**2 + 7*o. Let q(b) = y*g(b) + 5*i(b). Factor q(f).
-f*(f - 2)*(2*f + 1)*(5*f - 2)
Let g(u) be the second derivative of 0*u**5 + 1/3*u**3 - 2/15*u**6 + 2*u + 1/3*u**4 + 0 + 0*u**2 - 1/21*u**7. Factor g(b).
-2*b*(b - 1)*(b + 1)**3
Let t(f) = f**2 + 3*f + 2. Let c be t(-5). Find i, given that -c*i + 12*i - 2*i**2 + 3*i**3 + 5*i**2 = 0.
-1, 0
Let k(f) be the third derivative of 0*f**3 + f**2 + 0*f + 1/6*f**4 + 1/60*f**6 + 1/10*f**5 + 0. Factor k(w).
2*w*(w + 1)*(w + 2)
Let v(o) = 2*o**3 + 64*o**2 - 280*o + 384. Let x(u) = -u**3 - 21*u**2 + 93*u - 128. Let s(g) = 3*v(g) + 8*x(g). Factor s(r).
-2*(r - 4)**3
Suppose -w - 2*l + 4 = 2*l, 4*w - 4*l = -4. Let t(o) be the third derivative of -1/20*o**4 - 2*o**2 + 2/15*o**3 + 0*o + 1/150*o**5 + w. Let t(j) = 0. What is j?
1, 2
Let c(p) be the third derivative of 3/40*p**5 + 0 + 0*p**3 + 0*p - 9/32*p**4 - 1/160*p**6 + 7*p**2. Factor c(n).
-3*n*(n - 3)**2/4
Suppose 3*t + 9*g - 2 = 7*g, 2*t = -2*g. Solve 0 - 3*i**3 - 3/5*i + 12/5*i**t + 6/5*i**4 = 0 for i.
0, 1/2, 1
Let t be (6 + -1)/(1 + 0). Suppose 5*c - 20 = -t*v, 2*c - 4*v - 8 = -v. Suppose i**2 - 2*i**3 + 2*i**3 - i**c = 0. What is i?
-1, 0, 1
Let b(i) be the first derivative of -4*i**3/3 + 4*i**2 + 3. Factor b(s).
-4*s*(s - 2)
Let h(u) be the third derivative of u**7/630 + u**6/180 - u**4/36 - u**3/18 - 7*u**2. Let h(f) = 0. What is f?
-1, 1
Let x(h) be the first derivative of 0*h + 0*h**3 - 1 + 1/5*h**2 - 1/10*h**4. Find j such that x(j) = 0.
-1, 0, 1
Factor 5 + 2*w**4 - 3 - 2*w**3 - 4*w**2 + 6*w**3 - 2*w - 2*w**5.
-2*(w - 1)**3*(w + 1)**2
Factor 0*d + 1/4*d**4 + 0*d**3 + 0 - 1/4*d**2.
d**2*(d - 1)*(d + 1)/4
Factor -11*z - 121/6*z**2 - 3/2.
-(11*z + 3)**2/6
Let u(i) = i**2 + 9*i + 11. Let v be u(-9). Let b = v + -9. Suppose 0 + 2/7*d**b - 8/7*d**3 + 6/7*d**4 + 0*d = 0. What is d?
0, 1/3, 1
Suppose 5 = -5*q + 20. Let c be 1 + q - 1 - 1. Let 2/3*r**c - 1/3*r - 2/3*r**4 + 1/3*r**3 + 0 = 0. Calculate r.
-1, 0, 1/2, 1
Let u(f) be the first derivative of -2*f**6/75 + 3*f**5/50 - f**4/30 - 4*f - 5. Let x(j) be the first derivative of u(j). Factor x(q).
-2*q**2*(q - 1)*(2*q - 1)/5
Let o(g) be the third derivative of -g**6/420 + g**5/42 - g**4/14 + g**2 + 1. Factor o(y).
-2*y*(y - 3)*(y - 2)/7
Determine n, given that -1/7*n + 0 - 3/7*n**3 + 4/7*n**4 - 4/7*n**2 + 4/7*n**5 = 0.
-1, -1/2, 0, 1
Let b(h) be the first derivative of h**8/1176 - h**6/210 + h**4/84 - h**2/2 - 2. Let r(t) be the second derivative of b(t). Factor r(j).
2*j*(j - 1)**2*(j + 1)**2/7
Let m(v) be the first derivative of 1/2*v**2 + 1/3*v**3 - 3 + 0*v. Factor m(s).
s*(s + 1)
Let c(n) be the third derivative of n**6/60 + n**5/6 + 2*n**4/3 + 4*n**3/3 - n**2. Factor c(m).
2*(m + 1)*(m + 2)**2
Let q(c) be the first derivative of c**4 - 16*c**3/3 + 8*c**2 - 8. Factor q(p).
4*p*(p - 2)**2
Let l = -26 + 28. Suppose -2/3*u**l - 2/9 + 2*u**3 - 10/9*u = 0. What is u?
-1/3, 1
Let f(a) be the second derivative of -1/50*a**5 - a + 0*a**2 - 1/10*a**4 + 0 - 2/15*a**3. Factor f(z).
-2*z*(z + 1)*(z + 2)/5
Let r(v) = -v**2 + v + 4. Suppose 0*s + s = 0. Let c be r(s). Factor -j**5 - 3*j**3 + 0*j**5 + c*j**3.
-j**3*(j - 1)*(j + 1)
Let n = -4 + 19. Suppose -3*u**2 + u**4 + 15 - 2*u - n = 0. What is u?
-1, 0, 2
Let c = 1669/10 + -333/2. Solve 0 + 0*y - c*y**2 = 0 for y.
0
Let t(w) be the first derivative of -12*w**3 + 5/2*w**4 + 16*w + 12*w**2 + 1. Factor t(a).
2*(a - 2)**2*(5*a + 2)
Let s(h) be the first derivative of -h**7/280 - h**3/3 - 3. Let q(m) be the third derivative of s(m). Factor q(j).
-3*j**3
Suppose -1 - 2/3*d - 1/9*d**2 = 0. What is d?
-3
Let z be (-10)/(-4) - 3*(-1)/6. Solve 2/7*y - 2/7*y**z + 0 + 0*y**2 = 0.
-1, 0, 1
Let t be (-2)/(-3) + 8/(-48). Solve 0*y**2 - t*y**3 + 3/2*y - 1 = 0.
-2, 1
Let m be (-7 - -4)*2*1. Let i = 25/4 + m. Factor -i - 1/4*a**2 - 1/2*a.
-(a + 1)**2/4
Let h be (6 - 1) + 363/(-77). Factor 0 + 0*q**2 + 2/7*q - h*q**3.
-2*q*(q - 1)*(q + 1)/7
Factor 2/5*f**2 - 2/5*f - 4/5.
2*(f - 2)*(f + 1)/5
Let z(o) = o**3 + 1. Let v be (1 + 1 + -3)*-3. Let k(x) = -2*x**4 + 4*x**3 + x**2 + 5. Let s(b) = v*k(b) - 15*z(b). Factor s(y).
-3*y**2*(y + 1)*(2*y - 1)
Let a(j) = -5*j**4 + 15*j**3 + 5*j - 5. Let u(c) = 2*c**4 - 8*c**3 - 3*c + 3. Let r(l) = 3*a(l) + 5*u(l). Factor r(f).
-5*f**3*(f - 1)
Let j(x) = -x**3 + 9*x**2 - x + 11. Let z be j(9). Suppose -m - z = -5. Factor 0 + 2/9*n + 4/9*n**4 - 2/9*n**5 - 4/9*n**2 + 0*n**m.
-2*n*(n - 1)**3*(n + 1)/9
Let -2/9*a**2 - 16/9 + 4/3*a = 0. What is a?
2, 4
Let l(u) be the third derivative of -u**6/300 - 8*u**5/75 - 16*u**4/15 - 59*u**2. Factor l(q).
-2*q*(q + 8)**2/5
Let y be (5 + -5)/(0/4 + 1). Factor y + 2/15*l**4 + 4/15*l**2 + 2/5*l**3 + 0*l.
2*l**2*(l + 1)*(l + 2)/15
Let c(y) be the third derivative of y**7/420 - 11*y**6/240 - y**5/10 + 38*y**2. Factor c(u).
u**2*(u - 12)*(u + 1)/2
Let j(s) = -5*s**4 - 7*s**3 + 10*s**2 + 6*s - 2. Let x(w) = 4*w**4 + 6*w**3 - 9*w**2 - 7*w + 3. Let p(g) = 3*j(g) + 2*x(g). Factor p(r).
-r*(r - 1)*(r + 2)*(7*r + 2)
Let i = -7351/11 - -669. Suppose 2/11*w**4 - 10/11*w**2 + i + 0*w + 0*w**3 = 0. Calculate w.
-2, -1, 1, 2
Let b be 10/(-3 + 5) - 1. Determine m, given that -11/4*m**3 - 3/2*m**b - 3/4*m**2 + 3/4*m + 1/4 = 0.
-1, -1/3, 1/2
Factor 3/7*o + 9/7*o**2 + 0 + 6/7*o**3.
3*o*(o + 1)*(2*o + 1)/7
Let g(y) = -y**5 + 11*y**4 - 3*y**3 - 5*y**2 + y. Let u(z) = -4*z**5 + 32*z**4 - 8*z**3 - 16*z**2 + 4*z. Let i(h) = 8*g(h) - 3*u(h). Factor i(b).
4*b*(b - 1)**3*(b + 1)
Let v(z) be the third derivative of -z**5/100 - z**4/20 - 6*z**2. Suppose v(s) = 0. What is s?
-2, 0
Let n be ((-6)/2)/((4 - 12) + 7). Solve 0 + 0*q + 1/2*q**2 + 1/2*q**n = 0.
-1, 0
Let r(p) = -6*p**3 - p**2 - 5*p + 7. Let g(x) = -x**3 - x**2 + 1. Let k(n) = -15*g(n) + 3*r(n). Factor k(w).
-3*(w - 2)*(w - 1)**2
Solve -482*g**3 - 79*g**2 - 360*g**4 - 101*g**2 - 7*g - 13*g - 3*g**3 - 80*g**5 = 0.
-2, -1/4, 0
Let f(k) be the second derivative of -1/6*k**3 + 0*k**2 - k - 1/12*k**4 + 0. Determine z, given that f(z) = 0.
-1, 0
Let n(y) be the first derivative of 0*y**5 - 1/2*y**2 + 0*y + 3 - 1/36*y**4 + 0*y**3 + 1/180*y**6. Let f(l) be the second derivative of n(l). Factor f(t).
2*t*(t - 1)*(t + 1)/3
Factor 6/7*n + 0 + 2/7*n**2.
2*n*(n + 3)/7
Let r(t) be the third derivative of -t**6/180 - t**5/30 - t**4/12 + t**3/2 - t**2. Let j(p) be the first derivative of r(p). Solve j(g) = 0 for g.
-1
Let i(n) be the third derivative of -n**5/90 + n**4/36 + 15*n**2. Solve i(w) = 0.
0, 1
Let 160*j**2 + 162*j**2 - 325*j**2 + 24*j = 0. Calculate j.
0, 8
Let u be (-34)/(-8) - 4/16. Suppose 0 = -i - u*i. Factor 0*g + i*g**3 - g + 2*g**3 + 4*g**2 + 3*g.
2*g*(g + 1)**2
Find u, given that -1/9*u**2 - 2/9*u + 2/9*u**3 + 0 + 1/9*u**4 = 0.
-2, -1, 0, 1
Let c(w) = -5*w**4 + 7*w**3 - 9*w**2 - 8*w. Let j(q) = -q**4 + 2*q**3 - 2*q**2 - 2*q. Let a(g) = 6*c(g) - 26*j(g). Factor a(l).
-2*l*(l + 1)*(l + 2)*(2*l - 1)
Find o such that 6*o + 4*o**2 + 2 - 3*o**4 + 12*o**3 - 2 - 19*o**2 = 0.
0, 1, 2
Let n(t) be the first derivative of -t**4/8 + 3*t**2/4 - t + 9. Suppose n(r) = 0. Calculate r.
-2, 1
Let z(f) = 4*f**2 + 13*f + 3. Let v be z(-3). Factor 8/5*r**2 - 8/5*r**4 + v*r**3 + 0 - 4/5*r**5 + 4/5*r.
-4*r*(r - 1)*(r + 1)**3/5
Let c(i) be the second derivative of -2/21*i**3 + 0 - 1/7*i**2 - 1/42*i**4 + 2*i. Suppose c(t) = 0. What is t?
-1
Suppose -n - 25 = -4*y + 4*n, 15 = 4*y - 3*n. Factor y*h + 1/2*h**2 - 1/2.
(h - 1)*(h + 1)/2
What is t in -4*t**4 + 5*t**4 + 4*t**5 - 5*t**5 = 0?
0, 1
Let q be (133/(-21) + 6)*-6. Solve 0*a + 3/2*a**5 + 0 - 3*a**4 - 3/2*a**3 + 3*a**q = 0 for a.
-1, 0, 1, 2
Let y(s) be the first derivative of -3*s**4/16 + s**3/4 + 3*s**2/4 + 4. Solve y(k) = 0 for k.
-1, 0, 2
Let k(h) be the third derivative of -13*h**5/330 - h**4/12 + 2*h**3/33 + h**2. Factor k(m).
-2*(m + 1)*(13*m - 2)/11
Let y be 4/4 - (-3 + -1). Factor -1/4*d + 0 + 0*d**4 - 1/4*d**y + 0*d**2 + 1/2*d**3.
-d*(d - 1)**2*(d + 1)**2/4
Let i = -6 - -4. Let l(j) = -j**3 - j**2 + 2*j. Let m(u) = 5*u**3 + 4*u**2 - 9*u. Let w(s) = i*m(s) - 9*l(s). Suppose w(r) = 0. What is r?
0, 1
Factor 18/5 + 2/5*h**2 - 12/5*h.
2*(h - 3)**2/5
Let j(n) be the third derivative of -3*n**6/220 + 8*n**5/165 - 5*n**4/132 - 2*n**3/33 + 25*n**2. Determine s so that j(s) = 0.
-2/9, 1
Suppose 3*p = -m, -21*p + 23*p = -2*m. Suppose 1/4*i**2 + m*i - 1