t 0 + 41*q**3 - 9/2*q + 36*q**4 - 9/2*q**5 - 4*q**2 = 0.
-1, -1/3, 0, 1/3, 9
Let t(v) be the first derivative of 0*v - 5/4*v**4 + 0*v**2 + 20*v**3 + 70. Factor t(f).
-5*f**2*(f - 12)
Let t(p) = -18*p**3 + 1146*p**2 - 1960*p - 562. Let n(c) = 19*c**3 - 1145*c**2 + 1964*c + 563. Let q(i) = -2*n(i) - 3*t(i). What is m in q(m) = 0?
-1/4, 2, 70
Let r(a) be the third derivative of -5/72*a**4 + 1/12*a**3 - 5*a**2 + 0 + 1/30*a**5 - 3*a - 1/120*a**6 + 1/1260*a**7. Determine i so that r(i) = 0.
1, 3
Let v(y) be the first derivative of y**6/15 - 3*y**5/10 - 2*y**4/3 - 38*y + 27. Let n(d) be the first derivative of v(d). Factor n(s).
2*s**2*(s - 4)*(s + 1)
Solve -485*x**2 + 188*x**2 - 22*x - 177*x**2 + 474 + 3*x**3 + 19*x = 0 for x.
-1, 1, 158
Let w(s) = -6*s + 7. Let x be w(2). Let p(a) = 13*a + 68. Let i be p(x). Factor 2/9*t**i + 2/3*t - 10/9*t**2 + 2.
2*(t - 3)**2*(t + 1)/9
Suppose -1658*y + 1642*y = -48. Let t(o) be the third derivative of 9*o**2 + 17/6*o**4 + 0*o + 0 + 4*o**y + 1/3*o**5. Factor t(s).
4*(s + 3)*(5*s + 2)
Factor 16081*b - 15941*b + 20*b**2 + 3*b**3 + 194*b**2 + 3*b**3.
2*b*(b + 35)*(3*b + 2)
Let g = -4878 + 4882. Let y = 2 + 0. Factor 4*z**3 - y*z**5 - 2*z - 2 + 4*z**5 - 4*z**5 + 4*z**2 - 2*z**g.
-2*(z - 1)**2*(z + 1)**3
Suppose 35 = -4*b + 8*b - 5*k, -3*b = 5*k. Let p be (8/(-50))/((-2)/5)*b. Factor -4*v - 12 - 1/3*v**p.
-(v + 6)**2/3
Let i(a) = 12*a**4 - 8*a**3 - 12*a**2 + 32*a. Let p(q) be the first derivative of q**5/5 + q**3/3 + q**2/2 - 69. Let z(r) = -i(r) + 8*p(r). Factor z(o).
-4*o*(o - 3)*(o - 1)*(o + 2)
Let n = 26306/19545 + -82/6515. Factor 2/3*h**2 - 1/3*h**5 + 0 + n*h**4 - 5/3*h**3 + 0*h.
-h**2*(h - 2)*(h - 1)**2/3
Suppose 39*r + 5*t - 38 = 42*r, 3*r = -21*t + 222. Let 0*l - 6/5*l**r + 0*l**2 + 0 + l**3 + 1/5*l**5 = 0. What is l?
0, 1, 5
Let f(n) = -6188*n + 470292. Let s be f(76). Let d = 3 - 0. Determine z so that 2/3*z**s - 2/3*z**d - 2*z**2 + 4/3 + 2/3*z = 0.
-1, 1, 2
Let r = 18362/15 - 1224. Let l(t) be the third derivative of -2/3*t**3 + r*t**5 - 1/6*t**4 + 0 + 12*t**2 + 0*t. Factor l(x).
4*(x - 1)*(2*x + 1)
Let t be (-27)/(-243) + 8/90. Let h(p) be the third derivative of 0*p + 1/30*p**6 - 35*p**2 + 0 - t*p**5 + 1/3*p**4 + 0*p**3. Suppose h(r) = 0. Calculate r.
0, 1, 2
Let n(j) be the second derivative of -j - 8/3*j**3 + 1/6*j**4 + 11 + 0*j**2. Factor n(w).
2*w*(w - 8)
Suppose 0 = -2*y + 4, -5*s + s + 3*y - 6 = 0. Suppose n + 5*l + 122 = 92, 5*n - l = 6. Factor s - 4/3*f**2 + 0*f - 2/3*f**5 + n*f**4 + 2*f**3.
-2*f**2*(f - 1)**2*(f + 2)/3
Factor 0*o - 10*o**3 + 19/6*o**4 - 1/6*o**5 + 0 + 0*o**2.
-o**3*(o - 15)*(o - 4)/6
Let d(c) = -2*c**3 - 60*c**2 + 210*c + 265. Let h(f) = -4*f**3 - 180*f**2 + 624*f + 792. Let n(l) = 8*d(l) - 3*h(l). Let n(q) = 0. Calculate q.
-1, 8
Factor -3*h**3 + 6328*h + 0*h**3 - 558*h**2 + 53016 - 31708*h.
-3*(h - 2)*(h + 94)**2
Suppose -1530 = 2*n + 5*p, -4*p = -4*n + 445 - 3533. Let g be (n/(-484))/(-35)*(-25 + 1). Solve -g*x + 0 + 2/11*x**2 = 0 for x.
0, 6
Let h(b) = b**3 + 35*b**2 - 2*b - 58. Let m be h(-35). What is w in -120 - m*w + 116 + 2*w**3 - 12*w**2 - 6*w**3 = 0?
-1
Let l = 24593 + -24589. Let h(b) be the second derivative of -17*b + 0*b**3 + 0*b**2 + 1/66*b**l + 0. Solve h(i) = 0 for i.
0
Let i(t) = 14*t**2 + 12*t - 100. Let c be i(11). Let p = c + -8618/5. Factor -2/5*r**4 + 14/5*r**2 + 0*r + p*r**3 + 0.
-2*r**2*(r - 7)*(r + 1)/5
Let g(b) = -3*b**3 + 20*b**2 + 14*b - 49. Let d be g(7). Let s(u) be the second derivative of d - 2/23*u**2 + 16*u - 3/23*u**3 - 7/138*u**4. Factor s(c).
-2*(c + 1)*(7*c + 2)/23
Let z(c) be the second derivative of -c**7/42 - c**6/10 + 13*c**5/20 + 17*c**4/4 + 6*c**3 - c + 641. Determine u so that z(u) = 0.
-3, -1, 0, 4
Let w(k) be the third derivative of k**5/40 + 341*k**4/16 - 557*k**2. Factor w(y).
3*y*(y + 341)/2
Solve 72*v**3 - 3045*v**2 - 720*v + 1527*v**2 + 1762*v**2 + 400 + 4*v**4 + 0*v**4 = 0 for v.
-10, 1
Let p(a) be the second derivative of a**7/84 - a**6/5 - 2*a**5/5 + 17*a**4/12 + 21*a**3/4 + 13*a**2/2 - 296*a. Solve p(w) = 0 for w.
-1, 2, 13
Let a = 62404 + -312018/5. Factor -2/5*q**2 + a*q + 12/5.
-2*(q - 3)*(q + 2)/5
Let -386/7*c - 390/7*c**3 - 778/7*c**2 + 2/7 = 0. Calculate c.
-1, 1/195
Suppose -22*w = 5*l - 19*w - 38, l = 7*w - 38. Let f(g) be the second derivative of 0*g**2 - 13/24*g**l + 0 + 6*g - 11/40*g**5 - 1/6*g**3. Solve f(p) = 0 for p.
-1, -2/11, 0
Suppose -4206*n**3 + 2107*n**3 + 8 + 56*n + 88*n**2 + 2*n**4 + 2133*n**3 - 8 = 0. What is n?
-14, -2, -1, 0
Let a(l) be the second derivative of l**4/66 - 2152*l**3/33 + 1157776*l**2/11 + 1427*l - 1. Factor a(w).
2*(w - 1076)**2/11
Let q(g) be the third derivative of g**6/10 + 121*g**5/30 - 79*g**4/4 + 110*g**3/3 + g**2 + 3123. Factor q(h).
2*(h - 1)*(h + 22)*(6*h - 5)
Factor -2484/11*z**2 - 39366/11 - 23328/11*z + 288/11*z**3 - 6/11*z**4.
-6*(z - 27)**2*(z + 3)**2/11
Let 24*o**2 - 44 + 0*o**3 - 18*o - o**3 - 12*o**3 - o**3 + 12*o**3 = 0. What is o?
-1, 2, 11
Let r be 8 - (-8 + 9)*1. Let d be ((-3)/(-24))/(r/42). Factor 0*b**4 + b**5 - d*b**3 + 1/4*b**2 + 0 + 0*b.
b**2*(b + 1)*(2*b - 1)**2/4
Let j(u) be the first derivative of 5*u**3/18 + 1925*u**2/12 - 645*u + 10958. Find v, given that j(v) = 0.
-387, 2
Let s(c) be the first derivative of -c**4 - 88*c**3/3 - 274*c**2 - 1040*c + 1691. Factor s(u).
-4*(u + 4)*(u + 5)*(u + 13)
Let n(c) be the first derivative of -5*c**4/12 + 15*c**3/2 - 45*c**2 - 219*c - 26. Let s(t) be the first derivative of n(t). Determine k so that s(k) = 0.
3, 6
Let i(y) be the first derivative of y**4/2 - 322. Factor i(q).
2*q**3
Let r(y) be the third derivative of y**8/210 + 2*y**7/525 - y**6/50 - y**5/75 + y**4/30 - 156*y**2 - 11. Determine s so that r(s) = 0.
-1, 0, 1/2, 1
Let y(t) be the first derivative of 7*t**4/15 + 16*t**3/15 + 2*t**2/5 + 5*t - 2. Let c(p) be the first derivative of y(p). Factor c(h).
4*(h + 1)*(7*h + 1)/5
Let z(g) = -6*g**2 - 6*g + 53. Let d(u) = -u**2 - 1. Let s(w) = -5*d(w) + z(w). Let r be s(-11). Solve -1/3*c**2 + 0*c**r + 0*c + 0 + 1/3*c**4 = 0.
-1, 0, 1
Let z(h) be the first derivative of -h**5/40 + 3*h**4/8 - 9*h**3/4 - h**2/2 + 4*h + 49. Let f(x) be the second derivative of z(x). What is w in f(w) = 0?
3
Suppose -7*w + 3*w + 5*j + 4755 = 0, 4*w - 3*j - 4749 = 0. Factor 6 - v**2 - w*v + 11 + 1172*v - 3.
-(v - 1)*(v + 14)
Let n(c) = c**3 + 23*c**2 - 5*c + 2. Let k be n(-23). Find a such that -405*a**2 - 45*a**5 + 395*a**3 - 68*a**4 + k*a + 13*a**4 + 40 - 47*a = 0.
-4, -2/9, 1
Let z be -732 + 768 - 27/12. Find u such that -250 - z*u**4 - 3465/2*u**2 - 3645/4*u**3 - 1135*u = 0.
-25, -2/3
Solve 41*d - 483/4 - 1/4*d**2 = 0.
3, 161
Let k(b) be the first derivative of 0*b + 2/3*b**3 + 0*b**2 - 1/16*b**4 + 111. Factor k(z).
-z**2*(z - 8)/4
Let w = -428 - -431. Let p be w/1 + (-1 - 13)/(-14). Factor 0*l**2 + 88/5*l**4 + 0 + 0*l + p*l**5 + 32/5*l**3.
4*l**3*(l + 4)*(5*l + 2)/5
Let t(v) be the third derivative of v**6/420 - 43*v**5/210 + 5*v**4 - 213*v**2 - v. Determine r, given that t(r) = 0.
0, 15, 28
Let q be (-18)/33 - (-5480)/4521. Factor -8/3*z + q*z**3 - 4/3 - z**2 + 1/3*z**4.
(z - 2)*(z + 1)**2*(z + 2)/3
Let i = 6/30077 + 360894/150385. Suppose -28/5*y + i*y**4 - 116/5*y**2 + 24/5 - 52/5*y**3 = 0. Calculate y.
-1, 1/3, 6
Let h = 124 + -74. Determine a, given that 91*a**3 - 22*a - h*a**3 - 40*a**3 + 21*a**2 = 0.
-22, 0, 1
Factor -37 - 22*j + 226*j - 4*j**2 - 216 - 245 + 106.
-4*(j - 49)*(j - 2)
Solve -770/13*w + 68/13*w**2 - 2/13*w**3 + 2904/13 = 0.
11, 12
Suppose j = -4*g + 2, -4*j + 2*j = 2*g - 22. Let -5*k - j + k**3 + 15 + 5 - 2*k**2 = 0. Calculate k.
-2, 1, 3
Find i such that -411845/3 - 5/3*i**2 - 2870/3*i = 0.
-287
Let f(z) be the third derivative of 0*z**4 - 7/12*z**5 + 0*z + 0*z**3 - 1/42*z**7 - 1/3*z**6 + 126 + 2*z**2. Factor f(q).
-5*q**2*(q + 1)*(q + 7)
Let r(v) = 3*v**5 + v**4 + v**3 + v**2. Let f(j) = 6*j**5 - 174*j**4 + 872*j**3 - 1224*j**2 + 318*j. Let i(t) = 2*f(t) - 2*r(t). Suppose i(w) = 0. Calculate w.
0, 1/3, 2, 3, 53
Let -948 + 948 - l + 18*l + l**3 + 18*l**2 = 0. Calculate l.
-17, -1, 0
Let i = 13 - 8. Let o = 572 + -566. Factor 3*h**2 - 6*h**4 - 12*h**2 - o*h**3 - 4*h + i*h**4.
-h*(h + 1)**2*(h + 4)
Let m(z) be the second derivative of 2*z**6/45 + 8*z**5/5 - 896*z**4/3 + 102400*z**3/9 - 196608*z**2 - 3711