) be the third derivative of 5/12*c**4 - 6*c**2 - 1/3*c**3 + 0*c + 1/6*c**6 - 1/21*c**7 + 0 + 1/168*c**8 - 1/3*c**5. Factor d(m).
2*(m - 1)**5
Factor -16*s**2 - 18 + s + 3*s + 18.
-4*s*(4*s - 1)
Let c be 8/(-44) - 13/(-11). Let x be c/(-5) + 2/10. Factor 0 + 6/5*t**3 - 3/5*t**2 - 3/5*t**4 + x*t.
-3*t**2*(t - 1)**2/5
Suppose -5*h + x = -3*x + 234, 0 = 2*h - 4*x + 84. Let g = h + 76. Let 4 + 3*k + 11*k + 6*k**3 - 4*k**2 - 6*k**2 + g*k**2 = 0. What is k?
-1, -2/3
Let u(o) = -o**2 + 5*o - 4. Let g be u(3). Determine k so that k**2 - 3*k**4 + k**2 + k**g = 0.
-1, 0, 1
Factor 3*z + 0 - 3/2*z**3 - 3/2*z**2.
-3*z*(z - 1)*(z + 2)/2
Let j(b) be the second derivative of b**7/45 + b**6/90 - 7*b**5/90 - b**4/18 + b**2/2 - 3*b. Let r(u) be the first derivative of j(u). Solve r(c) = 0.
-1, -2/7, 0, 1
Suppose -c - 2*c + 4*c = 0. Let y(l) be the second derivative of -1/120*l**6 + c - 1/40*l**5 - 2*l - 1/48*l**4 + 0*l**3 + 0*l**2. Factor y(p).
-p**2*(p + 1)**2/4
Let -12 + 9*m**2 - 5*m**2 - 57*m + 10*m = 0. What is m?
-1/4, 12
Let l(t) be the first derivative of -t**3/6 + t**2/10 - 5. Suppose l(j) = 0. What is j?
0, 2/5
Let m = 10 + -14. Let o(t) = t**2 + 3*t. Let h be o(m). Factor 1/5*d**2 + 0 - 1/5*d**h + 0*d**3 + 0*d.
-d**2*(d - 1)*(d + 1)/5
Let n(i) be the first derivative of 1/300*i**6 + 2 - 1/60*i**4 + 1/150*i**5 + i**2 + 0*i - 1/15*i**3. Let r(u) be the second derivative of n(u). Factor r(v).
2*(v - 1)*(v + 1)**2/5
Let u = -2/147 - -17/49. Find b, given that -13/3*b**2 + 2*b**3 - u*b**4 + 4*b - 4/3 = 0.
1, 2
Let p(a) = -11*a**2 + a - 8. Let b(w) = -5*w**2 + w - 4. Let x(q) = -9*b(q) + 4*p(q). Suppose x(g) = 0. What is g?
1, 4
Let j(s) be the third derivative of s**5/20 - 3*s**4/4 + 9*s**3/2 - 6*s**2. Let j(k) = 0. Calculate k.
3
Let y(l) be the first derivative of -l**6/7 + 4*l**5/7 - 6*l**4/7 + 4*l**3/7 - l**2/7 - 3. Factor y(m).
-2*m*(m - 1)**3*(3*m - 1)/7
Let i = 115/39 - 21/13. Let y = 5/3 - i. Let 4/3*s**5 - y*s - 5/3*s**4 + 5/3*s**2 - s**3 + 0 = 0. What is s?
-1, 0, 1/4, 1
Let s(b) be the second derivative of -2*b**6/15 + 5*b. Solve s(k) = 0 for k.
0
Let l(q) be the third derivative of q**6/420 + q**5/70 + q**4/42 + 5*q**2. Factor l(r).
2*r*(r + 1)*(r + 2)/7
Let o(u) be the second derivative of -u**5/110 - 2*u**4/33 - u**3/11 - 2*u - 5. Factor o(y).
-2*y*(y + 1)*(y + 3)/11
Suppose -5 - 1 = -w. Suppose 3*t = 6 + w. Factor -2*x**2 - 1 + 0*x**3 + 3*x**t + 2*x**3 - 3*x + 2*x**5 - x**5.
(x - 1)*(x + 1)**4
Let c be ((-3)/(-1))/(21/14). Factor -2*g - 7*g**2 + 4*g**c + 0*g + 2*g**2.
-g*(g + 2)
Let x(o) = 8*o**2 - 7*o - 2*o**2 + o**2. Let i(z) = -6*z**2 + 6*z. Let d(q) = -6*i(q) - 5*x(q). Find a, given that d(a) = 0.
0, 1
Let o = 29 + 3. Factor o - 2*j**2 + 3*j**5 - 32 + 4*j**4 - j**3.
j**2*(j + 1)**2*(3*j - 2)
Suppose -4*v - v = 0. Determine y so that v*y - 4/5*y**3 + 0 + 2/5*y**2 - 6/5*y**4 = 0.
-1, 0, 1/3
What is v in -9/4*v**2 + 9/4*v**3 - 3/4*v**4 + 3/4*v + 0 = 0?
0, 1
Let x(u) be the third derivative of -u**8/2184 + 4*u**7/1365 - u**6/260 - 2*u**5/195 + u**4/39 - 53*u**2. Let x(l) = 0. Calculate l.
-1, 0, 1, 2
Let b(a) = -a - 4. Let m be b(-5). Let y = -1 + m. Factor 2/5*r**2 + 0*r + y.
2*r**2/5
Let -4*p**3 + 12*p**2 + 2 - 10 + 16*p - 4*p**4 - 12*p = 0. Calculate p.
-2, -1, 1
Let u(y) be the third derivative of -y**8/2016 + y**7/252 - y**6/72 + y**5/36 - 5*y**4/144 + y**3/36 + 8*y**2. Solve u(i) = 0.
1
Suppose 2*b + 9 = 5*b. Let y(m) = m**3 - 4*m**2 + 4*m - 3. Let p be y(b). Factor 3/2*g**2 + 3/2*g**3 + p - 3/2*g - 3/2*g**4.
-3*g*(g - 1)**2*(g + 1)/2
Let a(m) be the first derivative of m**4/2 + 14*m**3/3 + 15*m**2 + 18*m + 4. Determine b so that a(b) = 0.
-3, -1
Factor 0 - 10/9*o**4 + 4/9*o**5 - 2/9*o + 2/9*o**2 + 2/3*o**3.
2*o*(o - 1)**3*(2*o + 1)/9
Suppose f - 2*f = 2*t - 4, -4*f + 60 = -3*t. Suppose -f = -h + 3*d, -4*h - 2*d + 1 = 9. Factor 1/2 + h*q**2 - 1/2*q**4 - q**3 + q.
-(q - 1)*(q + 1)**3/2
Let j(a) = 4*a**4 + 6*a**3 + 8*a**2 + 2*a - 2. Let w(q) = 9*q**4 + 12*q**3 + 17*q**2 + 4*q - 5. Let l(d) = 5*j(d) - 2*w(d). Let l(y) = 0. Calculate y.
-1, 0
Let a = 431 + -3877/9. What is s in a*s**2 - 2/9*s + 0 = 0?
0, 1
Let v = 72 + -70. Find o such that -9/5*o**3 - 6/5*o**v + 6/5 + 9/5*o = 0.
-1, -2/3, 1
Let n(l) be the second derivative of l**7/6 + 11*l**6/120 - l**5/3 + l**4/6 - l**2 - 5*l. Let j(b) be the first derivative of n(b). Factor j(g).
g*(g + 1)*(5*g - 2)*(7*g - 2)
Let d(r) be the third derivative of -r**7/210 - r**3/3 - 7*r**2. Let w(m) be the first derivative of d(m). Factor w(b).
-4*b**3
Let x(h) = -3*h**3 + 18*h**2 + h - 6. Let y be x(6). Suppose 6 = -0*m + 3*m. Factor 2/7*t**m + y + 0*t.
2*t**2/7
Let x(q) = 5*q**2 - q - 3. Let c(m) = 36*m**2 - 6*m - 22. Let g(b) = 6*c(b) - 44*x(b). Factor g(u).
-4*u*(u - 2)
Let l = 704 - 4920/7. Suppose 2/7*u**4 + 12/7*u**2 + l*u**3 + 8/7*u + 2/7 = 0. Calculate u.
-1
Let c(a) be the third derivative of 0 + 1/1050*a**7 + 0*a**4 + 0*a - 1/600*a**6 + 1/1680*a**8 - 1/300*a**5 + 0*a**3 + 3*a**2. Find w such that c(w) = 0.
-1, 0, 1
Let d be 7/2 + (-3)/6. Let q(l) be the second derivative of -1/45*l**6 - 1/9*l**4 + 0 + 1/10*l**5 + 0*l**d + 0*l**2 - 4*l. Factor q(c).
-2*c**2*(c - 2)*(c - 1)/3
Let g = -1/345 - 1303/115. Let r = 38/3 + g. Factor 2/3*a**3 + 2*a**4 + 0 - r*a**2 + 0*a.
2*a**2*(a + 1)*(3*a - 2)/3
Let n(c) be the first derivative of -c**7/840 - c**6/480 + c**5/240 + c**4/96 - c**2 + 1. Let b(u) be the second derivative of n(u). What is g in b(g) = 0?
-1, 0, 1
Let v = 140 - 1258/9. Let t(l) be the first derivative of 1/3*l**2 - 2/3*l + 3 - 1/6*l**4 + v*l**3. Solve t(a) = 0 for a.
-1, 1
Let b(n) = n**5 + 3*n**4 - 6*n**3 - 4*n**2 - 6*n + 6. Let d(o) = o**3 + o - 1. Let v(i) = b(i) + 6*d(i). Let v(z) = 0. What is z?
-2, 0, 1
Suppose a = 2 + 1. Factor r**4 + 1/3*r**2 + r**a + 0*r + 1/3*r**5 + 0.
r**2*(r + 1)**3/3
Find z, given that 2/9*z**2 - 4/9*z + 2/9 = 0.
1
Suppose -7*n = -2*n - 20. Suppose -n*l = -9*l. Factor 2/7*a**2 + 2/7*a + l - 2/7*a**4 - 2/7*a**3.
-2*a*(a - 1)*(a + 1)**2/7
Let z(i) be the first derivative of -i**9/3024 - i**8/1680 - 2*i**3/3 - 2. Let t(w) be the third derivative of z(w). Suppose t(k) = 0. Calculate k.
-1, 0
Factor -15*v - 3/4*v**2 - 75.
-3*(v + 10)**2/4
Let f(u) = 4*u**5 - 5*u**4 - 2*u**3 - 3*u**2. Let p(j) = -j**5 + j**4 + j**3 + j**2. Let n(i) = -f(i) - 5*p(i). Let n(v) = 0. Calculate v.
-1, 0, 2
Let v(m) be the third derivative of -9*m**7/70 + 9*m**6/40 - 3*m**5/20 + m**4/24 + 9*m**2. Determine h so that v(h) = 0.
0, 1/3
Let d be (-137)/(-9) + (-2)/9. Suppose 0 = -3*q + d, g = 6*g - 4*q + 5. Find j such that 2*j**4 - 2*j**g + 4*j**3 + 0*j**4 = 0.
-1, 0
Suppose 8*y - 40*y**3 + 132*y**2 - 152*y + 131*y**4 - 127*y**4 = 0. Calculate y.
0, 3, 4
Factor 3 - 9*w**3 - 4*w**4 + 39*w + 5 + 14*w**2 - 3*w.
-(w - 2)*(w + 2)**2*(4*w + 1)
Let a(x) be the third derivative of -x**5/40 + x**4/12 + x**3/3 + 25*x**2. Factor a(q).
-(q - 2)*(3*q + 2)/2
Solve 1/7*i**3 + 5/7 + 3/7*i**2 - 9/7*i = 0 for i.
-5, 1
Suppose 25 = 5*f - 0*f. Factor p**4 - 3*p**4 - p**3 + 2*p**f - p**3 + 2*p**2.
2*p**2*(p - 1)**2*(p + 1)
Let a be -2 + 20/4 + -1. Let p(j) be the second derivative of 0*j**2 + 1/10*j**5 - 1/3*j**4 - a*j + 0 + 1/3*j**3. Let p(r) = 0. What is r?
0, 1
Let v(t) be the first derivative of t**5/40 - t**4/24 - t - 1. Let l(m) be the first derivative of v(m). Find k, given that l(k) = 0.
0, 1
Let r be 26/10 + 12/30. Suppose -12 = 4*u - 4*o, r*o = -u - 5 + 22. Determine z, given that 2/5 + 2/5*z - 4/5*z**3 + 2/5*z**4 + 2/5*z**5 - 4/5*z**u = 0.
-1, 1
Suppose -g = o - 2*g - 1, -5*o + 5 = -2*g. Let t(r) be the first derivative of -o - 2/3*r**3 + 2*r**2 - 2*r. Factor t(h).
-2*(h - 1)**2
Let d = -3/2 + 13/6. Let g(w) be the first derivative of -1/2*w**4 + 1/3*w**6 + d*w**3 - 2/5*w**5 + 0*w**2 + 0*w + 3. Determine a, given that g(a) = 0.
-1, 0, 1
Find p such that 18*p - 2*p**2 - 15 - 3*p**2 - 3*p**2 + 5*p**2 = 0.
1, 5
Determine q so that -2/3*q**2 - 2/3 + 4/3*q = 0.
1
Let m(d) be the third derivative of d**5/15 + d**4/6 - 36*d**2. Find l such that m(l) = 0.
-1, 0
Let t(u) = 9*u**2 - 17*u + 3. Let o(v) = -4*v**2 + 8*v - 2. Let l(j) = -5*o(j) - 2*t(j). Factor l(c).
2*(c - 2)*(c - 1)
Let h(v) be the second derivative of 3*v**5/20 - 3*v**4/4 + 3*v**3/2 - 3*v**2/2 - v. Factor h(r).
3*(r - 1)**3
Let c(j) be the t