose 0 = -205*t + 180*t. Let f(b) be the first derivative of -8/15*b**5 + t*b**2 + 0*b + 1/6*b**6 - 4 + 1/4*b**4 + 2/9*b**3. Suppose f(g) = 0. Calculate g.
-1/3, 0, 1, 2
Let d(s) be the first derivative of 5*s**4/4 - 5*s**3 + 5*s**2 + 256. Suppose d(b) = 0. What is b?
0, 1, 2
Let k = -2380/9 - -2383/9. Solve k*i**3 + 0 - 1/6*i**4 - 1/6*i**2 + 0*i = 0.
0, 1
Factor -7 + 1/2*a**2 + 13/2*a.
(a - 1)*(a + 14)/2
Suppose 2 = -65*o + 66*o. Let i be 6/12*(o/4 - 0). Factor -1 - i*t**4 - 13/4*t**2 - 3/2*t**3 - 3*t.
-(t + 1)**2*(t + 2)**2/4
Factor 5*u**2 - 138222 + 45897 - 9*u**2 + 1648*u - 77419.
-4*(u - 206)**2
Let r(d) be the first derivative of 2*d**6/3 + 16*d**5/5 + 3*d**4 + 62. Let r(s) = 0. What is s?
-3, -1, 0
Suppose -5*a - 7 = 5*n - 57, 4*n - 5 = 3*a. Let k = n + -2. Factor -u**2 - k*u - 6*u - 4 + 5*u.
-(u + 2)**2
Let n(h) be the third derivative of -h**6/120 + h**5/30 + h**4/24 - h**3/3 - 73*h**2. Factor n(k).
-(k - 2)*(k - 1)*(k + 1)
Let w be 0/((3 + -1)*-1). Suppose w = p + 1 - 6. Determine m, given that -6 - 4*m**p + 6 = 0.
0
Suppose -j = -5*j + b + 5, 2*j + 4*b - 16 = 0. Find i, given that 5*i**j - 8*i + 4*i**2 + 5*i**2 = 0.
0, 4/7
Let x(p) = -p**3 - p**2 + 1. Let i be x(-2). Suppose -2*s - 2*c + 10 = 0, -4*s + i*c - 10*c = -23. Determine q so that 4/5*q**s + 12/5*q + 8/5 = 0.
-2, -1
Suppose 3*i - 3*c = 24, i + i + c = 25. Let y(t) = 4*t - 21. Let v be y(i). Factor 32 - 41*m**2 + v*m**2 + 20*m**2 - 16*m.
2*(m - 4)**2
Suppose 5*t + 4 = 6*t. Suppose 0 = 3*v + 4*u - 13, -t*v + 3 = -3*u - 6. Factor v + 4 + 224*o**3 + 49*o**4 + 1 + 100*o + 4 + 263*o**2.
(o + 1)*(o + 3)*(7*o + 2)**2
Solve -3/7*j**2 - 87/7*j + 90/7 = 0.
-30, 1
Let x(k) be the first derivative of -16/3*k**2 - 128/3*k + 2/15*k**5 - 11/6*k**4 - 4 + 8*k**3. What is i in x(i) = 0?
-1, 4
Let i(h) = -h + 3. Let n be i(5). Let t(q) = -q. Let o(w) = -2*w**3 - 8*w**2 - 4*w. Let d(f) = n*t(f) - o(f). Solve d(a) = 0 for a.
-3, -1, 0
Let j(v) be the first derivative of -5/6*v**6 + 0*v**4 - 7 + 0*v**3 - v**5 + 0*v + 0*v**2. Find a, given that j(a) = 0.
-1, 0
Let z(b) be the third derivative of -b**5/60 - b**4/24 - b**2 - 54*b. What is j in z(j) = 0?
-1, 0
Factor 5/3*g**3 + 1/3*g + 2/3*g**4 + 0 + 4/3*g**2.
g*(g + 1)**2*(2*g + 1)/3
Let h(d) be the third derivative of d**6/360 - 19*d**5/360 + d**4/48 + 3*d**3/2 - 14*d**2 + 15*d. Factor h(u).
(u - 9)*(u - 2)*(2*u + 3)/6
Let p(q) = 2*q - 5. Let o be p(10). Let t = o + -12. Factor -3*n**2 - 3*n**t + 3*n + 4*n + 0*n - n.
-3*n*(n - 1)*(n + 2)
Let j(b) be the first derivative of -15*b**4/4 + 20*b**3/3 - 5*b**2/2 - 29. Factor j(t).
-5*t*(t - 1)*(3*t - 1)
Let a(h) be the third derivative of 6*h**2 + 0*h**4 - 1/1848*h**8 + 0*h**3 + 0*h + 2/1155*h**7 - 1/660*h**6 + 0*h**5 + 0. Factor a(k).
-2*k**3*(k - 1)**2/11
Let z(o) = -2*o**4 + 4*o**3 - 2*o**2 + 2*o + 2. Let i = 22 + -24. Let f(y) = y**3 - y**2 + y + 1. Let g(t) = i*f(t) + z(t). Let g(p) = 0. Calculate p.
0, 1
Let f(c) = 6*c**2 + 6*c - 3. Let p(q) = -12*q**2 - 11*q + 5. Suppose -4*d = -7*d + 9. Let o(r) = d*p(r) + 5*f(r). Factor o(h).
-3*h*(2*h + 1)
Let g = -741 - -1257. Solve -8*h - 60*h + 62 + g + 2*h**2 = 0.
17
Let a(y) = -7*y**3 - y**2 + 5*y - 10. Let d(v) = 6*v**3 + v**2 - 4*v + 10. Let g(q) = -4*a(q) - 5*d(q). Let o(r) be the first derivative of g(r). Factor o(w).
-2*w*(3*w + 1)
Factor -4*t**5 + 6*t**3 - 206*t + 19*t**3 + 8*t**4 - 7*t**2 + 62*t - 41*t**2 + 19*t**3.
-4*t*(t - 3)**2*(t + 2)**2
Find o such that -32 - 8*o**5 - 3*o**3 + 5*o**5 - 57*o**2 + 18*o**4 + 9*o**2 + 33*o**3 - 99*o - 10 = 0.
-1, 2, 7
Let x = -63/4 - -16. Let v(b) = 104*b + 624. Let u be v(-6). Suppose u*s + x*s**3 + 0 - 1/4*s**4 + 0*s**2 = 0. Calculate s.
0, 1
Let t be 375/10 + 3 + -4. Let l = t - 36. Let l + 1/4*i**2 + 3/4*i = 0. What is i?
-2, -1
Let t(l) be the second derivative of -l**5/20 - l**4/4 + l**3/2 + 3*l**2/2 + 3*l. Let u(f) = 2*f**3 + 7*f**2 - 7*f - 7. Let g(z) = 5*t(z) + 2*u(z). Factor g(q).
-(q - 1)*(q + 1)**2
Factor 2 + 1/6*k**2 + 7/6*k.
(k + 3)*(k + 4)/6
Let r = 187288/343321 - 2/31211. Suppose -r*m**2 - 4/11*m - 2/11*m**3 + 0 = 0. What is m?
-2, -1, 0
Let t(w) be the third derivative of -w**7/42 + w**5/12 + 26*w**2. Suppose t(o) = 0. What is o?
-1, 0, 1
Let f = 123412 + -1114453/9. Let j = 417 + f. Factor 2/3*c**4 + 0*c + 2/9*c**3 - j*c**5 + 0*c**2 + 0.
-2*c**3*(c - 1)*(4*c + 1)/9
Let m = -232 - -234. Let f(s) be the third derivative o