2. Factor s(f).
(f - 1)*(2*f - 1)/5
Determine q, given that 3/2*q**3 - 3/2 + 3/2*q**2 - 3/2*q = 0.
-1, 1
Let v(w) be the first derivative of -w**7/140 + w**5/20 - w**3/4 + 9*w**2/2 - 1. Let c(r) be the second derivative of v(r). Factor c(m).
-3*(m - 1)**2*(m + 1)**2/2
Let x be (13/(-4))/(4/384). Let r = x + 2192/7. Factor -2/7*k**2 + 8/7*k - r.
-2*(k - 2)**2/7
Let c(a) be the second derivative of -a**5/4 + 5*a**4/6 + 12*a. Factor c(b).
-5*b**2*(b - 2)
Suppose 2*n = -2*n. Let t(b) be the second derivative of n*b**4 - 1/7*b**7 + 0 + 0*b**3 - 1/15*b**6 + b + 1/5*b**5 + 0*b**2. Let t(x) = 0. Calculate x.
-1, 0, 2/3
Let d(u) be the second derivative of -u**9/1680 + u**8/2240 + u**7/420 - u**4/6 - 3*u. Let k(z) be the third derivative of d(z). Determine i so that k(i) = 0.
-2/3, 0, 1
Let t(c) be the first derivative of -12/5*c**5 + 0*c + 4 - 4*c**4 + 4/3*c**3 + 4*c**2. Find f such that t(f) = 0.
-1, 0, 2/3
Let o(d) be the second derivative of 0 - 1/6*d**4 + d**2 + 0*d**3 + 2*d. Suppose o(i) = 0. What is i?
-1, 1
Let z(l) be the second derivative of l**7/420 + l**6/120 + l**5/120 - 9*l**2/2 + 7*l. Let m(t) be the first derivative of z(t). What is s in m(s) = 0?
-1, 0
Factor -1/4*x**2 - 1/2 + 3/4*x.
-(x - 2)*(x - 1)/4
Let d(g) be the first derivative of 2/3*g**3 + g**4 + 0*g**2 + 0*g - 6/5*g**5 + 3. Suppose d(a) = 0. What is a?
-1/3, 0, 1
Let r(v) = v**4 + v**3 - v**2 - v - 1. Let g(t) = -7*t**5 + 12*t**4 + 8*t**3 - 12*t**2 - t - 3. Let f(i) = -g(i) + 3*r(i). Solve f(z) = 0 for z.
-1, 0, 2/7, 1
Let s(f) be the third derivative of f**8/3360 - f**7/1260 - 5*f**4/24 + 7*f**2. Let o(w) be the second derivative of s(w). Factor o(q).
2*q**2*(q - 1)
Let w be (13/(-3))/(-1) - 4. Factor -1/3*h**4 + w*h**2 + 0 + 1/3*h - 1/3*h**3.
-h*(h - 1)*(h + 1)**2/3
Let w(u) be the second derivative of u**6/360 + u**5/30 + u**4/6 + u**3/2 + 2*u. Let q(h) be the second derivative of w(h). Determine k so that q(k) = 0.
-2
Let m(i) = 17*i**4 + 5*i**3 + 17*i**2 + 13*i - 13. Let s(v) = -8*v**4 - 2*v**3 - 8*v**2 - 6*v + 6. Let c(x) = 6*m(x) + 13*s(x). Factor c(j).
-2*j**2*(j - 1)**2
Let u(j) = 2*j**4 + j**3 + j**2 + j + 8. Let g(i) = -i**4 - i**3 - i**2 - i. Let h(x) = -g(x) - u(x). Let o(t) be the first derivative of h(t). Factor o(n).
-4*n**3
Let i(h) be the second derivative of h**5/20 - h**4/12 - 2*h**3/3 + 2*h**2 + 33*h. Determine c, given that i(c) = 0.
-2, 1, 2
Suppose -5*t + 174 = 59. Suppose 10 = 2*r - h, 3*r - 2 - t = 4*h. Suppose 0 - 2/7*j - 8/7*j**r + 10/7*j**2 = 0. Calculate j.
0, 1/4, 1
Solve -16/9*c**2 - 38/9*c**3 + 0 - 14/9*c**4 + 8/9*c = 0.
-2, -1, 0, 2/7
Let u = 405 + -2023/5. Factor 8/5*i**4 + 0 + 12/5*i**3 + 2/5*i + u*i**5 + 8/5*i**2.
2*i*(i + 1)**4/5
Let c(t) = 5*t**2 + 2*t - 2. Let w be c(1). Let a = -3 + w. Suppose -2*b**3 + 2*b**a - 2/3*b + 0 + 2/3*b**4 = 0. What is b?
0, 1
Solve 6*a**2 + 4*a - a**2 - 5 - 6*a**2 + 1 = 0 for a.
2
Let w(n) be the first derivative of -4/3*n**5 - 1/3*n**6 + 0*n - 4/3*n**3 - 1/3*n**2 - 2*n**4 + 2. Find h, given that w(h) = 0.
-1, -1/3, 0
Let u(l) = 2*l**4 - 4*l**3 - l**2. Let c(n) = n**2 + 0*n**3 + 5*n**3 + n**2 - 3*n**4. Let k(d) = 3*c(d) + 4*u(d). Factor k(a).
-a**2*(a - 1)*(a + 2)
Let m(o) be the second derivative of -o**4/60 + 2*o**3/15 - 2*o**2/5 + 11*o. Factor m(c).
-(c - 2)**2/5
Let i(s) = 4*s**4 - 2*s**3 - 2*s**2 + 4*s + 2. Let n(p) = p**5 - 9*p**4 + 3*p**3 + 3*p**2 - 9*p - 4. Let x(a) = 5*i(a) + 2*n(a). Solve x(d) = 0.
-1, 1
Suppose -15 + 9 = -3*g. Factor 4/3 - 10/3*o + g*o**2.
2*(o - 1)*(3*o - 2)/3
Let t(g) be the first derivative of -1/2*g**2 + 1/120*g**5 + 1/48*g**4 - 2 + 0*g + 0*g**3. Let k(r) be the second derivative of t(r). Factor k(j).
j*(j + 1)/2
Let i = -107693/5 + 21467. Let r = i + 72. Find y, given that -4/5*y**4 + 0*y**2 - r*y**3 - 2/5*y**5 + 0 + 0*y = 0.
-1, 0
Determine r so that 2/13*r**2 + 10/13*r + 8/13 = 0.
-4, -1
Let o = 44 + -41. Let i(k) be the second derivative of -5/6*k**o + 0 - 1/3*k**4 + 2*k - 1/20*k**5 - k**2. Find z such that i(z) = 0.
-2, -1
Let c = 8 + -5. Let x be -2 + 4/c*3. Factor 0*f - 1/4*f**x + 1/4.
-(f - 1)*(f + 1)/4
Find y, given that 0*y - 4/3*y**4 + 0 + 4/3*y**2 + 20/9*y**5 - 20/9*y**3 = 0.
-1, 0, 3/5, 1
Factor 0 - 6/7*r**2 + 0*r - 9/7*r**3.
-3*r**2*(3*r + 2)/7
Let v(y) = -24*y**4 + 260*y**3 - 1704*y**2. Let d(x) = 5*x**4 - 52*x**3 + 341*x**2. Let o(h) = -28*d(h) - 6*v(h). Solve o(a) = 0.
0, 13
Let s(k) be the third derivative of -k**9/181440 + k**7/15120 + k**5/12 + 4*k**2. Let f(b) be the third derivative of s(b). Factor f(q).
-q*(q - 1)*(q + 1)/3
Let z be (-15)/(-5 - 0) - 1. Let s(h) be the second derivative of 0*h**2 - 1/21*h**3 + 1/21*h**4 - 1/70*h**5 + 0 - z*h. Suppose s(r) = 0. Calculate r.
0, 1
What is j in -120/7*j + 8/7 + 450/7*j**2 = 0?
2/15
Suppose 0 = -7*z - 34 - 22. Let u be (3/10)/((-3)/z). Factor -u + 2/5*t**2 + 2/5*t.
2*(t - 1)*(t + 2)/5
Let m(q) be the first derivative of -q**4/2 - 14*q**3 - 147*q**2 - 686*q + 5. Factor m(b).
-2*(b + 7)**3
Let i(r) be the first derivative of r**6/36 + r**5/30 - r**4/24 - r**3/18 - 2. Factor i(c).
c**2*(c - 1)*(c + 1)**2/6
Let c(q) = -4*q**3 - q**2 - q - 1. Let r be c(-1). Factor 4*x**2 - x**2 + x**2 + 2*x**r.
2*x**2*(x + 2)
Let h = 380 - 378. Factor 0*k + 1/3*k**h - 1/3*k**3 + 1/3*k**5 - 1/3*k**4 + 0.
k**2*(k - 1)**2*(k + 1)/3
Suppose u**4 + 0 + 1/4*u**5 + 3/2*u**3 + 1/4*u + u**2 = 0. Calculate u.
-1, 0
Let r(d) be the first derivative of 2*d**3/13 - 8*d**2/13 + 8*d/13 + 2. Solve r(m) = 0 for m.
2/3, 2
Find i, given that -2/9 + i**2 + 1/3*i = 0.
-2/3, 1/3
Let x(l) be the second derivative of l**7/105 - 4*l**6/75 + 2*l**5/25 - 3*l. What is f in x(f) = 0?
0, 2
Let y = 0 - -2. Let k(o) be the second derivative of -1/8*o**y - 2*o - 1/168*o**7 + 1/40*o**5 + 1/24*o**4 - 1/24*o**3 + 0 - 1/120*o**6. Factor k(r).
-(r - 1)**2*(r + 1)**3/4
Let y(t) be the second derivative of -t**7/63 - 2*t**6/45 + t**4/9 + t**3/9 - 4*t. Determine i, given that y(i) = 0.
-1, 0, 1
Let v be (-4*1)/(1/(-4)). Suppose m + 8 = -2*u, 2*u = 2*m + m - v. Factor 2 - q - 2 - q**m.
-q*(q + 1)
Let h(l) be the second derivative of l**5/5 + l**4/3 - 2*l**3/3 - 2*l**2 - 17*l. Solve h(f) = 0 for f.
-1, 1
Let g = 10 - 10. Let g*q**2 - 18*q - 2 - 25 - q**2 - 2*q**2 = 0. What is q?
-3
Let d(f) = f**2 - 15*f + 16. Let c be d(14). Factor -20*q**2 - 5*q + 4*q + 13*q**c + 6*q**2.
-q*(q + 1)
Let i(d) be the second derivative of 0 + 212*d**4 + 49/2*d**7 + 24*d**2 + 1239/5*d**5 + 96*d**3 + 1323/10*d**6 - 5*d. What is m in i(m) = 0?
-2, -1, -2/7
Let q(f) be the second derivative of -f**4/12 - 5*f**3/6 - 2*f**2 + 8*f. What is c in q(c) = 0?
-4, -1
Let a(u) = 5*u. Let j be a(1). Let k = -1 + j. Factor -1/2*p**k - p**3 + 1/2*p - 1/2 + p**2 + 1/2*p**5.
(p - 1)**3*(p + 1)**2/2
Factor 3/2*c**2 + 3/2*c**3 + 0 + 1/2*c**4 + 1/2*c.
c*(c + 1)**3/2
Let c(x) be the second derivative of -x**5 + x**4 + 10*x**3/3 - 6*x**2 - 2*x. Factor c(s).
-4*(s - 1)*(s + 1)*(5*s - 3)
Let y(z) be the second derivative of z**4/15 + 2*z**3/3 + 8*z**2/5 + 2*z - 45. Factor y(q).
4*(q + 1)*(q + 4)/5
Factor -2/3*k**3 + 1/6 + 3/2*k**2 - k.
-(k - 1)**2*(4*k - 1)/6
Let j(n) = n**3 + 9*n**2 + 2. Let h be j(-9). Let 5/3*l**h + 2/3 - 7/3*l = 0. What is l?
2/5, 1
Let n(c) = -c**2 + c. Let f(a) = 20*a**2 - 20*a. Let z(p) = 2*f(p) + 44*n(p). Factor z(y).
-4*y*(y - 1)
Let p = 68 + -68. Solve -1/3*g + 0*g**4 - 1/3*g**5 + p*g**2 + 0 + 2/3*g**3 = 0.
-1, 0, 1
Let m be 2 + 2 + (-1 - 8). Let u be (2/m)/((-128)/80). Factor u*o**2 + o + 1.
(o + 2)**2/4
Let g = -6 + 12. Let x(w) be the second derivative of -w + 0*w**2 + 1/4*w**4 + 0 - 1/18*w**3 + 3/10*w**g - 9/20*w**5. Find y, given that x(y) = 0.
0, 1/3
Let a = 69 + -343/5. Let h = -65/4 - -333/20. Factor h*u**3 + a*u**2 - 2/5*u - 2/5.
2*(u - 1)*(u + 1)**2/5
Let i = 83/24 - 10/3. Let o(t) be the third derivative of -i*t**4 + 1/3*t**3 + 0*t + 0*t**5 + 1/120*t**6 + 0 - 2*t**2. Determine l, given that o(l) = 0.
-2, 1
Let g(x) be the first derivative of -x**6/8 + 3*x**5/20 + 13. Determine s so that g(s) = 0.
0, 1
Determine q so that 0*q**3 + 0 + 6/7*q**2 - 2/7*q**4 + 4/7*q = 0.
-1, 0, 2
Factor 4*b**2 + 0*b - 6*b + 9*b + 13*b.
4*b*(b + 4)
Suppose -5*u - 4*l + 45 = 0, 3*l - 30 = -4*u + l. Let q(y) be the second derivative of 1/10*y**u + 0*y**4 - 1/3*y**3 + 0*y**2 - 3*y + 0. Factor q(p).
2