u**4/4 + 20*u**3 + 114*u**2 + 1988*u + 1. Factor f(g).
3*(g + 2)*(g + 38)
Suppose -h - 4*m - 2 + 12 = 0, 4*h - 6 = m. Suppose 409 + 30*f - 382 - 5*f**2 + 8*f**h = 0. Calculate f.
-9, -1
Suppose 48/7*k**2 - 12/7*k**4 + 48/7*k + 0 + 0*k**3 - 3/7*k**5 = 0. Calculate k.
-2, 0, 2
Let u(h) be the second derivative of h + 9/2*h**2 - 13/2*h**3 + 0 + h**4. Find s, given that u(s) = 0.
1/4, 3
Let s(j) be the first derivative of -1/9*j**3 - 4/3*j - 2/3*j**2 + 60. Determine y so that s(y) = 0.
-2
Let l = 4149/15380 - 76/3845. Find f, given that 1/4*f**2 - 1/2*f + l = 0.
1
Let g(v) = -18*v**3 + 542*v**2 - 59*v - 28. Let c be g(30). Determine d, given that 0*d + 0 - d**4 - 8/5*d**3 - 4/5*d**c - 1/5*d**5 = 0.
-2, -1, 0
Let q(p) be the second derivative of -p**6/180 + 3*p**4/4 - 14*p**3/3 + p - 53. Let z(o) be the second derivative of q(o). Let z(g) = 0. What is g?
-3, 3
Let f(b) be the second derivative of b**4/8 - 135*b**3/2 - 408*b**2 - 2*b - 164. Factor f(j).
3*(j - 272)*(j + 2)/2
Let a(o) be the third derivative of o**8/112 - o**7/35 - 3*o**6/8 + 9*o**5/5 + 96*o**2 + 19*o. Solve a(p) = 0.
-4, 0, 3
Let r(v) be the first derivative of 0*v - 62 - 7/4*v**2 - 1/6*v**3. Suppose r(a) = 0. What is a?
-7, 0
Factor -1/7*q**2 - 407/7*q + 0 + 1/7*q**4 + 407/7*q**3.
q*(q - 1)*(q + 1)*(q + 407)/7
Factor -21/2*s**2 - 38*s + 48 + 1/2*s**3.
(s - 24)*(s - 1)*(s + 4)/2
Suppose -408 - 824*n - 526*n**2 + 372*n**3 + 3*n**4 + 349*n**3 - 833*n**3 - 5*n**4 = 0. What is n?
-51, -2, -1
Let m = -730457 - -9495947/13. Factor 0 - 2/13*b**2 + m*b.
-2*b*(b - 3)/13
Let f(y) be the third derivative of 0*y + 2/105*y**7 - 69*y**2 + 4/15*y**6 + 13/15*y**5 + y**4 + 0*y**3 + 0. Find s such that f(s) = 0.
-6, -1, 0
Let f(r) = -2*r**4 + 13*r**3 + 32*r**2 + 29*r - 18. Let i(w) = 3*w**4 - 25*w**3 - 64*w**2 - 59*w + 30. Let l(s) = -5*f(s) - 3*i(s). Find c, given that l(c) = 0.
-4, -2, 0
Let n(k) = 2*k**4 - 740*k**3 + 89296*k**2 - 3631272*k - 8. Let i(t) = -t**3 - t**2 + 53*t - 1. Let x(s) = 8*i(s) - n(s). Factor x(a).
-2*a*(a - 122)**3
Let p(c) = -9*c**2 + 61*c - 91. Let y(a) = -4*a**2 + 30*a - 46. Let v = -109 + 114. Let n(q) = v*y(q) - 2*p(q). Determine d, given that n(d) = 0.
2, 12
Let d(t) be the third derivative of -8/3*t**3 - 1/15*t**5 + 5/6*t**4 - 1 + 0*t - 17*t**2. Factor d(p).
-4*(p - 4)*(p - 1)
Suppose -8 = -3*u + 19. Suppose 0 = -u*k + 42 - 6. Factor -8*p**2 - 4*p**3 - 1 + k - 3.
-4*p**2*(p + 2)
Suppose -11163*k + 11116*k = -94. Factor 4/3 - 20/3*y**4 - k*y**5 + 0*y**2 - 20/3*y**3 + 10/3*y.
-2*(y + 1)**4*(3*y - 2)/3
Factor -530*y + 15*y**3 + 18*y**3 + 27*y**3 - 34*y**3 - 25*y**3 - 529*y**2.
y*(y - 530)*(y + 1)
Let z(j) = 5*j + 9 + 6 - j**3 - 9*j**2 + 8. Let n be z(-12). Solve k**4 - 135*k**5 - 375*k**3 + n*k**4 + 9 - 17 - 16 + 60*k + 78*k**2 = 0 for k.
-2/5, 2/3, 1
Suppose -11*u - 216*u + 681 = 0. Let d(t) be the second derivative of 0 + 3/10*t**2 + 20*t + 0*t**u - 1/20*t**4. Factor d(k).
-3*(k - 1)*(k + 1)/5
Let m(w) = -12*w**2 - 930*w - 4350. Let o be m(-5). Solve -16/3*r - 2/9*r**2 + o = 0.
-24, 0
Let u = -14393 - -14393. Let o(d) be the third derivative of -11*d**2 + d**4 + u*d + 0 + 1/40*d**6 + 0*d**3 - 3/10*d**5. Suppose o(r) = 0. What is r?
0, 2, 4
Let r(o) be the second derivative of 0 - 1/84*o**4 - 22*o + 0*o**2 - 1/504*o**6 - 1/120*o**5 + 7/6*o**3. Let n(g) be the second derivative of r(g). Factor n(v).
-(v + 1)*(5*v + 2)/7
Let k(n) be the first derivative of -6*n**3/13 - 1627*n**2/13 + 724*n/13 + 1804. Let k(o) = 0. Calculate o.
-181, 2/9
Suppose 0 = -5*f + 11*c + 26, 3*c = -f - 0*c. Let a(n) be the first derivative of 15 + 4*n**f - 3/4*n**4 + 0*n - 6*n**2. Factor a(l).
-3*l*(l - 2)**2
Let v = 159 + -143. Factor 19*f - 2*f + v*f**2 + 8*f + 4*f**2 - 5*f**3.
-5*f*(f - 5)*(f + 1)
Let f(i) be the first derivative of 6*i**4 - 4/5*i + 71/15*i**3 + 36 - 16*i**5 - 6/5*i**2. Let f(t) = 0. What is t?
-1/4, 2/5
Let x(j) be the second derivative of -j**5/60 + 323*j**4/36 - 643*j**3/18 + 107*j**2/2 - 1631*j. Factor x(y).
-(y - 321)*(y - 1)**2/3
Factor 167*h + 90*h**2 + 224 - 86*h**2 + 114*h + 39*h - 92*h.
4*(h + 1)*(h + 56)
Let p be (5265/28431)/((-1)/(-27)). Determine g, given that 0*g**3 + 32/13*g**4 + 0*g - 2/13*g**p + 0 + 0*g**2 = 0.
0, 16
Let f(p) be the second derivative of -3/190*p**5 + 1/114*p**4 + 0*p**3 + 0 + 1/95*p**6 + 31*p + 0*p**2 - 1/399*p**7. Find j, given that f(j) = 0.
0, 1
Solve 124/7*q + 1/7*q**3 + 156/7 - 31/7*q**2 = 0.
-1, 6, 26
Let b be (16/(-6) + 144/24)/(-2)*78/(-65). Factor 2*q + 1/6*q**3 + 4/3 + q**b.
(q + 2)**3/6
Find y such that -128*y**2 - 2700*y**4 + 336*y**5 + 100*y + 1104*y**5 + 2250*y**3 - 360*y**5 - 597*y**2 - 5 = 0.
1/6, 1
Suppose -3*a + f + 4 = 3*f, 4*a + 4*f - 4 = 0. Let w**a + 69 + w + 75 - 216 + 70 = 0. Calculate w.
-2, 1
Let l(t) = 54*t**2 - 102*t - 235 - 102*t**2 + 62*t**2 + 5*t. Let u(v) = -16*v**2 + 94*v + 234. Let m(a) = 6*l(a) + 5*u(a). Factor m(i).
4*(i - 30)*(i + 2)
Let o = -563 + 560. Let i(n) = n**5 - 21*n**4 + 29*n**3 + 49*n**2 - 57*n - 64. Let p(u) = u**4 + u**2 - u. Let b(z) = o*p(z) - i(z). Solve b(a) = 0.
-1, 2, 16
Let k(j) = -5*j**3 - 4*j**2. Let l(g) = 0*g + 3*g**2 + 5*g**3 + 0*g. Let q be ((-105)/14)/15 - (-39)/6. Let t(u) = q*l(u) + 4*k(u). Factor t(z).
2*z**2*(5*z + 1)
Factor -151 - 411 + 870*z**3 - 86 + 205*z - 2162*z**2 + 1922*z - 78*z**4 - 111*z + 2*z**5.
2*(z - 18)**2*(z - 1)**3
Suppose -12*g = -52*g - 160. Let p be -1 + g - 851/(-148). Factor p*v + 1/4*v**3 + 0 - v**2.
v*(v - 3)*(v - 1)/4
Solve 24/7 + 4/7*j**2 - 20/7*j = 0 for j.
2, 3
Let b = -1578 + 1578. Let u(c) be the third derivative of 0*c**4 + 15*c**2 + 0 + 1/120*c**6 + 0*c**3 + 0*c + b*c**5. Factor u(t).
t**3
Find f, given that -3886*f + 2268*f - f**2 + 9647236 - 9846*f - 960*f + 5*f**2 = 0.
1553
Solve -1488*o**2 + 129*o - 41*o + 1492*o**2 = 0.
-22, 0
Factor -83550*g - 5*g**2 + 83675*g + 140 - 370.
-5*(g - 23)*(g - 2)
Find f, given that 22/13*f**3 + 230/13*f**2 + 0 + 56/13*f - 8/13*f**4 = 0.
-4, -1/4, 0, 7
Let v(h) be the second derivative of 10 + 3*h**2 + 9/40*h**5 + 1/20*h**6 - h - 3/4*h**3 - 5/8*h**4. Factor v(y).
3*(y - 1)**2*(y + 1)*(y + 4)/2
Let t(f) be the second derivative of f**9/7560 - f**8/480 + f**7/84 - f**6/40 - 35*f**4/6 - f + 28. Let i(a) be the third derivative of t(a). Factor i(k).
2*k*(k - 3)**2*(k - 1)
Suppose -16/3*q**4 - 38/3*q**3 + 79/6*q + 31/3*q**2 - 5 - 1/2*q**5 = 0. What is q?
-6, -5, -1, 1/3, 1
Suppose -3*n - v - 45166 = -45172, -5*n - 5*v + 10 = 0. Factor -40/13 + 10/13*m**3 + 72/13*m + 66/13*m**n.
2*(m + 2)*(m + 5)*(5*m - 2)/13
Let l be (-2 - -1)*(-20 - -800). Let p = 785 + l. Solve 3*z**3 + 3/2 + 3*z + 21/2*z**4 - 12*z**2 - 6*z**p = 0 for z.
-1, -1/4, 1
Let w(y) be the first derivative of 8*y**6/3 - 1884*y**5/5 + 350*y**4 + 156*y**3 + 8277. Suppose w(g) = 0. What is g?
-1/4, 0, 1, 117
Factor 2/15*j**2 - 176/5 + 76/15*j.
2*(j - 6)*(j + 44)/15
Let x(f) be the third derivative of 1/420*f**6 + 1/210*f**5 + 0*f + 3 - 1/735*f**7 + 0*f**3 + 6*f**2 - 1/84*f**4. Suppose x(q) = 0. Calculate q.
-1, 0, 1
Solve -1/4*r**2 + 135/2 - 133/4*r = 0 for r.
-135, 2
Let q(u) = -276*u**2 + 74 - 314 + 271*u**2 - 250*u. Let t(l) = -5*l**2 - 250*l - 239. Let z(g) = -6*q(g) + 5*t(g). Factor z(w).
5*(w + 1)*(w + 49)
Suppose 0 = -3*r + 3*z - 42, 35*r + 56 = 37*r + 4*z. Find f, given that r - 6/5*f**3 + 0*f + 204/5*f**2 = 0.
0, 34
Let i(m) be the third derivative of 0 + 0*m + 1/330*m**5 + 184*m**2 + 10/33*m**3 + 7/132*m**4. Factor i(b).
2*(b + 2)*(b + 5)/11
Let k = 8/18565 + 92809/37130. Solve 24*c**3 - 61/4*c**2 - 9/4*c**4 + 0 + k*c = 0.
0, 1/3, 10
Let w(o) be the third derivative of 2*o**7/105 - 109*o**6/30 + 854*o**5/5 + 11194*o**4/3 + 67280*o**3/3 - o**2 - 8599*o. Factor w(b).
4*(b - 58)**2*(b + 2)*(b + 5)
Let h(w) = -2*w**2 + 15*w - 37. Suppose 20 = -5*o + f, 7*o + 4*f - 20 = 12*o. Let k(z) = z**2 - 16*z + 36. Let d(g) = o*h(g) - 5*k(g). Factor d(m).
(m + 8)*(3*m - 4)
Let x = -7381 - -29545/4. Factor -1/2*m**3 - 9/8 - x*m - 25/8*m**2.
-(m + 3)**2*(4*m + 1)/8
Let r = 568 - 563. Suppose -h - 4*w + 17 = -7, -4*h - 5*w = -41. What is x in 3*x**2 + 12 + 8*x**r - 31*x**5 + 69*x**3 - 48*x + 2*x**5 - 15*x**h = 0?
-2, -1, 2/7, 1
Let r(f) = 6*f**2 + 10*f + 16. Let w(z) = 7*z**2 + 9*z + 15. Let h be -2 + (-4)/(-4)*(-3 - -9). Let n(a) = h*w(a) - 5*r(a). Factor n(b).
-