 30*g**4 + 15*g**3 - 5*g**2 - 5*g + 5. Let b(o) = -7*o**5 + 15*o**4 - 8*o**3 + 2*o**2 + 2*o - 2. Let k(l) = 5*b(l) + 2*n(l). Factor k(i).
-5*i**3*(i - 2)*(i - 1)
Let h(q) be the second derivative of -q**3 + 25*q + 0 - 2/5*q**5 + 0*q**2 - 7/6*q**4. Find t, given that h(t) = 0.
-1, -3/4, 0
Let r(h) be the first derivative of 5*h**3/18 + h**2 - 16*h/3 + 163. Suppose r(b) = 0. What is b?
-4, 8/5
Let v(c) be the third derivative of c**8/4032 - c**7/84 + c**6/4 + c**5/4 - 2*c**2. Let u(x) be the third derivative of v(x). Factor u(o).
5*(o - 6)**2
Let m be (6/4)/((-24)/(-64)). Let -5*f**m - 4*f**5 - 22*f**3 + 8*f**3 + 13*f**3 = 0. What is f?
-1, -1/4, 0
Let s(w) = 5*w**4 + 30*w**3 + 45*w**2 + 40*w + 15. Let k(l) = 64*l + l**3 - 131*l + 1 + 68*l. Let x(f) = -5*k(f) + s(f). Let x(m) = 0. Calculate m.
-2, -1
Let j(q) = 2*q**3 + q**2 - 2*q. Let g(y) = 15*y**3 + 62*y**2 - 91*y + 20. Let x(k) = -g(k) + 6*j(k). Factor x(b).
-(b - 1)*(b + 20)*(3*b - 1)
Let t be ((-8)/(-162))/(64/192). Let u(b) be the first derivative of 3 - 1/18*b**4 + t*b**3 - 1/9*b**2 + 0*b. Determine d so that u(d) = 0.
0, 1
Let -156*s + 21*s**3 + 84*s**2 - 45*s**3 + 20*s**3 + 76 = 0. Calculate s.
1, 19
Suppose 6*x - 11*x = -255. Factor -x*d**3 - 96*d**4 - 192*d**5 - 53*d**4 - 3*d**2 - 91*d**4.
-3*d**2*(d + 1)*(8*d + 1)**2
Let q = 5 - -1. Suppose -q*c + 1 = -11. Factor z**2 + 2*z + z**2 - 5*z**c.
-z*(3*z - 2)
Let v(l) be the third derivative of l**6/600 + 2*l**5/75 + 7*l**4/120 + 24*l**2. What is h in v(h) = 0?
-7, -1, 0
Solve 16/9*v**2 + 0 - 2/9*v + 2*v**3 = 0 for v.
-1, 0, 1/9
Let j(r) = -r**3 + 4*r**2 + 7*r - 8. Let v be j(5). Let n(i) be the first derivative of 5 + 0*i + 4*i**3 + 3/4*i**4 + 0*i**v. Solve n(u) = 0.
-4, 0
Let p(r) be the second derivative of 0*r**3 + 0 - 1/10*r**5 - 1/6*r**4 + r + 0*r**2. Factor p(v).
-2*v**2*(v + 1)
Let s(p) = 12*p**2 - 651*p - 690. Let f(y) = 3*y**2 - 163*y - 172. Let c(w) = -9*f(w) + 2*s(w). Find b such that c(b) = 0.
-1, 56
Factor -m**4 - 2*m**4 + 128*m - 62 - 19 - 30*m**3 + 18*m**2 - 2*m - 30*m**2.
-3*(m - 1)**2*(m + 3)*(m + 9)
Find u such that 24 - 80/7*u - 2/7*u**2 = 0.
-42, 2
Let c(j) be the second derivative of j**4/20 - 41*j**3/5 + 5043*j**2/10 + 2*j - 37. Suppose c(f) = 0. What is f?
41
Let y(z) be the first derivative of -z**4/6 + 4*z**2/3 - 566. Solve y(t) = 0 for t.
-2, 0, 2
Suppose 8*b = 7*b + 1. Let o be (-6)/((-19 + 3)/b). Factor -o*q + 1/8*q**3 - 1/4 + 0*q**2.
(q - 2)*(q + 1)**2/8
Let y(p) be the first derivative of 8/15*p**3 + 0*p + 0*p**2 + 1/10*p**4 - 31. Let y(f) = 0. What is f?
-4, 0
Let h be -1*4/(-4) + 7. Factor 12*k - 14 + 2*k**2 + 0*k**2 + h*k + 64.
2*(k + 5)**2
Let n = 2256/61 - 37. Let z = 59/122 - n. Suppose 1/2*v**3 + 3/2*v + z + 3/2*v**2 = 0. Calculate v.
-1
Let g(u) be the second derivative of 0*u**4 - 1/2*u**2 + 1/10*u**5 + 1/30*u**6 - 1/3*u**3 + 0 - 22*u. Factor g(w).
(w - 1)*(w + 1)**3
Let u = -3/35 - -66/35. Let c(f) be the first derivative of -9*f**2 - 15/2*f**4 - 5 + 3*f + 12*f**3 + u*f**5. Factor c(i).
3*(i - 1)**3*(3*i - 1)
Suppose -3*r + 4*r**4 - 3*r**4 + 1661*r**3 - 1656*r**3 - 9*r - 8*r**2 = 0. Calculate r.
-6, -1, 0, 2
Let u = 8653/43065 + -8/8613. Factor 196/5 + u*z**2 + 28/5*z.
(z + 14)**2/5
Suppose -a = f - 4*a - 9, -15*f - 2*a = 6. Factor 0 + f*j + 0*j**3 + 0*j**2 + 2/9*j**4 + 2/9*j**5.
2*j**4*(j + 1)/9
Let c(z) be the second derivative of -1/15*z**3 + 30*z + 1/60*z**4 + 0*z**2 + 0. Find x, given that c(x) = 0.
0, 2
Factor -28/13*t**2 - 2*t + 2/13.
-2*(t + 1)*(14*t - 1)/13
Suppose -3*n + 6*z - 2*z + 45 = 0, 110 = 5*n + 5*z. Solve -12*i**4 + 13*i**3 + 6*i - 15*i**2 + n*i**4 - 11*i**4 - 1 + i = 0 for i.
1/4, 1
Let m(a) = -2*a**2 - 5*a + 1. Let y(p) = -p - 11. Let r be y(-5). Let c(i) = 1 - 7*i - 9*i**2 + 3 - 14*i. Let f(v) = r*c(v) + 26*m(v). Factor f(n).
2*(n - 1)**2
Let a(d) = -d**2 + 1. Let w(r) = r**4 + 6*r**3 + 7*r**2 - 2. Let h(q) = 6*a(q) + 3*w(q). What is z in h(z) = 0?
-5, -1, 0
Let c(j) = -60*j**2 + 60. Let y(o) = -5*o**2 + 5. Let h(n) = n**2 - 17*n - 25. Let z be h(17). Let k = -28 - z. Let a(d) = k*c(d) + 35*y(d). Factor a(u).
5*(u - 1)*(u + 1)
Let t(v) be the third derivative of v**9/7560 + v**8/2100 + v**7/2100 - 5*v**3/2 - 4*v**2. Let m(h) be the first derivative of t(h). Factor m(b).
2*b**3*(b + 1)**2/5
Let o be 2/(-4) + 2/(-4). Let i be (-38)/(-3) - o/3. Solve -k**2 - i*k + 0*k**2 + 6 + 4*k**2 + 4*k = 0 for k.
1, 2
Factor 2/5*k**2 + 22/5*k + 36/5.
2*(k + 2)*(k + 9)/5
Factor 20*s**3 + 21*s**3 - 29*s**3 - 2*s**5 + 4*s**4 - 2*s**4.
-2*s**3*(s - 3)*(s + 2)
Let -3528/5 + 546/5*d + 2/5*d**3 + 76/5*d**2 = 0. Calculate d.
-21, 4
Let g be 1 + (0 - (-2 - 0)). What is x in -3*x**g + 4*x + 0*x + 4*x**5 - 3*x**3 - 2*x**3 = 0?
-1, 0, 1
Let o be (-170)/(-595) + (-138)/(-252). What is c in 1/3 + 1/2*c**4 + o*c - 5/6*c**3 - 5/6*c**2 = 0?
-1, -1/3, 1, 2
Let x(h) = 36*h**2 - 16*h + 48. Let p(z) = 2*z**2 - 2*z + 1. Let k(t) = 20*p(t) - x(t). What is w in k(w) = 0?
-1, 7
Let b be (6/3 - 1)*7. Let v = -3 + b. Factor -3*c + 2 - 2*c + c - v*c**2 + 2*c.
-2*(c + 1)*(2*c - 1)
Suppose 3*n + 22 = 1. Let i = 10 + n. Suppose -4*v + 10*v + 6 + i*v**2 - 15*v = 0. What is v?
1, 2
Let q(f) be the third derivative of -1/210*f**5 + 5*f**2 + 1/735*f**7 + 0 + 0*f + 0*f**4 + 1/1176*f**8 + 0*f**3 - 1/420*f**6. Factor q(t).
2*t**2*(t - 1)*(t + 1)**2/7
Let b(c) = 12*c**5 + 9*c**4 - 27*c**3 + 33*c**2 + 9. Let q(k) = 3*k**5 + 2*k**4 - 7*k**3 + 8*k**2 + 2. Let w = -1 + 3. Let j(v) = w*b(v) - 9*q(v). Factor j(z).
-3*z**2*(z - 1)**2*(z + 2)
Let b = -1268 + 1270. Let i(l) be the second derivative of 0 + 1/5*l**3 + 1/50*l**5 - 1/10*l**4 + 10*l - 1/5*l**b. Factor i(z).
2*(z - 1)**3/5
Let j be (0 + ((-8)/10 - -2))*(-5)/(-15). Determine g so that 0 - j*g - 8/5*g**4 + 8/5*g**2 + 2/5*g**3 = 0.
-1, 0, 1/4, 1
Let z = 665 - 665. Let l(h) be the first derivative of -8/21*h**3 + 16/7*h**4 + 7/3*h**6 + 5 + z*h**2 - 22/5*h**5 + 0*h. Suppose l(j) = 0. Calculate j.
0, 2/7, 1
Suppose -25*p + 30 + 150 = 20*p. What is o in 0*o**3 + 0*o + 0 + 2/9*o**p - 8/9*o**2 = 0?
-2, 0, 2
Let q = -86449/35 + 17294/7. Factor q*x**2 - 2/5 - x.
(x - 2)*(3*x + 1)/5
Factor 14*z - 4*z**3 - 4*z**2 + 5*z**3 + 7*z + 14*z - 46*z - 6.
(z - 6)*(z + 1)**2
Let z(p) be the first derivative of p**3/6 - 7*p**2/4 - 9*p + 66. Factor z(v).
(v - 9)*(v + 2)/2
Factor 28*r**3 + 5*r**4 + 4945*r**2 - 5017*r**2 - r**4.
4*r**2*(r - 2)*(r + 9)
Let k(i) be the third derivative of 0*i**3 - 1/20*i**5 + 0*i + 17*i**2 + 7/8*i**4 + 0. Solve k(v) = 0 for v.
0, 7
Let l(b) be the third derivative of -19*b**2 + 0*b - 1/40*b**6 - 1/10*b**5 + 0 + 0*b**3 + 3/8*b**4. Factor l(d).
-3*d*(d - 1)*(d + 3)
Let u(r) be the third derivative of 0 + 0*r**3 - 1/15*r**4 - 1/75*r**5 - 5*r**2 + 2/525*r**7 + 0*r + 1/75*r**6. Factor u(n).
4*n*(n - 1)*(n + 1)*(n + 2)/5
Suppose 8 = g + 5*q, 4*g - 24 = g - 3*q. Let z = -4 + g. Factor -2*j**4 + 5*j**3 - 3*j**3 - z*j**3.
-2*j**3*(j + 1)
Factor -1/4*u**2 - 53*u - 2809.
-(u + 106)**2/4
Let t be (-32)/(13 - 17)*(-1)/(-2). Let n(z) be the first derivative of 4/7*z**2 + 5 + 5/14*z**t + 2/35*z**5 + 0*z + 16/21*z**3. Factor n(b).
2*b*(b + 1)*(b + 2)**2/7
Suppose -3*n + 3 = -4*c, 4*c = 5*n - 7 - 6. Solve 0 + 0*k + 1/2*k**c - 1/2*k**4 + k**2 = 0.
-1, 0, 2
Let w be (-25)/5*(2 - 3). Suppose 0*s + 0 - 2/5*s**w + 0*s**2 + 0*s**4 + 2/5*s**3 = 0. What is s?
-1, 0, 1
Let z be (6332/(-2382))/(8/(-36)*15). Let n = 1/397 + z. Solve -1/5*j**5 - n*j**2 - 4/5*j**4 - 6/5*j**3 - 1/5*j + 0 = 0 for j.
-1, 0
Let n(g) = g**3 + 120*g**2 - 461*g + 489. Let c(f) = 24*f**2 - 92*f + 98. Let x = -1 - -23. Let l(o) = x*c(o) - 4*n(o). Factor l(w).
-4*(w - 5)**2*(w - 2)
Let p be (1 + 0)*11 - (-8)/(-2). Factor -201*v**2 - p - 4*v**4 + 63*v**2 + v**4 - 36*v**3 - 180*v - 68.
-3*(v + 1)**2*(v + 5)**2
Let p(j) = 65*j**2 + 290*j + 3350. Let x(s) = 2*s**2 + s - 1. Let u(k) = -p(k) + 30*x(k). Factor u(b).
-5*(b + 26)**2
Let h(b) be the first derivative of -5*b**2 - 4*b + 11 - 8/3*b**3. Let j(n) = 25*n**2 + 30*n + 12. Let d(m) = 7*h(m) + 2*j(m). Solve d(f) = 0.
-1, -2/3
Let m(t) be the first derivative of t**3/5 + 123*t**2/5 + 243*t/5 + 569. Factor m(q).
3*(q + 1)*(q + 81)/5
Let t(j) = -67*j - 132. Let m be t(-2). Factor -5/2*x**m + 1 + 3/2*x.
-(x - 1)*(5*x + 2)/2
Let p(f) be the first derivative of 2*f**5/35 - f**4/42 - 1