*5/210 - a**4/84 + 2*a**3/21 - a**2 + 2*a. Let x(q) be the first derivative of f(q). Solve x(j) = 0 for j.
-2, 1
Factor 3*d**3 - 9*d - 6 - 13*d**3 + 4*d**3 + 9*d**3.
3*(d - 2)*(d + 1)**2
Let y = -24 + 13. Let i = -8 - y. Find v such that 3*v**i - v**4 + v**2 + 2 - 2*v**2 + 0*v - 3*v = 0.
-1, 1, 2
Let o be (-165)/(-50) - 3*4/(-8). Suppose 0*z**2 + 0*z + o*z**4 - 8/5*z**3 + 0 - 2*z**5 = 0. Calculate z.
0, 2/5, 2
Let q(y) be the first derivative of y**6/40 - y**5/5 + y**4/2 + y**2/2 + 1. Let c(p) be the second derivative of q(p). Factor c(v).
3*v*(v - 2)**2
Let i(p) = -p**3 - 6*p**2 + 7*p + 2. Let r be i(-7). Suppose -u + 3*u**2 - u**r - 2*u**2 + u**2 = 0. What is u?
0, 1
Let y(b) be the third derivative of 4*b**6/165 - 28*b**5/165 + 25*b**4/132 - b**3/11 - b**2. Suppose y(o) = 0. What is o?
1/4, 3
Let r = -511/3 + 171. Let y(o) be the first derivative of -1/3*o**3 + r*o + 1/15*o**5 - 1/6*o**2 + 4 + 1/12*o**4. Factor y(q).
(q - 1)**2*(q + 1)*(q + 2)/3
Let z(m) = -6*m**3 - 2*m**2 + 6*m - 3. Let i(s) = 7*s**3 + 2*s**2 - 7*s + 4. Let k(p) = 5*i(p) + 6*z(p). Solve k(x) = 0.
-2, -1, 1
Let z(t) = -t**3 - 3*t**2 + 5*t - 2. Let q(v) = -v**4. Let h(a) = q(a) - z(a). Determine n, given that h(n) = 0.
-2, 1
Let o(s) be the first derivative of s**6 - 3*s**5/5 - 3*s**4/4 + 1. Factor o(k).
3*k**3*(k - 1)*(2*k + 1)
Let h(b) = 2*b**2 + 10*b. Let n be h(-5). What is p in n + 3/2*p + 0*p**3 - 3/2*p**5 - 3*p**2 + 3*p**4 = 0?
-1, 0, 1
Let k = 1/60 + 29/60. Factor k*l**3 + 0 - 1/4*l**4 - 1/4*l**2 + 0*l.
-l**2*(l - 1)**2/4
Let x(w) = w**2 - 3*w - 1. Let y be x(-4). Let t be 6/y - 16/(-9). Factor -2*j**2 + 2*j - t + 2*j**2 + 2*j**2 - 2*j**3.
-2*(j - 1)**2*(j + 1)
Suppose -5*o + 18 = r + 4, -o + r = 2. Factor o*y**3 + 4*y**2 - 3*y**3 - 3*y**2 + 0*y**3.
-y**2*(y - 1)
Let f be 4 - (-1 + 28209/33). Let b = f + 852. Find h such that 70/11*h**5 + 46/11*h**3 + b*h**2 - 12*h**4 - 8/11*h + 0 = 0.
-2/5, 0, 2/7, 1
Let i(r) = -r**3 + 4*r**2 - 2*r - 2. Let z(u) = -u + 8. Let y be z(6). Let g be i(y). Factor 0 - 2*m**4 - 2/5*m**g - 16/5*m**3 + 4/5*m.
-2*m*(m + 1)**2*(5*m - 2)/5
Factor 2/3*f**3 + 0 + 4/3*f**2 + 2/3*f.
2*f*(f + 1)**2/3
Let j = 32/39 - 2/13. Suppose -m = -8*m + 8*m. Let m + 2/3*p - j*p**2 = 0. What is p?
0, 1
Suppose 2*n = 5*a - 18, 2*a - 14 = -a + 2*n. Factor -2*l**2 - 6*l - a + 6 + 4*l**2.
2*(l - 2)*(l - 1)
Let x(m) be the third derivative of m**8/672 - m**6/120 + m**4/48 - m**2 + 35. Factor x(t).
t*(t - 1)**2*(t + 1)**2/2
Let u(r) be the first derivative of r**6/21 + 32*r**5/7 + 1280*r**4/7 + 81920*r**3/21 + 327680*r**2/7 + 2097152*r/7 + 27. Solve u(i) = 0.
-16
Let q be (-74)/(-259)*42/8. Factor 7/2*k**3 - 3/2*k**2 + 1 - 3/2*k**4 - q*k.
-(k - 1)**3*(3*k + 2)/2
Let z(c) be the first derivative of c**3 + 0*c + 1 + 3/2*c**2. Factor z(k).
3*k*(k + 1)
Let o(w) be the second derivative of -w**7/120 + 2*w**6/45 - 11*w**5/120 + w**4/12 + 2*w**3/3 + 2*w. Let r(z) be the second derivative of o(z). Factor r(b).
-(b - 1)**2*(7*b - 2)
Let l(y) be the second derivative of 1/75*y**6 + y - 1/50*y**5 + 1/15*y**3 + 0*y**2 + 0 - 1/30*y**4. Find k, given that l(k) = 0.
-1, 0, 1
Let f(g) = -g**4 - 7*g**3 + g**2 + 4*g - 3. Let x(a) = 3*a**4 + 13*a**3 - 3*a**2 - 8*a + 5. Let q(u) = -5*f(u) - 3*x(u). Factor q(p).
-4*p*(p - 1)*(p + 1)**2
Let k(d) = -5*d**4 + 9*d**3 - 6*d**2 - 2*d + 2. Let p(t) = 6*t**4 - 9*t**3 + 6*t**2 + 3*t - 3. Let l(z) = -3*k(z) - 2*p(z). Factor l(s).
3*s**2*(s - 2)*(s - 1)
Factor 0*w**2 - 1/3*w**4 + 0*w + 1/3*w**3 + 0.
-w**3*(w - 1)/3
Let b(i) be the first derivative of 4*i**3/3 + 7*i**2 + 6*i + 1. Determine a so that b(a) = 0.
-3, -1/2
Let c = 33/8 + -19/24. What is a in 0 - 4/3*a**3 + 10/3*a**2 + 4/3*a - c*a**4 = 0?
-1, -2/5, 0, 1
Suppose 5 - 16 = -5*d + 2*x, -5*d - x + 17 = 0. Solve 4*t**3 + t**2 - 7*t**3 - t - 1 + 4*t**3 + 0*t**d = 0 for t.
-1, 1
Let k(x) = -x**2 + 1. Let j(l) = -l**2 + 1. Suppose -4 - 6 = 2*d. Let t(h) = d*k(h) + 2*j(h). Factor t(m).
3*(m - 1)*(m + 1)
Let j(y) = 3*y**2 + y. Let z be j(-1). Let h be (-39)/(-9) + (-2)/6. Solve -n**h + 2 + n - 5 + n**5 + 2*n**z - 2*n**3 + 2 = 0 for n.
-1, 1
Suppose 0 = -2*k + k. Let c be (-8)/(-6) + 1 + k. Solve -2/3 - c*n**4 - 5/3*n + 5/3*n**3 + 3*n**2 = 0 for n.
-1, -2/7, 1
Let g(u) be the first derivative of -2*u**3/3 - 7*u**2 - 12*u - 21. Suppose g(k) = 0. What is k?
-6, -1
Let v = 145/12 + -34/3. Let r = 179/120 + 1/120. Find c, given that r*c + 3/4*c**2 + v = 0.
-1
Factor 28 + 6*c - 2*c**2 - 14 - 14.
-2*c*(c - 3)
Suppose 3*j = 5*j. Let c be (j - -8)*2/14. Factor 2/7*p**5 + 2/7*p - c*p**4 + 0 - 8/7*p**2 + 12/7*p**3.
2*p*(p - 1)**4/7
Suppose z + 2 = 5. Let k = -5 + 7. Factor 4*g + z*g**2 - 3*g + g + g**3 - k - g**4 - 3*g.
-(g - 2)*(g - 1)*(g + 1)**2
Let s(x) = 4*x**4 - 4*x**3 + 2*x**2 + x + 3. Let a(i) = 3*i**2 + 7*i**4 - 3 + 8 - 5*i**3 - 2*i**3 + 2*i. Let o(r) = -6*a(r) + 10*s(r). Factor o(w).
-2*w*(w - 1)**2*(w + 1)
Factor 1/4*t**2 + 0 - 1/2*t.
t*(t - 2)/4
Let y(j) = -5*j**3 - 13*j**2 - 9*j - 9. Let z(a) = a**3 + 3*a**2 + 2*a + 2. Let o(g) = 2*y(g) + 9*z(g). Factor o(u).
-u**2*(u - 1)
Let b(a) = -a**2 + 7*a + 20. Let y be b(9). Solve 2/3*k**y + 2/3 + 4/3*k = 0 for k.
-1
Let z(c) = 7*c + 2 + 2*c**2 - 3*c**2 - c. Let n be z(6). Factor -2/7*y**n + 0*y + 0.
-2*y**2/7
Let m(l) be the first derivative of -l**3/12 + 9*l/4 - 35. Factor m(h).
-(h - 3)*(h + 3)/4
Let v(d) = -d**3 + 4*d**2 - 4*d + 3. Let g be v(3). Suppose g = 2*j + 2*j - 4. Solve -5/4*k**2 - 1/4*k**3 - 2*k - j = 0.
-2, -1
Let v(g) be the second derivative of 0 + 1/3*g**2 + 1/36*g**4 + 4*g - 1/6*g**3. Factor v(d).
(d - 2)*(d - 1)/3
Let v be (-1)/(-3) - (-15)/9. Suppose 4*z - 3*d - 2*d = 18, -3*z - 2*d = -v. Factor 13*w**3 - z*w**2 - 10*w**3 - 4*w**2 + 3*w.
3*w*(w - 1)**2
Let b be (-264)/(-42) + (-24)/4. Factor b*j**2 + 2/7 + 4/7*j.
2*(j + 1)**2/7
Let i(k) = -8*k**2 - 4*k + 2. Let o(f) = f**2 + f. Let n(u) = -2*i(u) - 14*o(u). Let b(a) = -2*a**2 + 7*a + 4. Let l(m) = 4*b(m) + 5*n(m). Factor l(r).
2*(r - 2)*(r + 1)
Let m = 2101/30 - 70. Let o(w) be the third derivative of -1/150*w**5 + 0 + m*w**4 - 1/15*w**3 + w**2 + 0*w. Factor o(j).
-2*(j - 1)**2/5
Let u = 55 - 107/2. Let j(n) be the first derivative of 6*n - 1 - n**3 + u*n**2. Factor j(o).
-3*(o - 2)*(o + 1)
Let i(l) be the first derivative of -4/5*l**5 + 0*l - 1 + 0*l**2 + 1/4*l**4 + 1/2*l**6 + 0*l**3. Find s, given that i(s) = 0.
0, 1/3, 1
Let u(x) = -18*x**4 + 12*x**3 + 41*x**2 + 5*x + 11. Let t(q) = -6*q**4 + 4*q**3 + 14*q**2 + 2*q + 4. Let n(o) = 17*t(o) - 6*u(o). Factor n(b).
2*(b - 1)**2*(b + 1)*(3*b + 1)
Suppose -8*j**4 - 985 + 8*j**2 + 985 - 36*j**5 + 36*j**3 = 0. Calculate j.
-1, -2/9, 0, 1
Let g be (132/(-231))/((-52)/42). Factor -14/13*z**2 - 10/13*z**3 - g*z - 2/13*z**4 + 0.
-2*z*(z + 1)**2*(z + 3)/13
Let n be (-2)/(-1) - (4 + -6). What is i in -5*i**4 + i**4 - 2*i**2 - 2*i**5 - i**n - 6*i**3 - i**4 = 0?
-1, 0
Factor 0 + 0*z + 14/13*z**4 - 2/13*z**2 + 8/13*z**5 + 4/13*z**3.
2*z**2*(z + 1)**2*(4*z - 1)/13
Let f(g) be the third derivative of g**8/1344 + g**7/560 - g**6/120 - g**5/30 + g**2. Let r(c) be the third derivative of f(c). Factor r(s).
3*(s + 1)*(5*s - 2)
Let j(y) = 2*y**2 - y - 2. Let x be j(-2). Factor 1 + 12*i + 3 - x*i + i**2.
(i + 2)**2
Let a be ((-1 - -4) + -4)*0/2. Factor a + 0*n + 2/11*n**2.
2*n**2/11
Suppose 0*k - 12 = -3*k. Factor -10*z - 5*z**k + 18*z**4 + 4 + z**4 - 18*z**2 + 10*z**3.
2*(z - 1)*(z + 1)**2*(7*z - 2)
Let u(y) be the third derivative of -y**5/420 + y**4/168 + y**2. Factor u(p).
-p*(p - 1)/7
Let w be (-2)/4 - 2/4. Let m be (-2)/12 - 222/(-36). Let s(q) = 5*q**2 + 2*q - 6. Let d(j) = j**2 - 1. Let n(h) = m*d(h) + w*s(h). Factor n(l).
l*(l - 2)
Let t(g) be the second derivative of -g**7/1260 - g**6/360 + g**4/12 - g. Let c(h) be the third derivative of t(h). Factor c(u).
-2*u*(u + 1)
Suppose 648*y + 612*y**3 + 89*y**4 + 137 + 1134*y**2 + 12*y**5 - 380 + 52*y**4 = 0. What is y?
-3, 1/4
Let d(x) = -4*x**4 + 4*x**2 - 2*x - 4. Let g(i) = -i**4 - i - 1. Let v(p) = d(p) - 2*g(p). Find r, given that v(r) = 0.
-1, 1
Factor 0 + 0*y**2 - 1/11*y**3 + 4/11*y.
-y*(y - 2)*(y + 2)/11
Let s be (8/(-8))/((-2)/6). Suppose -2*c = -8 + 4. Factor -2/3*t**s + 4/3*t - t**c + 1/3*t**4 + 4/3.
(t - 2)**2*(t + 1)**2/3
Let b(m) be the first derivative of -4/11*m - 1 - 2/33*m**3 - 3/11*