1, 0
Let f = -88/3 - -30. Let i(y) be the first derivative of 2/3*y**3 - y**2 - 1/6*y**4 + f*y + 2. Factor i(g).
-2*(g - 1)**3/3
Let a be (-240)/(-252) - ((-16)/(-7) + -2). Factor 2/3 + 0*k - a*k**2.
-2*(k - 1)*(k + 1)/3
Let y(l) be the first derivative of l**5/5 + 3*l**4/4 + l**3 + l**2/2 + 6. Factor y(p).
p*(p + 1)**3
Let i(w) be the first derivative of 5*w**4/8 - 5*w**2/4 - 7. Factor i(b).
5*b*(b - 1)*(b + 1)/2
Factor 2*m + m - 2*m**2 - 2*m**2 + m**3 + m.
m*(m - 2)**2
Let c be 12/(-54) - (-20)/9. Suppose -2*r - c*r = -8. Factor -f**4 - 1/3*f**5 + 0*f - 1/3*f**r + 0 - f**3.
-f**2*(f + 1)**3/3
Let a(q) be the first derivative of q**4/2 + 8*q**3/3 - 19*q**2/4 + 5*q/2 + 21. Factor a(d).
(d + 5)*(2*d - 1)**2/2
Let w(s) be the second derivative of s**5/5 - 4*s**4/3 + 8*s**3/3 + 5*s. Find c such that w(c) = 0.
0, 2
Let k(z) be the second derivative of -1/3*z**4 - 1/9*z**3 - 3/10*z**5 - 2*z - 4/45*z**6 + 0*z**2 + 0. Suppose k(x) = 0. What is x?
-1, -1/4, 0
Let b(g) be the second derivative of 0 - 1/4*g**2 - 3/16*g**4 - 3*g + 11/24*g**3. Solve b(z) = 0 for z.
2/9, 1
Let c(l) be the third derivative of l**6/96 - l**5/120 - 5*l**4/96 + l**3/12 - 8*l**2. Factor c(q).
(q - 1)*(q + 1)*(5*q - 2)/4
Let v(k) be the first derivative of 4*k + 2/3*k**3 - 3*k**2 + 3. Factor v(z).
2*(z - 2)*(z - 1)
Factor 2*k**2 + 144 + 4*k - 70 - 72.
2*(k + 1)**2
Let j be ((-10)/4)/((-2)/4). Suppose 54 = u - a, -j*u - 5*a = -2*u - 178. What is o in 4*o**2 + u*o**4 + 30*o**3 - 4 - 47*o**2 - 30*o - 9*o**2 = 0?
-1, -2/7, -1/4, 1
Let s(z) be the first derivative of z**4/60 - z**3/15 + 2*z + 1. Let r(b) be the first derivative of s(b). Suppose r(v) = 0. What is v?
0, 2
Let d be 2/(-9) - (-15)/54. Let i(g) be the third derivative of 1/90*g**6 - d*g**4 + 0*g**5 - 3*g**2 + 0*g + 1/9*g**3 + 0 - 1/315*g**7. Factor i(v).
-2*(v - 1)**3*(v + 1)/3
Let k(u) = -3*u - 3. Let t be k(-1). Factor t*s + 1/3*s**2 + 0.
s**2/3
Let d be (-9)/(-21) - 3186/(-504). Factor 0*z - 21/4*z**4 + 0 - d*z**3 - 3/2*z**2.
-3*z**2*(z + 1)*(7*z + 2)/4
Let h(j) = -48*j**4 + 96*j**3 - 33*j**2 - 129*j + 48. Let i(g) = -3*g**4 + 6*g**3 - 2*g**2 - 8*g + 3. Let l(b) = 2*h(b) - 33*i(b). Let l(q) = 0. What is q?
-1, 1
Let q(g) be the first derivative of -16/3*g**3 + 7 - 18*g**2 - 8*g. Find x, given that q(x) = 0.
-2, -1/4
Let b(m) be the second derivative of -m - 1/9*m**3 - 1/10*m**5 + 1/45*m**6 + 0*m**2 + 1/6*m**4 + 0. Determine n so that b(n) = 0.
0, 1
Let m(d) = -d**5 + d**3 + d**2 - d. Let f(j) = 45*j**5 - 40*j**4 - 30*j**2 + 25*j. Let l(b) = -f(b) - 30*m(b). Find o such that l(o) = 0.
-1/3, 0, 1
Let l(g) be the second derivative of -g**7/630 - g**6/144 - g**5/120 - 2*g**4/3 - 4*g. Let q(x) be the third derivative of l(x). Factor q(k).
-(k + 1)*(4*k + 1)
Suppose -4*g - a - 12 = 2*a, -5*a = 5*g + 20. Suppose 0*n + g + 3/2*n**3 - n**2 - 1/2*n**4 = 0. Calculate n.
0, 1, 2
Let v(f) = 4*f - 3. Let u be v(2). Factor -3*d**5 + d**5 - 4*d**3 + 3*d**3 + 3*d**u.
d**3*(d - 1)*(d + 1)
Let s(k) be the first derivative of k**5/20 - k**4/16 - 21. Factor s(w).
w**3*(w - 1)/4
Let j(m) = -m**2 - 6*m + 5. Let p(b) = -b - 6. Let i be p(-7). Let a(u) = -u + 1. Let s(t) = i*j(t) - 5*a(t). Factor s(x).
-x*(x + 1)
Let v(y) = y**3 + 3*y**2 + 2*y + 2. Suppose 3*j = 2*m - 12, -m + 9 + 2 = -4*j. Let q be v(j). Determine i, given that 10 - 7*i**2 - 2 + q*i + 5*i**3 - 8 = 0.
0, 2/5, 1
Let l be (-7 + (-119)/(-14))/2. Suppose -3/4 - 3/4*n + 3/4*n**2 + l*n**3 = 0. What is n?
-1, 1
Let k be 1/(-2)*((-1)/2 + -1). Factor 0*y + 0 - k*y**2.
-3*y**2/4
Let 3/7*p**5 - 16/7*p + 8*p**3 + 22/7*p**4 + 48/7*p**2 - 32/7 = 0. What is p?
-2, 2/3
Factor -1/2*c**3 - 1/2*c**4 + 1 + 5/2*c + 3/2*c**2.
-(c - 2)*(c + 1)**3/2
Suppose -5*h + 161 = -i, 68 + 27 = 3*h + i. Factor 3*b**2 - 32 - 3*b + h.
3*b*(b - 1)
Let n(z) = -2*z - 16. Let s be n(-7). Let x be s + 10*1/2. Factor 0 - 2/3*m**2 - 2/3*m**4 + 0*m + 4/3*m**x.
-2*m**2*(m - 1)**2/3
Suppose 3*k - 2*k + 5 = 0, 3*j - 2*k - 10 = 0. Suppose -o + 4 - 2 = j. Suppose 50*u**5 - 42*u**3 + 40*u**4 - 40*u**o - 8*u + 16 - 16 = 0. Calculate u.
-1, -2/5, 0, 1
Let y(a) be the first derivative of -1/10*a**2 - 2/5*a + 1/15*a**3 + 3. Determine k, given that y(k) = 0.
-1, 2
Suppose 10*z**2 + 0 - 104*z - 8 - 348*z**2 = 0. What is z?
-2/13
Suppose -c = 2*c - 21. Suppose 28 = 4*l + 3*d - c*d, l + 1 = -d. What is j in 4 + 7*j - j**3 - j**l - j = 0?
-1, 2
Suppose 2*c - o = -3*o, -5*c + 4 = o. Let g(s) be the first derivative of 0*s - c - 1/3*s**3 - 1/2*s**2. Factor g(f).
-f*(f + 1)
Let w = 1/12 - -1/4. Factor w*r - 1/3*r**3 + 1/3*r**2 - 1/3.
-(r - 1)**2*(r + 1)/3
Let t(n) be the third derivative of n**6/240 + 4*n**5/15 + 16*n**4/3 - n**2 - 43*n. Factor t(k).
k*(k + 16)**2/2
Suppose 19 = a + 17. Let t(m) be the second derivative of 1/9*m**3 + 2/9*m**4 + 0 + 1/10*m**5 + 0*m**a + m. Factor t(s).
2*s*(s + 1)*(3*s + 1)/3
Find p such that -8/3*p**4 + 0 - 16/3*p**3 + 0*p + 4/3*p**5 + 32/3*p**2 = 0.
-2, 0, 2
Let g(s) be the third derivative of s**10/50400 - s**9/10080 + s**7/840 - s**6/240 + s**5/30 + s**2. Let p(y) be the third derivative of g(y). Factor p(t).
3*(t - 1)**3*(t + 1)
Let s be (-1 - 2)/(-4 - (0 + -2)). Factor -3/2*d + s*d**2 + 3/2*d**3 - 3/2.
3*(d - 1)*(d + 1)**2/2
Suppose -22 + 1 = -3*o. Let x be -2 + (o - 3) + -2. Factor 0*f + 0*f**3 + x - 2/5*f**4 + 0*f**2.
-2*f**4/5
Let q(s) be the third derivative of s**8/5040 + s**7/1260 + s**6/1080 - 2*s**3/3 + 4*s**2. Let h(k) be the first derivative of q(k). What is m in h(m) = 0?
-1, 0
Let p(o) be the second derivative of -o**6/10 + 9*o**5/20 - o**4/4 - 3*o**3/2 + 3*o**2 - 4*o. What is l in p(l) = 0?
-1, 1, 2
Let j(s) be the second derivative of s**6/540 - s**5/270 - s**4/108 + s**3/27 - 5*s**2/2 - 5*s. Let o(i) be the first derivative of j(i). Factor o(f).
2*(f - 1)**2*(f + 1)/9
Let v(x) = 4*x**2 - 3*x - 4. Let i(h) = -11*h**2 + 8*h + 11. Let t(y) = 3*i(y) + 8*v(y). Factor t(b).
-(b - 1)*(b + 1)
Let b(f) be the first derivative of -5*f**4/4 + 5*f**3/3 + 10*f**2 - 20*f + 24. Factor b(m).
-5*(m - 2)*(m - 1)*(m + 2)
Determine i so that -15*i**2 - 4*i**3 + 3*i**3 + 6*i**3 + 10*i = 0.
0, 1, 2
Let g(s) be the first derivative of -1/12*s**6 + 0*s**3 + 0*s**2 - 4 + 1/5*s**5 + 0*s - 1/8*s**4. Factor g(l).
-l**3*(l - 1)**2/2
Let p(a) = 13*a + 26. Let h be p(-2). Factor 2/11*i + h - 2/11*i**3 + 0*i**2.
-2*i*(i - 1)*(i + 1)/11
Let z be (1/3)/(1/6). Solve -3*g**2 - g - 2*g**3 + 0*g**3 + 4*g**z + 3*g**3 - 1 = 0.
-1, 1
Let a = -5/7 + 17/14. Let k(v) be the first derivative of -v + 2/3*v**3 - 1/5*v**5 + 1 - 1/2*v**2 - 1/6*v**6 + a*v**4. Factor k(y).
-(y - 1)**2*(y + 1)**3
Let d(u) be the first derivative of 0*u**2 - 5 + 2/33*u**3 - 8/11*u. Solve d(o) = 0 for o.
-2, 2
Suppose -2*l - 2*r = 3*l - 6, 0 = 4*l + 4*r - 12. Let o(n) be the first derivative of 3 + l*n**2 + 3/4*n - 1/4*n**3. Factor o(t).
-3*(t - 1)*(t + 1)/4
Let q(s) be the first derivative of -s**6/39 - 2*s**5/65 + s**4/26 + 2*s**3/39 - 5. Factor q(b).
-2*b**2*(b - 1)*(b + 1)**2/13
Let t(r) be the first derivative of -r**6/25 + r**5/50 - r - 1. Let c(w) be the first derivative of t(w). What is m in c(m) = 0?
0, 1/3
Let n = 6 + 0. Let k = 11 - 18. Let y(s) = -8*s**2 - 2*s + 6. Let w(u) = -7*u**2 - 2*u + 5. Let c(z) = k*w(z) + n*y(z). Factor c(x).
(x + 1)**2
Let j(d) be the second derivative of 0*d**2 + 0*d**4 - d - 1/60*d**5 - 1/126*d**7 + 0 + 1/45*d**6 + 0*d**3. Let j(q) = 0. Calculate q.
0, 1
Let q(m) be the second derivative of m**7/105 - 2*m**2 - m. Let c(a) be the first derivative of q(a). Factor c(x).
2*x**4
Let r(u) = 3 - 2 + 2*u + 2*u**2 - 2*u**3 + 4. Let x(i) = 2*i**3 - 2*i**2 - 2*i - 4. Let g(m) = 6*r(m) + 7*x(m). Factor g(n).
2*(n - 1)**2*(n + 1)
Let z(y) be the second derivative of -y**7/273 + 2*y**6/195 - y**5/130 + 15*y. Determine r, given that z(r) = 0.
0, 1
Factor 0*r - 2*r**3 - 4/3*r**2 + 0*r**4 + 0 + 2/3*r**5.
2*r**2*(r - 2)*(r + 1)**2/3
Let k be -16 - (0 - -1*2). Let o = k - -29. Let q(b) = 7*b**3 + 11*b. Let t(a) = 4*a**3 + 6*a. Let m(x) = o*t(x) - 6*q(x). Factor m(w).
2*w**3
Let t(h) be the second derivative of h**8/7560 + h**7/3780 - h**6/1620 - h**5/540 + h**3/3 + 4*h. Let i(p) be the second derivative of t(p). Factor i(q).
2*q*(q - 1)*(q + 1)**2/9
Let o(r) be the first derivative of -5*r**4/14 + 12*r**3/7 + 8*r**2/7 + 35. Fact