
Let f = -51 - -54. Suppose -2 = -2*w - a - a, -2*w + 12 = -f*a. Factor -2/19*k**w + 4/19*k + 0 + 2/19*k**2.
-2*k*(k - 2)*(k + 1)/19
Let o(t) be the first derivative of -t**3/4 + 3*t**2/8 - 47. Factor o(x).
-3*x*(x - 1)/4
Let c(v) be the second derivative of -v**6/165 - v**5/11 - 6*v**4/11 - 18*v**3/11 - 27*v**2/11 + 123*v. What is h in c(h) = 0?
-3, -1
Suppose -13*p**3 + 22*p**3 - p + 30 - 4*p**2 - 2*p**2 + 0 - 8*p**3 = 0. What is p?
-2, 3, 5
Determine v so that 34/5*v**2 - 34/5*v - 14/5*v**3 + 12/5 + 2/5*v**4 = 0.
1, 2, 3
Factor 162/19*h**3 + 230/19*h + 18*h**2 + 50/19.
2*(h + 1)*(9*h + 5)**2/19
Let c be 1/(3/16*(-156)/(-39)). Factor 0 + 4/3*f**4 + 4/3*f**5 - c*f**2 + 0*f - 4/3*f**3.
4*f**2*(f - 1)*(f + 1)**2/3
Suppose 13 = h - 2*l + 5, -4 = -5*h - 2*l. Suppose -2*t = g + t, 0 = -3*g - h*t. Factor 3/7*j**2 - 1/7*j**3 - 2/7*j + g.
-j*(j - 2)*(j - 1)/7
Suppose 5*w = -2*g + 4, 3*g + 10 = 4*w - 7. Determine t so that 9*t**3 - 6*t**w + 22*t**2 + 12*t - 7*t**2 + 15*t**2 = 0.
-2, -2/3, 0
Let v be (-3)/(-12) + ((-200)/(-32))/25. Solve -v*h + 0 + 1/2*h**2 = 0 for h.
0, 1
Let p(f) be the first derivative of 5*f**3/6 - 85*f**2/4 - 45*f + 46. Factor p(o).
5*(o - 18)*(o + 1)/2
Let y be (-3)/(-3) + -7 + 1653/261. Suppose 0*s**3 - 1/6*s**5 - 1/3*s**2 + 0 + 1/6*s + y*s**4 = 0. Calculate s.
-1, 0, 1
Let d be 337920/43680 + (-8)/26. Factor -2/7*q**2 - 338/7 + d*q.
-2*(q - 13)**2/7
Let u(x) = x**2 + 26*x - 354. Let r be u(-36). Let k(q) be the third derivative of -1/72*q**4 + 0*q**3 + 1/360*q**r + 0*q**5 + 0 + 0*q - 12*q**2. Factor k(m).
m*(m - 1)*(m + 1)/3
Find n, given that -3*n**4 + 4*n**4 - 9*n**2 - 3*n**2 - 68*n**3 + 10*n**4 + 4*n**3 = 0.
-2/11, 0, 6
Let d be 0 + 24/14 + 14/49. Let y(r) be the second derivative of 0 + 1/8*r**d + 1/48*r**4 + 1/12*r**3 + r. Factor y(t).
(t + 1)**2/4
Let v(t) = 27 - 33 + 14*t - 23 - 51. Let j be v(6). Factor -g + g**3 - 1/2 + 1/2*g**j + 0*g**2.
(g - 1)*(g + 1)**3/2
Let f = -12112 - -12114. Factor -3/7*t**f - 48/7 - 24/7*t.
-3*(t + 4)**2/7
Factor 0 + 2/5*b**2 - 12/5*b + 2/5*b**3.
2*b*(b - 2)*(b + 3)/5
Determine m, given that 5/3*m**2 - 40/3*m - 100/3 = 0.
-2, 10
Let k = 2579 + -2579. Factor 2/3*s + k + 8/9*s**2 + 2/9*s**3.
2*s*(s + 1)*(s + 3)/9
Let w = 3 - -3. Suppose 2*c = 4*t - 14, 4*t - 19*c = -16*c + 13. Find j, given that 3*j**3 + 6*j**2 + 7*j - 5*j**3 - 5*j**3 - t*j**4 - w + 4 = 0.
-2, -1, 1/4, 1
Let i(o) = -16*o**2 - 279*o + 9519. Let g(c) = -74*c**2 - 1394*c + 47596. Let x(h) = -3*g(h) + 14*i(h). Factor x(y).
-2*(y - 69)**2
Suppose 0 = 3*r - 3*m + 12, 217*m + 4 = -5*r + 218*m. Determine c so that -8/7*c**4 + r*c**2 + 0*c + 0 + 2/7*c**5 + 8/7*c**3 = 0.
0, 2
Let w = -2444/5 + 483. Let j = w + 266/45. Factor -j*f**2 + 1/3*f - 2/9.
-(f - 2)*(f - 1)/9
Let c(t) be the first derivative of 8/3*t**2 - 2*t**3 - 1/15*t**5 - 18 + 2/3*t**4 - 5/3*t. Factor c(q).
-(q - 5)*(q - 1)**3/3
Suppose 3 = -4*s - 5*j + 44, -2*s - 4*j + 28 = 0. Factor 0 + 0*f + 0*f**2 + 8/3*f**s - 4/3*f**5 + 0*f**3.
-4*f**4*(f - 2)/3
Let d(g) be the second derivative of g**7/84 - g**6/10 + 11*g**5/40 - g**4/12 - g**3 + 2*g**2 - 2*g - 35. Let d(i) = 0. What is i?
-1, 1, 2
Let s(p) be the first derivative of 95/8*p**4 + 51/2*p**5 + 15/4*p**6 - 20*p**2 - 31 - 295/6*p**3 + 50*p. What is f in s(f) = 0?
-5, -1, 2/3
Let m be (7/3)/((1/27)/1). Let t be 2 + ((-33)/m - 12/9). Factor -t*k**4 + 0*k**2 + 0*k + 3/7*k**3 + 0.
-k**3*(k - 3)/7
Suppose 5*h + 0*a - 3*a - 13 = 0, h - 2*a + 3 = 0. Suppose 3*w = h*w + 5*y + 13, -3 = -3*w - 3*y. Suppose 11*p - 11 - 21*p + w*p + 5 + 2*p**2 = 0. What is p?
-1, 3
Let x(i) be the third derivative of -i**8/8960 + i**7/840 - i**6/240 + i**5/60 + 5*i**2. Let t(w) be the third derivative of x(w). Let t(s) = 0. What is s?
2/3, 2
Factor -39/7*y**3 + 24/7 - 132/7*y - 150/7*y**2.
-3*(y + 2)**2*(13*y - 2)/7
Let d = 28510/3 - 9502. Factor -d*g**4 - 4/3*g**2 + 0 + 0*g + 8/3*g**3.
-4*g**2*(g - 1)**2/3
Let b(q) be the third derivative of q**7/315 + 2*q**6/15 + 59*q**5/45 - 26*q**4/3 + 169*q**3/9 - 75*q**2 - 2. Find d such that b(d) = 0.
-13, 1
Let -10*z + 1/4*z**2 + 39/4 = 0. Calculate z.
1, 39
Let u(f) = -3*f**4 + 7*f**3 + 3*f**2 - 7*f + 5. Let v(a) = a**4 - 3*a**3 - a**2 + 3*a - 2. Let w(l) = 2*u(l) + 5*v(l). Determine p, given that w(p) = 0.
-1, 0, 1
Let f(x) be the first derivative of -7/6*x**3 + 8/5*x**5 - 4 - 1/4*x**2 + 0*x - x**4. Factor f(s).
s*(s - 1)*(4*s + 1)**2/2
Find g such that g**3 + 0*g**2 + 0 + 0*g + 1/4*g**5 + g**4 = 0.
-2, 0
Let g(x) be the first derivative of -4*x + 16/3*x**3 + 15 + 6*x**2. Factor g(b).
4*(b + 1)*(4*b - 1)
Let k(b) = -b**3 - 6*b**2 + 2. Let o = 8 + -14. Let p be k(o). Find j such that -1/3 + 2/3*j - 1/3*j**p = 0.
1
Solve 135*z**2 - 32319*z + 27831*z - 2128 - z**3 - 2496 = 0 for z.
-1, 68
Let i be (-4)/(-18) - (-1344)/(-216). Let o be (5/i)/(6/(192/(-40))). Suppose 2/3 - o*a**2 - 1/3*a**3 + 1/3*a = 0. Calculate a.
-2, -1, 1
Let t(l) be the third derivative of 6*l**2 + 0*l**3 - 1/24*l**6 + 0*l + 0 - 1/12*l**5 + 0*l**4. Find z, given that t(z) = 0.
-1, 0
Let c(o) be the first derivative of -2*o**3/15 - 23*o**2/5 - 84*o/5 - 574. Find p such that c(p) = 0.
-21, -2
Suppose -f + 3*n + 87 = 2*f, -2*f - n + 67 = 0. Let r be f/6 - 8/6. Factor -8*d**3 + 0*d**4 + 4*d**4 + 2*d**4 + 4*d**5 - 2*d**r.
4*d**3*(d - 1)*(d + 2)
Suppose -5*d + 48 = 4*j, 17*d - 20*d + 30 = 3*j. Factor -28/9 - 4/9*u**3 + 28/9*u**j + 4/9*u.
-4*(u - 7)*(u - 1)*(u + 1)/9
Let y = 13126/5 - 2622. Find a, given that 0 - 4/5*a**3 - 16/5*a - y*a**2 = 0.
-2, 0
Let w(q) be the third derivative of -11*q**7/42 - 3*q**6/8 + q**5/6 + 6*q**2. Determine b so that w(b) = 0.
-1, 0, 2/11
Let g(x) be the third derivative of -x**7/3780 - x**6/216 - x**5/30 + x**4/2 - 11*x**2. Let c(t) be the second derivative of g(t). Solve c(v) = 0.
-3, -2
Let l(n) be the first derivative of 3*n**2 + 3*n - 3/4*n**5 - 7/2*n**3 + 1/10*n**6 - 1 + 9/4*n**4. Let i(b) be the first derivative of l(b). Factor i(c).
3*(c - 2)*(c - 1)**3
Let a(f) be the first derivative of 2/9*f**3 - 1/3*f**2 + 0*f - 28. Factor a(z).
2*z*(z - 1)/3
Suppose -22*f - 1593 = -13*f. Let l = -529/3 - f. Factor -1/6*r**2 + l*r - 1/2.
-(r - 3)*(r - 1)/6
Let 5/3*y**3 + 4/3 - 7/3*y**2 - 8/3*y = 0. What is y?
-1, 2/5, 2
Let t(q) = 15*q - q**3 + 2 - 4 + 1 + 14*q**2 + 6. Let j be t(15). Suppose 12*w - 3*w**j + 6*w**4 - 6*w**2 + 0*w**5 - 9*w = 0. Calculate w.
-1, 0, 1
Let y(w) be the second derivative of -3/2*w**2 - 3/2*w**4 + 17/6*w**3 - 2/5*w**5 - 5*w + 0. Factor y(s).
-(s + 3)*(2*s - 1)*(4*s - 1)
Suppose 14 = y - 7. Let r = y + -19. Factor -4/3*h**r - 2/3*h + 0 - 2/3*h**3.
-2*h*(h + 1)**2/3
Let d(w) be the first derivative of -w**4/14 + w**2/7 - 226. Suppose d(m) = 0. Calculate m.
-1, 0, 1
Let r(i) be the second derivative of -1/60*i**5 - 1/3*i**2 + 11/18*i**3 + 0 - 43*i - 1/3*i**4 + 2/45*i**6. Find a, given that r(a) = 0.
-2, 1/4, 1
Let m(p) = -p**3 + p**2 + 22*p - 10. Let z be m(5). Let y(r) be the first derivative of -1/24*r**4 + 0*r + z*r**2 - 1/18*r**3 + 3. Factor y(u).
-u**2*(u + 1)/6
Suppose -22 = 3*f - 28. Let z be 3 + (-3 - -7)/f. Factor -2/7*c + 12/7*c**3 + 16/7*c**4 + 6/7*c**z + 0 + 0*c**2.
2*c*(c + 1)**3*(3*c - 1)/7
Suppose -5*y = -b - 25, 0*b - 3*b - 15 = 0. Factor 15 + 45*g**2 + 35*g - 3*g**3 + 5*g**y + 28*g**3 - 5.
5*(g + 1)**3*(g + 2)
Let k(r) = r**2 - r - 1. Let u = 33 + -35. Let i(l) = -9*l**2 + 11*l + 5. Let y(c) = u*i(c) - 14*k(c). Solve y(a) = 0 for a.
1
Let o(z) be the second derivative of -1/14*z**5 + 1/105*z**6 + 0 + 3/14*z**4 + 2/7*z**2 - 1/3*z**3 - 14*z. Factor o(a).
2*(a - 2)*(a - 1)**3/7
Let q(w) be the first derivative of -2*w**3/27 - 5*w**2/9 - 4*w/3 - 123. Suppose q(n) = 0. Calculate n.
-3, -2
Solve 104*o**2 - 4*o**4 + 0*o**4 - 96*o**3 + 8*o**4 + 34*o**5 - 16*o - 12 - 18*o**5 = 0.
-3, -1/4, 1
Find g, given that -68/3*g**3 + 4/3*g**4 + 84*g**2 - 144 - 36*g = 0.
-1, 3, 12
Factor 0 + 2*f**2 - 6*f + 2/3*f**4 + 10/3*f**3.
2*f*(f - 1)*(f + 3)**2/3
Find o such that -17*o**4 + 79*o**3 - 30*o**5 - 17*o**5 - 80*o - 47*o**2 + 48*o**5 + 64 = 0.
-1, 1, 8
Let f(t) = t**3 - 30*t**2 - 30*t - 28. Let r be f(31). Determine m so that 4/3*m**5 + 0 + 0*m - 7/3*m**4 + 1/3*m**2 + 2/3*m**r = 0.
-1/4, 0, 1
Let v(x) be the second derivative of -2*x**2 + 0 - 43*x + 4/3*x**4 + 2*x**3. Factor v(b).
4*(b + 1)*(4*b - 1)
F