= f**2 - f. Suppose 3 = -0*n + 3*n. Let i(t) = 2*t**2 + t. Let o(x) = n*v(x) - i(x). Factor o(h).
-h*(h + 2)
Suppose -2/11*c**2 - 1/11*c**3 + 0*c + 0 + 1/11*c**4 = 0. What is c?
-1, 0, 2
Let g(j) be the second derivative of -j**8/40320 + j**7/7560 - j**6/4320 - 5*j**4/12 - 4*j. Let u(d) be the third derivative of g(d). Factor u(o).
-o*(o - 1)**2/6
Let l(n) = 17*n**4 - 2*n**3 - n**2 + 3*n - 3. Let d(c) = -16*c**4 + 2*c**3 - 4*c + 4. Let v(i) = 3*d(i) + 4*l(i). Suppose v(s) = 0. What is s?
-2/5, 0, 1/2
Let h(f) = -f**3 + f**2 - f + 4. Let g be h(0). Let t be (8 + -2)*15/18. Factor 6 - 3*p**5 + 4*p**3 + p**t - g + 2*p**4 - 2*p - 4*p**2.
-2*(p - 1)**3*(p + 1)**2
Let g be (6 - 24)*2/(-6). Let o be 44/56 + g/(-21). Factor -o*q - 1/2*q**2 + 0.
-q*(q + 1)/2
Suppose 0 = -88*u + 91*u - 6. Factor -1/5*o + 2/5*o**u - 1/5*o**3 + 0.
-o*(o - 1)**2/5
Let k = 37 - 109. Let v = 506/7 + k. Find w such that 0*w - 2/7*w**3 + 2/7*w**4 + 0 + 2/7*w**5 - v*w**2 = 0.
-1, 0, 1
Let d(i) be the first derivative of -i**6/180 - i**5/15 - i**4/3 + 2*i**3/3 - 4. Let b(m) be the third derivative of d(m). Factor b(c).
-2*(c + 2)**2
Let g be (-781)/(-5396) + 2/19. Determine t, given that 0*t - 1/8*t**4 - g*t**3 - 1/8*t**2 + 0 = 0.
-1, 0
Suppose 8 = -v + 5*v. Suppose 5*y = 4*p, -y - y = -p. Factor 0*h**3 + 1/4*h**5 + 0*h**v + p*h + 0 + 1/4*h**4.
h**4*(h + 1)/4
Let v(m) be the first derivative of -2*m**3 - m**3 + 9 + 2*m**3 + 3*m - 12. Determine o so that v(o) = 0.
-1, 1
Let h(w) be the third derivative of -2*w**7/105 - w**6/6 - 3*w**5/5 - 7*w**4/6 - 4*w**3/3 - 20*w**2. Let h(p) = 0. Calculate p.
-2, -1
Let k = -7 + 9. Factor -9*p + 4 + 8*p**2 + k*p**3 + 7*p + 12*p.
2*(p + 1)**2*(p + 2)
Let x = -633 - -37981/60. Let y(z) be the third derivative of 0*z**3 + 1/105*z**7 + 0*z**4 + 1/90*z**5 - 1/504*z**8 + 0*z + 3*z**2 + 0 - x*z**6. Factor y(b).
-2*b**2*(b - 1)**3/3
Suppose 4*j + 2*r + 4 = 10, -5*r = -3*j + 24. Let q(s) be the second derivative of 7/2*s**j + 0 - 12/5*s**5 - 2*s**4 + s - 3/2*s**2. What is t in q(t) = 0?
-1, 1/4
Let u(g) = g + 7. Let t be u(-4). Determine n, given that 0*n**2 - 2/3*n + 0 + 2/3*n**t = 0.
-1, 0, 1
Let m(a) be the second derivative of -3*a**5/5 - 4*a**4/3 - 8*a**3/9 + 12*a. Factor m(k).
-4*k*(3*k + 2)**2/3
Let z(q) be the third derivative of q**5/360 + q**4/48 + q**3/18 - q**2. Suppose z(g) = 0. Calculate g.
-2, -1
Let u = -2 + 5/2. Determine l, given that u - 1/2*l**2 + 0*l = 0.
-1, 1
Suppose -8 = -5*r + 2*x, 3*x + 20 = -2*r + 8. Let i = -16 + 33/2. Let -n + r + i*n**2 = 0. What is n?
0, 2
Find z, given that 0 + 6/7*z**3 - 6/7*z - 2/7*z**4 + 2/7*z**2 = 0.
-1, 0, 1, 3
Let f(n) = -8*n + 1. Let m be f(1). Let o(j) = -j - 4. Let t be o(m). Suppose 2/5*w**t + 1/5*w**4 + 0 + 1/5*w**2 + 0*w = 0. What is w?
-1, 0
Let v(s) = s - 1. Let h(p) = -27*p**2 - 38*p - 1. Let c(q) = -h(q) - 5*v(q). Factor c(g).
3*(g + 1)*(9*g + 2)
Factor 0 - 256*c - 1/2*c**4 - 12*c**3 - 96*c**2.
-c*(c + 8)**3/2
Let n(d) be the first derivative of -d**5/10 - 3*d**4/4 - 4*d**3/3 + 3*d**2/2 + 9*d/2 - 19. Let n(q) = 0. What is q?
-3, -1, 1
Let o(b) be the first derivative of 3 - 5*b**2 + 14/3*b**3 - 4*b. Find l such that o(l) = 0.
-2/7, 1
Let s(m) = 6*m**2 + m + 3. Let n be 9/2 + (-1)/2. Suppose 2*d + 10 = -0. Let b(h) = 6*h**2 + 2. Let k(t) = d*b(t) + n*s(t). Find a such that k(a) = 0.
-1/3, 1
Let r(i) be the third derivative of 1/60*i**5 + 0 + 0*i + 1/24*i**4 + 0*i**3 - i**2. Determine q so that r(q) = 0.
-1, 0
Suppose 8 = 2*j - h, -30 = -5*j - 5*h + 5. Suppose 5*m - 5 - 5 = 0. Factor 0*r**j + 0*r**2 + r**5 - 2*r**3 - r**3 - m*r**2.
r**2*(r - 2)*(r + 1)**2
Let z be 8 + -11 + (1 - -6). Let f(h) be the second derivative of 0*h**2 + 1/70*h**5 - 1/21*h**3 + h + 0 + 0*h**z. Factor f(i).
2*i*(i - 1)*(i + 1)/7
Let x be 2 + -10 + -1 + 4. Let n = x - -7. Let 2/5*d**n + 2/5 - 4/5*d = 0. What is d?
1
Let c be (-57)/(-133) - (-6)/(-14). Let -1/2*o**3 + 0*o**2 + 1/2*o**4 + 0*o + c = 0. Calculate o.
0, 1
Let z be (5 - 0) + -2 - -2. Suppose -2*v = 2*h - 16, -2*h - z*v = -42 + 14. Factor 4*u**h - 4*u**5 - u**3 + 8*u**5 - u**4.
u**3*(u + 1)*(4*u - 1)
Let p be ((-5)/(-175)*7)/(4/8). Factor -4/5 - 8/5*w**2 + 2*w + p*w**3.
2*(w - 2)*(w - 1)**2/5
Let c = 247 + -491/2. Suppose -c*o**2 + 0*o**3 + 0 + 3/4*o**5 + 3/2*o**4 - 3/4*o = 0. Calculate o.
-1, 0, 1
Let c be -14*(-3)/(6*1). Suppose 0 = 4*z + 3*q - 3, c*z - 4*z = 3*q + 18. Factor 12*m**2 - 2 - 42*m**4 + 6*m - 18*m**5 - 20*m**z - 2 + 2.
-2*(m + 1)**3*(3*m - 1)**2
Suppose -2 + 18 = 4*z. Suppose -4*v - v = -z*y - 23, 5*y + 16 = 2*v. What is a in -2*a**2 + 4 - a - 4 - a**v = 0?
-1, 0
Let 0 + 6/7*s**2 + 4/7*s + 2/7*s**3 = 0. Calculate s.
-2, -1, 0
Let y be 9 - (-17)/((-1309)/682). Factor 3/7*h**2 + 0 + 2/7*h - y*h**4 + 0*h**3.
-h*(h - 2)*(h + 1)**2/7
Suppose 6 - 3*r**2 + 3*r - 33 + 15*r = 0. What is r?
3
Solve -2/3*j + 2/3*j**2 - 4/3 = 0 for j.
-1, 2
Let a(l) = -4*l**2 - 2*l - 1. Let j(r) = r**4 + r**2 + 1. Let f(k) = 3*a(k) + 3*j(k). Factor f(y).
3*y*(y - 2)*(y + 1)**2
Let x be 1 + 1 + -3 + -7. Let b be (-2)/x - 23/(-4). Factor -14*m + 0*m**2 - 8 + b*m - 2*m**2.
-2*(m + 2)**2
Let f(k) be the first derivative of -k**5/20 - 3*k**4/8 - 13*k**3/12 - 3*k**2/2 - k + 8. Find x, given that f(x) = 0.
-2, -1
Let b(m) be the third derivative of 0*m**4 + 0 + 0*m**3 - 1/24*m**6 - 1/30*m**5 + m**2 + 0*m. Let b(w) = 0. Calculate w.
-2/5, 0
Let t(q) be the second derivative of 0*q**3 - 1/10*q**6 + 0 - 5/42*q**7 + 0*q**4 + 1/10*q**5 - 2*q + 0*q**2. Solve t(v) = 0 for v.
-1, 0, 2/5
Suppose 2*q + 17*r = 13*r + 16, 0 = 4*q + 5*r - 26. Factor 3 + 33*c**3 - 12*c**2 - 27*c**q - 9/2*c + 15/2*c**5.
3*(c - 1)**4*(5*c + 2)/2
Suppose -2 = -4*j - 18. Let c be (6/j)/(9/(-4)). Let 5/3*h**2 + c*h + 1/3*h**4 + 4/3*h**3 + 0 = 0. What is h?
-2, -1, 0
Let i = 661 - 3301/5. Factor -i*d - 1/5*d**2 - 3/5.
-(d + 1)*(d + 3)/5
Let i(t) = -t**3 + 8*t**2 - 13*t + 7. Let s be i(6). Let v(x) be the first derivative of -s + 1/6*x**2 - 1/9*x**3 + 0*x. Factor v(z).
-z*(z - 1)/3
Suppose 2 = q - 2. Let w(r) be the second derivative of -1/12*r**q + 0*r**3 + 0 + 1/20*r**5 - r + 0*r**2. Factor w(t).
t**2*(t - 1)
Let o be (8/(-6) + 2)*6. Suppose o = 5*k - 16. Factor 5*l**2 + l + l**k + 5*l**3 + l - l**3 + 0*l.
l*(l + 1)**2*(l + 2)
Suppose -4*p + 7 = -1. Suppose -p*w = -w - 2. Factor 0*d - 1/3*d**w + 0*d**3 + 0 + 1/3*d**4.
d**2*(d - 1)*(d + 1)/3
Factor 2/5 - 8/5*p**3 + 12/5*p**2 - 8/5*p + 2/5*p**4.
2*(p - 1)**4/5
Suppose 5*b = -n, 5*n + b = -2*b + 22. Let r(m) be the third derivative of 1/24*m**4 + 0 + 0*m**3 + 0*m - 3*m**2 - 1/60*m**n. What is c in r(c) = 0?
0, 1
Let f be (-74)/(-8) - (-3)/(-12). Let c = -9 + f. Factor 0*p + 2/9*p**4 + 0*p**3 + 0*p**2 + c + 2/9*p**5.
2*p**4*(p + 1)/9
Let y(f) be the first derivative of -f**6/15 + 8*f**5/25 - 2*f**4/5 - 4*f**3/15 + f**2 - 4*f/5 + 7. Suppose y(j) = 0. What is j?
-1, 1, 2
Let l(z) = 2*z**2 + 4*z + 3. Let h be ((-8)/(-10))/((-10)/25). Let w be l(h). What is d in -3*d**5 - 5*d**4 + d**3 + 3*d**2 + 5*d - w*d + 2*d**2 = 0?
-1, -2/3, 0, 1
Suppose 2*m + 3 = 13. Solve -7*p**2 + 11*p**2 - m*p**2 = 0.
0
Suppose -2*p + 5 = -p. Solve 4*o**3 - 2*o**3 + 2*o**4 - p*o**2 + 3*o**2 + 2*o**5 - 4*o**3 = 0 for o.
-1, 0, 1
Let v be (-7)/(-6) + 5 + 33/(-6). Factor -4/3*b**3 + 0*b - v*b**2 - 2/3*b**4 + 0.
-2*b**2*(b + 1)**2/3
Let k(x) be the second derivative of 3*x + 31/6*x**4 + 4*x**2 - 3/2*x**5 + 0 - 20/3*x**3. Find q such that k(q) = 0.
2/5, 2/3, 1
Let d be (-2)/4 + (-363)/1110. Let g = -1/37 - d. Solve -2/5*x**2 - g + 6/5*x = 0 for x.
1, 2
Let c(o) be the second derivative of -o**9/60480 + o**8/8960 - o**7/3360 + o**6/2880 + o**4/3 - 5*o. Let b(i) be the third derivative of c(i). Factor b(r).
-r*(r - 1)**3/4
Determine a so that a**2 - 2*a + 1 + 6*a - 2*a = 0.
-1
Let l = 3 - 1. Let w = l + 3. Factor -p**4 + 3*p**4 - p + 0*p**w - 2*p**2 + 0*p**4 + p**5.
p*(p - 1)*(p + 1)**3
Let y = 63 - 61. Let g(i) be the first derivative of -2/3*i + 2 + 1/9*i**3 - 1/6*i**y. Factor g(b).
(b - 2)*(b + 1)/3
Let s(p) = p**2 - 13*p - 21. Let r be s(15). What is b in r - 5 + 5*b**2 + b**2 + 7*b + 7*b = 0?
-2, -1/3
Let w be (60/(-36) + 2/3)/(-2). Let 0 + 1/4*i + 1/4*i**3 + w*i**2 = 0. What is i?
-1, 0
Let d(g) be the first derivative of 0*g**5 + 0*g**2 - 3 + 0*g**3 - 3/8*g**4 + 0*g + 1/4*g**6. Factor d(r).
