f**3 = 0.
-1, 0, 1
Let c(w) be the third derivative of -2*w**7/105 + w**6/15 + w**5/15 - w**4/3 - 3*w**2. Factor c(q).
-4*q*(q - 2)*(q - 1)*(q + 1)
Let k(o) be the second derivative of o**7/70 - o**6/15 + 7*o**5/60 - o**4/12 + 3*o**2 + 4*o. Let m(j) be the first derivative of k(j). Solve m(p) = 0 for p.
0, 2/3, 1
Let o(k) be the second derivative of 2*k**6/15 - k**5/10 - 5*k**4/6 - 2*k**3/3 + 4*k. Factor o(v).
2*v*(v - 2)*(v + 1)*(2*v + 1)
Suppose 3*u - 2*u - 2 = 0. Factor 0 + 2/5*g**u - 2/5*g.
2*g*(g - 1)/5
Determine c, given that -c - 3/4*c**3 - 5/4*c**4 + 0 + 3*c**2 = 0.
-2, 0, 2/5, 1
Let p(b) = b**4 - 4*b**3 + 2*b**2 - 2*b + 2. Let q(k) = -8*k**4 + 33*k**3 - 17*k**2 + 17*k - 17. Let i(x) = -51*p(x) - 6*q(x). Factor i(m).
-3*m**3*(m - 2)
Let f(z) be the first derivative of -z**6/6 - 3*z**5/5 - z**4/2 + 2*z**3/3 + 3*z**2/2 + z + 4. Let f(v) = 0. What is v?
-1, 1
Find b such that 3*b + 15*b**2 - 6*b**3 + 3*b**5 + 3 - 13*b**2 - 8*b**2 + 3*b**4 = 0.
-1, 1
Let b be 14/6 - (-3 + 6). Let i = b - -1. Factor i + 1/3*a**2 + 2/3*a.
(a + 1)**2/3
Suppose -4*a = 5 + 27. Let h(p) = p**4 - p**3. Let w(n) = 26*n**4 - 50*n**3 - 4*n**2 + 40*n - 16. Let q(u) = a*h(u) + w(u). Factor q(j).
2*(j - 2)*(j + 1)*(3*j - 2)**2
Let u = 41 - 59. Let j = 20 + u. Let -2/7*q**4 + 0*q + 4/7*q**3 + 0 - 2/7*q**j = 0. What is q?
0, 1
Let w(r) be the first derivative of -r**4/20 - r**3/15 - 34. Factor w(q).
-q**2*(q + 1)/5
Let c(h) = -3*h - 6. Let w be c(-4). Factor -8*n - 4*n + w*n + 3*n**2.
3*n*(n - 2)
Let q(p) be the third derivative of p**6/120 + p**5/30 - p**4/8 - 14*p**2. Factor q(x).
x*(x - 1)*(x + 3)
Let y(l) be the third derivative of -l**8/168 + l**7/105 + l**6/60 - l**5/30 - 6*l**2. Solve y(u) = 0 for u.
-1, 0, 1
Let w(i) be the third derivative of i**7/105 - i**6/18 + 2*i**5/15 - i**4/6 + i**3/9 - 33*i**2. Solve w(o) = 0.
1/3, 1
Let w be (24/16)/((-1)/(-4)). Let s be (-34)/(-28) + w/21. Factor 1 - 6*d**2 - 7/2*d**3 - s*d.
-(d + 1)**2*(7*d - 2)/2
Let r be (-1)/2*(-10 + 4). Let d be 11 - (-1)/(-1)*2. What is n in -8 - 3 - 6*n - 2*n**r + d - 6*n**2 = 0?
-1
Let -9*t**2 + 11*t**3 + t**2 - 3*t**5 - t**5 + t**3 = 0. Calculate t.
-2, 0, 1
Suppose -t + 4*t = 6. Solve -p + 0*p**2 - p**t - 2*p + p = 0 for p.
-2, 0
Let y(b) be the second derivative of -1/4*b**2 + 0 - 1/4*b**3 - 1/8*b**4 + 5*b - 1/40*b**5. Factor y(a).
-(a + 1)**3/2
Let v(s) be the first derivative of -14/55*s**5 + 3/11*s**6 - 1/11*s**4 + 0*s + 3 + 0*s**3 + 0*s**2. Suppose v(w) = 0. Calculate w.
-2/9, 0, 1
Let h = -1 + 0. Let p be (h/(-2))/((-2)/(-12)). Factor 0*i**p - 3*i + 1 + 3*i**3 - 3*i**2 + 4 - 2.
3*(i - 1)**2*(i + 1)
Let j(p) = p**2 + 13*p + 5. Let u be j(-9). Let o = u + 33. Factor 18/7*x**2 + 2/7*x**4 - o*x - 10/7*x**3 + 4/7.
2*(x - 2)*(x - 1)**3/7
Solve 6*g**2 - 4*g + 2*g**3 - 3*g**2 + 5*g**2 - 6*g**3 = 0 for g.
0, 1
Let t(y) be the first derivative of y**3/9 + y**2/6 + 6. Factor t(a).
a*(a + 1)/3
Let f(t) be the third derivative of 5*t**8/336 + t**7/42 - t**6/24 - t**5/12 + 6*t**2. Suppose f(o) = 0. What is o?
-1, 0, 1
Let p = 61 + -119/2. Let q = -11/14 + 9/7. Factor p*r + 1/2 + 3/2*r**2 + q*r**3.
(r + 1)**3/2
Let t(l) = 2*l**2 - 2 - 3*l**2 + 5*l + 5. Let v be t(5). Factor 2*m**v - 6*m**3 + 2*m**5 + 4*m - 2*m.
2*m*(m - 1)**2*(m + 1)**2
Let u(o) be the first derivative of -o**6/33 + o**4/11 - o**2/11 - 3. Solve u(r) = 0.
-1, 0, 1
Let k(i) = 27*i**3 + 60*i**2 - 54*i + 9. Let o(c) = c**2 + c. Let a(m) = -k(m) - 3*o(m). Suppose a(f) = 0. What is f?
-3, 1/3
Let u(i) = 4*i**2 - 11*i + 13. Let z(a) = -a**2 - a - 1. Let j(d) = u(d) + z(d). Factor j(k).
3*(k - 2)**2
Let l be (-1)/(4*1/16). Let m be 3*(32/(-42))/l. What is o in -8/7*o + 6/7*o**3 + m*o**4 - 2/7*o**5 + 0 - 8/7*o**2 = 0?
-1, 0, 2
Let f(s) be the second derivative of -s**7/3360 - s**6/720 - s**5/480 - s**4/4 + 3*s. Let b(w) be the third derivative of f(w). Factor b(l).
-(l + 1)*(3*l + 1)/4
Let l(k) be the first derivative of k**6/45 + 2*k**5/15 + k**4/3 + 4*k**3/9 + k**2/3 - k + 2. Let w(v) be the first derivative of l(v). Factor w(p).
2*(p + 1)**4/3
Let d be (-2)/6 - 16/(-3). Suppose 0 = -d*i + 3 + 7. What is y in 4*y**2 + i*y - 6*y**2 + 2*y = 0?
0, 2
Let h(z) be the second derivative of z**6/6 + 3*z**5/4 - 5*z**4/4 - 55*z**3/6 - 15*z**2 + 41*z. Factor h(j).
5*(j - 2)*(j + 1)**2*(j + 3)
Let c be (5/(-5))/(3/(-12)). Let r be 12/30*2/c. Determine g so that -1/5*g + 0 + r*g**2 = 0.
0, 1
Let p(u) be the third derivative of u**8/84 + 4*u**7/105 + u**6/30 - 8*u**2. Factor p(x).
4*x**3*(x + 1)**2
Let p(v) be the first derivative of -v**3/3 + v + 7. Let o(q) = -5*q**2 - q + 6. Let s(d) = -o(d) + 6*p(d). Factor s(a).
-a*(a - 1)
Factor 2/3 + 0*q**3 + 0*q + 2/3*q**4 - 4/3*q**2.
2*(q - 1)**2*(q + 1)**2/3
Let a be ((2 - 5) + 3)/(-1*2). Factor 8/5*b**4 + 4/5*b**2 + 2/5*b - 14/5*b**3 + a.
2*b*(b - 1)**2*(4*b + 1)/5
Let y = -24 - -28. Let s(a) be the second derivative of 3/80*a**5 - 1/24*a**3 + 0*a**y + 0*a**2 + 0 - 2*a - 1/60*a**6. Factor s(c).
-c*(c - 1)**2*(2*c + 1)/4
Find t, given that 34/7*t**2 + 12/7 + 2/7*t**4 - 34/7*t - 2*t**3 = 0.
1, 2, 3
Factor -1/6*y**3 + 0*y**2 - 1/3 + 1/2*y.
-(y - 1)**2*(y + 2)/6
Suppose 3*j - 6 = -3*n - 0, 10 = 5*n. Factor 0 + 1/5*t**2 + j*t - 1/5*t**3.
-t**2*(t - 1)/5
Let t(o) be the third derivative of -o**6/120 + o**5/20 + o**3/6 + 3*o**2. Let c(s) be the first derivative of t(s). Factor c(f).
-3*f*(f - 2)
Factor -v + 3*v - 3*v**2 - 3*v + 3*v + v**3.
v*(v - 2)*(v - 1)
Let v be (-248)/(-144) + 6/(-4). Let i(u) be the second derivative of 0 - v*u**3 + 1/3*u**2 - 4*u + 1/18*u**4. Find s, given that i(s) = 0.
1
Let a(p) be the second derivative of -3*p**5/16 + 7*p**4/16 + p**3 - 3*p**2/2 + 8*p. Factor a(d).
-3*(d - 2)*(d + 1)*(5*d - 2)/4
Let w(u) be the third derivative of -u**9/30240 + u**8/2520 - u**7/504 + u**6/180 + u**5/6 - 10*u**2. Let i(n) be the third derivative of w(n). Factor i(t).
-2*(t - 2)*(t - 1)**2
Let a(h) = -8*h - 48. Let r be a(-6). Solve r + 0*v + 1/5*v**2 = 0.
0
Suppose 4 = -h - 0*h, b = -2*h - 4. What is j in -b*j + 7*j**2 - j**3 - j**2 + j - 2*j**3 = 0?
0, 1
Let u(p) be the first derivative of -25*p**8/672 + p**7/84 + p**6/15 + p**5/30 - 3*p**2/2 + 2. Let t(z) be the second derivative of u(z). Solve t(k) = 0 for k.
-2/5, 0, 1
Let a(n) = 11*n**5 + 23*n**4 - 6*n**3 - 13*n**2 - 5. Let b(f) = -17*f**5 - 35*f**4 + 9*f**3 + 19*f**2 + 8. Let t(k) = 8*a(k) + 5*b(k). Factor t(m).
3*m**2*(m - 1)*(m + 1)*(m + 3)
Suppose -6*o + 4*o = -72. Let r be (5/(-15))/((-10)/o). Factor -r*h - 4/5 - 2/5*h**2.
-2*(h + 1)*(h + 2)/5
Let c(k) = -k**2 - 12*k - 14. Let j be c(-10). Let u(g) = -g**2. Let m(f) = 7*f**2 - 4*f + 4. Let r(a) = j*u(a) + m(a). Factor r(s).
(s - 2)**2
Let l be (-42)/63 + (-76)/(-42). Let -10/7*x**2 + l*x**3 + 4/7*x + 0 - 2/7*x**4 = 0. What is x?
0, 1, 2
Factor -4*f**5 - 4*f**4 - 5*f**2 + 7*f**2 + 4*f**2 - 4*f - 4 + 2*f**2 + 8*f**3.
-4*(f - 1)**2*(f + 1)**3
Let t = 1 + -1. Suppose t = f + 3*f - 8. Find p such that -3*p**2 + p + 2*p**4 + 2*p**3 - f*p**3 + 1 - p**3 = 0.
-1, -1/2, 1
Let n(q) = 4*q**5 - 12*q**4 - 12*q**3 + 23*q**2 - 2*q - 6. Let f(v) = -5*v**5 + 12*v**4 + 12*v**3 - 22*v**2 + v + 6. Let x(d) = -5*f(d) - 4*n(d). Factor x(t).
3*(t - 1)**3*(t + 1)*(3*t + 2)
Let 0 + 3/7*i + 3/7*i**4 + 9/7*i**3 + 9/7*i**2 = 0. Calculate i.
-1, 0
Let y(t) = -3*t**4 - 5*t**3 - 9*t**2 - 5*t + 2. Suppose 22 = 4*z + 6. Let v(l) = -l**4 - 2*l**3 - 4*l**2 - 2*l + 1. Let r(p) = z*y(p) - 10*v(p). Factor r(x).
-2*(x - 1)**2*(x + 1)**2
Let c(y) be the third derivative of y**8/2016 - y**7/1260 - y**6/720 + y**5/360 + 3*y**2. Factor c(j).
j**2*(j - 1)**2*(j + 1)/6
Let p be (-48)/(-15) - 9/45. Determine a, given that -2/7 - 6/7*a**2 - 6/7*a - 2/7*a**p = 0.
-1
Let q = -5 - -5. Factor 2*a**3 + q*a + 4*a**2 + 4*a - a - a.
2*a*(a + 1)**2
Let v(w) = -w**5 + w**4 + w**3 - w**2 + w. Let l(j) = -16*j**5 + 8*j**4 + 8*j**3 - 16*j**2 + 14*j. Let r(x) = -2*l(x) + 28*v(x). Let r(p) = 0. Calculate p.
-1, 0
Factor -2/7*x**2 + 0*x + 2/7.
-2*(x - 1)*(x + 1)/7
Let q be (-8)/36 + (-12)/(-27). Factor 0*o - q*o**2 + 2/9.
-2*(o - 1)*(o + 1)/9
Let o(z) be the second derivative of z**6/6 - 2*z**5/5 + z**4/12 + z**3/3 - 3*z + 11. Determine p, given that o(p) = 0.
-2/5, 0, 1
Let g = 4 + -26/7. Factor -2/7*l**2 + g - 2/7*l**3 + 2/7*l.
-2*(l - 1)*(l + 1)**2/7
Let