5*b**4 + 16/5*b**3 - 18/5*b**5 - 8/5*b**2 = 0.
-1, 0, 2/3
Let h(z) be the first derivative of 0*z + z**2 + 4/3*z**3 + 2 - 3/2*z**4. Factor h(k).
-2*k*(k - 1)*(3*k + 1)
Let p(h) = 3*h**5 - 3*h**4 + 5*h**2 + 5*h + 5. Let k(x) = -4*x**5 + 4*x**4 - 7*x**2 - 7*x - 7. Let g(q) = 5*k(q) + 7*p(q). Factor g(f).
f**4*(f - 1)
Suppose -10 = -3*g - 4. Let t be 27/21 + (g - 3). Let -t*k**3 + 0 + 0*k + 2/7*k**2 = 0. What is k?
0, 1
Factor 14/11*h**2 + 30/11*h + 18/11 + 2/11*h**3.
2*(h + 1)*(h + 3)**2/11
Determine o so that 81/11*o**2 + 63/11*o**3 + 0 + 19/11*o**4 + 2/11*o**5 + 27/11*o = 0.
-3, -1/2, 0
Let m(v) = 5*v + 37. Let o be m(-7). Let u(d) be the first derivative of d**2 - d**4 - 2/3*d**3 + 0*d + o. Factor u(a).
-2*a*(a + 1)*(2*a - 1)
Let l = -12 + 24. Suppose 6*v = 2*v + l. What is r in 2/3*r - 1/3*r**2 + 0 - 1/3*r**v = 0?
-2, 0, 1
Let g(q) be the first derivative of 1/11*q**2 + 1 - 4/11*q + 4/33*q**3 - 1/22*q**4. Factor g(x).
-2*(x - 2)*(x - 1)*(x + 1)/11
Let c(q) = q**3 + q**2 + q. Let k(u) = -2*u**3 + 3*u**2 + 8*u. Let s(h) = 3*c(h) - k(h). Factor s(a).
5*a*(a - 1)*(a + 1)
Let o(p) = p**2 - 12*p + 24. Let w be o(10). Suppose 2/7*z**2 + 0*z + 4/7*z**3 + 0 + 2/7*z**w = 0. What is z?
-1, 0
Suppose -2*u - 3*b + 16 = 0, 4*u - 14 = 2*b + 2. Factor 3/5 - 42/5*w**3 - 9/5*w**u - 18/5*w**2 + 3/5*w - 33/5*w**4.
-3*(w + 1)**4*(3*w - 1)/5
Let a(g) be the first derivative of 3/10*g**2 + 3 - 3/20*g**4 + 6/5*g - 3/5*g**3 + 3/25*g**5. Solve a(k) = 0 for k.
-1, 1, 2
Let k(n) = n**4 - n**3 + n**2 - n. Let g(v) = 4*v**4 - 5*v**3 + 4*v**2 - 3*v. Let h(a) = 4*g(a) - 12*k(a). Find f, given that h(f) = 0.
0, 1
Let d(k) be the second derivative of -7*k**4/36 + k**3/2 - k**2/3 - 4*k. Factor d(r).
-(r - 1)*(7*r - 2)/3
Let f be ((-20)/(-15))/(4/6). Factor -29*s**2 - 2 + 6 - 2*s**3 + 37*s**f - 10*s.
-2*(s - 2)*(s - 1)**2
Let z(g) be the second derivative of 2*g**6/3 - 4*g**5/5 - 11*g**4/3 - 4*g**3/3 + 7*g - 2. Suppose z(s) = 0. What is s?
-1, -1/5, 0, 2
Let w(o) be the third derivative of -o**6/300 + 2*o**5/75 - o**4/15 + 2*o**2 - 2. Factor w(i).
-2*i*(i - 2)**2/5
Let x = -16 - -21. Let s(p) be the second derivative of p - 1/27*p**3 - 1/15*p**x + 0 + 2/27*p**4 - 1/189*p**7 + 4/135*p**6 + 0*p**2. Factor s(f).
-2*f*(f - 1)**4/9
Factor 147 - 25*t**2 - 2*t**3 + 177 - 43*t**2 - 252*t - 2*t**3.
-4*(t - 1)*(t + 9)**2
Factor 6/5 - 7/5*n + 1/5*n**4 - 3/5*n**2 + 3/5*n**3.
(n - 1)**2*(n + 2)*(n + 3)/5
Let l = 34 + -33. Let o(k) be the first derivative of k**3 - l + 0*k + 1/2*k**2. Find f, given that o(f) = 0.
-1/3, 0
Let z(t) = t**3 + 8*t**2 - t - 5. Let s be z(-8). Factor 3/4*l + 3/4*l**2 + 1/4*l**s + 1/4.
(l + 1)**3/4
Let b(c) = -c**2 - 2*c. Let o(t) = -t**2. Let n(f) = 3*b(f) - 6*o(f). Factor n(i).
3*i*(i - 2)
Let c(x) = 1. Let n(y) = -49*y**4 + 77*y**3 - 32*y**2 + 4*y + 5. Let f(i) = 5*c(i) - n(i). Suppose f(u) = 0. What is u?
0, 2/7, 1
Suppose 3 = -3*k + 4*k. Let q(l) be the second derivative of 0*l**2 - 1/105*l**7 + 0*l**4 - 2/75*l**6 + 0*l**k - 1/50*l**5 + 3*l + 0. Find v such that q(v) = 0.
-1, 0
Suppose 0 = 2*u + 2*u. Factor -6/7*y**2 - 2/7*y + u - 2/7*y**4 - 6/7*y**3.
-2*y*(y + 1)**3/7
Let u(p) be the second derivative of -p**6/360 + p**5/60 - p**4/24 - p**3/2 - 3*p. Let n(m) be the second derivative of u(m). Solve n(h) = 0 for h.
1
Let r(s) = -s**3 + s**2 - 2*s + 2. Let y(t) = -t**3 - 2*t + 3. Let j(b) = 3*r(b) - 2*y(b). What is o in j(o) = 0?
0, 1, 2
Let a(i) be the second derivative of -i**7/2100 - i**6/300 - i**5/100 - i**4/60 - i**3/2 - 2*i. Let q(v) be the second derivative of a(v). Factor q(y).
-2*(y + 1)**3/5
Let t(x) be the third derivative of -x**7/10080 + x**6/720 - x**5/120 - x**4/12 - 7*x**2. Let z(r) be the second derivative of t(r). Factor z(u).
-(u - 2)**2/4
Factor 251 - j**5 + 3*j**4 - 251.
-j**4*(j - 3)
Find j such that -3/5*j + 3/5*j**3 + 0 + 0*j**2 = 0.
-1, 0, 1
Let x be (9/((-315)/28))/((-28)/120). Factor -8/7 + x*n + 2*n**2.
2*(n + 2)*(7*n - 2)/7
Find n, given that n**3 + 11*n**2 - 2*n**2 + 4*n - 4*n**2 + 0*n = 0.
-4, -1, 0
Suppose -5*n - 3*r + 27 = 0, 0 = 4*n - 7*n - r + 13. Factor -32/3 - 80/3*k**2 - 40/3*k**n - 80/3*k - 1/3*k**5 - 10/3*k**4.
-(k + 2)**5/3
Let h(o) be the third derivative of o**7/1260 - o**6/180 + o**4/24 + 4*o**2. Let i(u) be the second derivative of h(u). Factor i(f).
2*f*(f - 2)
Suppose -165*z + 157*z = -16. Solve 2*m**z - 16/3*m + 8/3 = 0 for m.
2/3, 2
Let x be (20/(-6))/5*-6. Factor -6*d + 0*d + 3 - x*d**3 + d**4 + 2*d + 6*d**2 - 2.
(d - 1)**4
Let c(h) = 2*h**3 - 10*h**2 - h + 7. Let w be c(5). Suppose -8/5 + 8/5*z - 2/5*z**w = 0. What is z?
2
Suppose -3*s = 4*n - 9 - 7, -3*n + 12 = 5*s. Let c be (1 - (1 - 0))/(-2). Determine g so that c*g**2 + 2/7*g**3 - 2/7*g**4 + 0*g + s = 0.
0, 1
Let r be 76/60 - (-18)/(-30). Factor 2/3*q**3 - r*q**2 + 0*q + 0.
2*q**2*(q - 1)/3
Factor 0 - 2/7*d + 2/7*d**3 + 1/7*d**2 - 1/7*d**4.
-d*(d - 2)*(d - 1)*(d + 1)/7
Factor -10/3 - 5*v + 5*v**3 + 5/3*v**2 + 5/3*v**4.
5*(v - 1)*(v + 1)**2*(v + 2)/3
Let a(y) be the first derivative of -7*y**3/3 + 12*y**2 - 48*y + 8. Let g(v) = 6*v**2 - 24*v + 48. Let j(k) = -3*a(k) - 4*g(k). Factor j(n).
-3*(n - 4)**2
Let o(w) be the second derivative of -w**7/12600 - w**6/900 - w**5/150 + w**4/2 - w. Let h(x) be the third derivative of o(x). Factor h(f).
-(f + 2)**2/5
Let -1/8*y**5 + 0 + 3/8*y**4 - 3/8*y**3 + 1/8*y**2 + 0*y = 0. Calculate y.
0, 1
Let g(o) = -1. Let x(i) = 3. Let n(z) = -2*g(z) - x(z). Let d(a) = 2*a**2 + 4*a - 6. Let t(q) = -d(q) + 6*n(q). Factor t(b).
-2*b*(b + 2)
Let p(h) be the second derivative of -3/20*h**5 + 4/5*h**3 + 1/70*h**7 + 1/50*h**6 + 3*h + 0 - 1/20*h**4 - 6/5*h**2. Factor p(k).
3*(k - 1)**3*(k + 2)**2/5
Factor -20*q - 40*q**3 + 16*q**3 + 80*q**2 - 5*q**3 - 6*q**3.
-5*q*(q - 2)*(7*q - 2)
Suppose 5*g - j - 8 = -0*j, 6 = 5*g - 2*j. Let b be ((-6)/(-3))/(-1) + g. Factor 1/5*h + 1/5*h**2 + b.
h*(h + 1)/5
Let u = -4 + 6. Let -4*t**3 + 3*t**2 + 10*t**4 + 12*t**5 - 3*t**2 - 2*t**u = 0. Calculate t.
-1, -1/3, 0, 1/2
Suppose g = -3*g. Let p = g - -2. Solve 4/5*a + 2/5 + 2/5*a**p = 0.
-1
Let s = 104 - 726/7. Suppose -2/7*q**4 + 0*q**2 + 0*q**3 - s*q**5 + 0 + 0*q = 0. What is q?
-1, 0
Factor -4/9*w - 2/9*w**2 - 2/9.
-2*(w + 1)**2/9
Let h(s) be the first derivative of s**6/2 - 6*s**5/5 + 2*s**3 - 3*s**2/2 + 7. Factor h(b).
3*b*(b - 1)**3*(b + 1)
Suppose 2/5*r**2 + 6/5*r**4 - 8/5*r**3 + 0*r + 0 = 0. Calculate r.
0, 1/3, 1
Factor -36 - 363*w**2 - 1331/6*w**3 - 198*w.
-(11*w + 6)**3/6
Factor 3*w**2 + 0*w + 3/8*w**5 - 3/2*w**3 + 0 - 3/4*w**4.
3*w**2*(w - 2)**2*(w + 2)/8
Let f(t) be the first derivative of 14*t**3/15 + 58*t**2/5 + 32*t/5 + 33. Factor f(s).
2*(s + 8)*(7*s + 2)/5
Suppose 5*f + 18 = -27. Let o(t) = 13*t**3 + 13*t**2. Let n(q) = -3*q**3 - 3*q**2. Let r(x) = f*n(x) - 2*o(x). Factor r(z).
z**2*(z + 1)
Let m = 78 + -544/7. Let -4*o**3 + 18/7*o**5 + 4/7*o**2 + m - 6/7*o**4 + 10/7*o = 0. What is o?
-1, -1/3, 1
Let d(g) be the first derivative of -g**4/12 + g**3/6 + 5*g - 4. Let v(q) be the first derivative of d(q). Determine i, given that v(i) = 0.
0, 1
Let j(c) be the second derivative of -c**10/60480 - c**4/4 + 3*c. Let h(q) be the third derivative of j(q). Factor h(t).
-t**5/2
Let p(s) = -s + 7. Let x be p(5). Suppose -x*r = 2*f + 3*f, -2*f = 4*r. Determine g so that -1/2*g**4 + r*g + 0 + g**3 - 1/2*g**2 = 0.
0, 1
Let s(m) be the second derivative of m**6/105 - m**5/70 - m**4/21 - 32*m. Factor s(t).
2*t**2*(t - 2)*(t + 1)/7
Let o(k) be the third derivative of 0*k + 0 - 1/24*k**4 + k**2 - 1/6*k**3. Let f(w) = -w**3 + w**2 + 5*w + 5. Let i(l) = f(l) + 5*o(l). Factor i(m).
-m**2*(m - 1)
Let a(r) be the second derivative of -r**4/12 - 8*r**3/3 + 2*r**2 - 9*r. Let d(f) = f**2 + f - 1. Let c(j) = a(j) + 4*d(j). Solve c(z) = 0 for z.
0, 4
Let l be 3/10*(-30)/(-108). Let o(h) be the second derivative of 1/12*h**3 + 0 + 3*h + 0*h**2 + 1/40*h**5 - l*h**4. Factor o(n).
n*(n - 1)**2/2
Let 0 - 4/7*c**2 - 12/7*c = 0. What is c?
-3, 0
Suppose -4/9*y + 1/3 + 1/9*y**2 = 0. Calculate y.
1, 3
Factor -2/3*m**3 - 10/9*m**2 + 0 - 4/9*m.
-2*m*(m + 1)*(3*m + 2)/9
Let u(n) be the first derivative of n**6/4 + 3*n**5 + 39*n**4/8 - 30*n**3 + 27*n**2 + 42. Suppose u(l) = 0. Calculate l.
-6, 0, 1
Let n(a) be the second derivative of a**7/70 + a**6/60 + a**2/2 - 3*a. Let w(