*k**4 + 18*k**3 + 10*k**2 - 6*k. Let i(v) = 16*v**4 - 17*v**3 - 9*v**2 + 5*v. Let u(w) = -5*g(w) - 6*i(w). Factor u(j).
-4*j**2*(j - 1)*(4*j + 1)
Suppose 14 = 3*p - 2*q, 18 = 3*p - 0*q - 3*q. Determine m, given that -2*m**2 + 0*m - m**3 + m - p*m = 0.
-1, 0
Let g(o) be the third derivative of 0*o + 1/150*o**5 + 0 - 1/120*o**4 - 1/600*o**6 - 2*o**2 + 0*o**3. Factor g(x).
-x*(x - 1)**2/5
Let m(z) = z - 11. Let c be m(15). Let q(h) be the third derivative of -3*h**2 + 0*h**c + 0 + 0*h + 1/8*h**3 - 1/80*h**5. Suppose q(d) = 0. Calculate d.
-1, 1
Suppose -9*h - 5 = -32. Suppose -2*o = 3*q - 13, -q + 7 = o + o. Solve o*m - m + 6*m**2 + 6*m**h + m + 2*m**4 = 0 for m.
-1, 0
Let t(c) = -c**3 - 4*c**2 - c + 1. Let l be t(-4). Find r, given that r**3 - r**4 + 3*r**3 + 0*r**5 + r**2 - r**l - 3*r**3 = 0.
-1, 0, 1
Let q(z) be the third derivative of -z**8/336 + 13*z**7/210 - 19*z**6/120 - 29*z**5/12 - 22*z**4/3 - 32*z**3/3 - 55*z**2. Factor q(y).
-(y - 8)**2*(y + 1)**3
Factor 3*h + 3/2 + 3/2*h**2.
3*(h + 1)**2/2
Let k(v) be the first derivative of 1/30*v**5 + 0*v - 1/18*v**3 - 1/6*v**2 + 1/8*v**4 - 1/36*v**6 - 6. Suppose k(y) = 0. What is y?
-1, 0, 1, 2
Let o(h) be the third derivative of -h**6/240 - 3*h**5/80 - h**4/8 + h**3/2 - 6*h**2. Let j(m) be the first derivative of o(m). Factor j(q).
-3*(q + 1)*(q + 2)/2
Let u(j) be the second derivative of -1/165*j**6 + 0*j**2 + 0 + 5*j + 0*j**3 + 1/66*j**4 + 0*j**5. Factor u(x).
-2*x**2*(x - 1)*(x + 1)/11
Let m be (3/(-5))/(((-77)/(-35))/(-11)). Determine b, given that 0 + 1/3*b - 1/6*b**m + 1/6*b**2 = 0.
-1, 0, 2
Suppose -2*y + 43 - 1 = 0. Factor 19*f**4 - 2*f**5 - f**3 - y*f**4 + 2*f**2 + 3*f**3.
-2*f**2*(f - 1)*(f + 1)**2
Let t(d) be the first derivative of 0*d**2 + 0*d**3 - 1/15*d**5 + 3 - 2*d + 1/45*d**6 + 0*d**4. Let z(c) be the first derivative of t(c). Factor z(r).
2*r**3*(r - 2)/3
Suppose -8 = -j + 3*s, -2*j = -j + 3*s - 2. Let f(k) be the first derivative of 0*k + 0*k**2 + 0*k**3 - 2 - 1/6*k**4 - 2/15*k**j. Factor f(x).
-2*x**3*(x + 1)/3
Find o such that -4*o**3 + o**2 + 2*o**2 + 3*o**3 - 2*o**2 = 0.
0, 1
Suppose -4*c + 4*n + 35 = 7, 23 = 2*c - 5*n. Let -v**2 - 3*v**3 + c*v**3 - 2*v**3 = 0. Calculate v.
-1, 0
Let o(y) be the first derivative of -y**4/28 - 2*y**3/21 - 27. Suppose o(z) = 0. What is z?
-2, 0
Let a = 24461/6 - 4061. Let k = a + -31/2. Factor -8/3*t**4 + 1/3*t - 1/3 + 5/3*t**2 - k*t**3 - 4/3*t**5.
-(t + 1)**3*(2*t - 1)**2/3
Let s = -1 + 4. What is d in -5 - d**s - 3*d**4 + 7*d**3 - 3*d**2 + 5 = 0?
0, 1
Let x(k) be the second derivative of -k**5/30 + 5*k**4/18 + 2*k**3/3 - 2*k + 5. Factor x(c).
-2*c*(c - 6)*(c + 1)/3
Let z(i) be the third derivative of -i**7/12600 + i**6/1800 + i**5/200 - i**4/8 - 5*i**2. Let y(m) be the second derivative of z(m). Factor y(q).
-(q - 3)*(q + 1)/5
Suppose s = 8 + 2. Solve -33*q - 2 + 10 + s + 9*q**2 + 0 = 0.
2/3, 3
Let d(l) be the first derivative of 2*l**5/15 + l**4/6 - 2*l**3/3 - 5*l**2/3 - 4*l/3 + 6. Factor d(h).
2*(h - 2)*(h + 1)**3/3
Let b = -16 - -18. Factor -42 + 9*d**b + 6*d + 42 + 3*d**3.
3*d*(d + 1)*(d + 2)
Let n = 25/68 - 2/17. Factor n*v**2 + 0 + 0*v + 1/4*v**3.
v**2*(v + 1)/4
Let u(t) = t**2 + 4*t - 2. Let v be u(-5). Factor v*z**2 + 3 + 12*z + 8 + 1.
3*(z + 2)**2
Let g(z) be the first derivative of -z**4/42 - 8*z**3/21 - 16*z**2/7 - 4*z - 4. Let w(q) be the first derivative of g(q). Let w(k) = 0. Calculate k.
-4
Let u(o) be the first derivative of o**6/2 + 9*o**5/5 + 3*o**4/4 - 3*o**3 - 3*o**2 + 8. Find p, given that u(p) = 0.
-2, -1, 0, 1
Let j(c) be the third derivative of 7*c**2 + 1/10*c**7 - 1/5*c**5 + 0*c**4 + 1/2*c**6 + 0*c**3 + 0*c + 0 - 7/8*c**8. What is r in j(r) = 0?
-1/2, 0, 2/7
Factor -4/7 + 4/7*k**2 - 4/7*k + 4/7*k**3.
4*(k - 1)*(k + 1)**2/7
Let k(r) = 7*r**3 - 3*r**2 - 6*r + 6. Let h(s) = 20*s**3 - 9*s**2 - 17*s + 17. Let u(p) = 6*h(p) - 17*k(p). Factor u(j).
j**2*(j - 3)
Let q(n) = 11*n - 42. Let s be q(4). Let 4/7*h + 0 - 2/7*h**s = 0. What is h?
0, 2
Let k = 40/77 - 3/154. Determine w, given that 0 + 0*w - k*w**2 = 0.
0
Let f be ((-3)/(-18) + 0)*(-2)/(-20). Let b(a) be the third derivative of 0*a**4 - a**2 - 1/210*a**7 + 0*a - f*a**5 + 0 - 1/60*a**6 + 0*a**3. Factor b(y).
-y**2*(y + 1)**2
Factor -32*g**3 - 20*g**4 + 4*g**2 + 22*g**4 + 62*g**4.
4*g**2*(4*g - 1)**2
Let -16/9*h**4 + 8/9*h**5 + 0 + 0*h + 10/9*h**3 - 2/9*h**2 = 0. Calculate h.
0, 1/2, 1
Suppose -3*h = -0 - 6. Let q(d) = -d**3 + 3*d**2 - d - 2. Let i be q(h). Determine k, given that 0*k**3 + i + 0*k + 1/2*k**2 - 1/2*k**4 = 0.
-1, 0, 1
Factor 8/3*j**2 - 4/3*j + 0 - 8/3*j**4 + 4/3*j**5 + 0*j**3.
4*j*(j - 1)**3*(j + 1)/3
Let m(l) = -l - 3*l**3 - 2 + 0 - l**2 + 1. Let d be m(-1). Find b, given that 5*b - 5*b - b**5 - 2*b**3 + 3*b - 4*b**4 + 1 + 2*b**d + b**4 = 0.
-1, 1
Suppose -4*j + 3 = -9. Suppose -4*h = -0 + 16, 4*m - 20 = j*h. Factor a**3 - 9/4*a - 5/2*a**m - 1/2 + 3*a**4 + 5/4*a**5.
(a - 1)*(a + 1)**3*(5*a + 2)/4
Factor 35*t**2 + 5/3*t**3 - 605/3 + 165*t.
5*(t - 1)*(t + 11)**2/3
Solve 16*f**2 + 3*f - f + 6*f**3 - 8*f**2 + 0*f = 0.
-1, -1/3, 0
Let m be (-2 - -2) + (-4)/(-2). Factor -y - 3*y**2 + 3*y**m - 2*y**2 - 3*y - 2.
-2*(y + 1)**2
Let j(f) be the second derivative of 9*f**5/190 + 8*f**4/57 - 4*f**3/57 - 53*f. Determine d, given that j(d) = 0.
-2, 0, 2/9
Factor 3/2*z**5 - 21/2*z - 3*z**3 + 3 + 12*z**2 - 3*z**4.
3*(z - 1)**4*(z + 2)/2
Let q(y) = -y**3 - 8*y**2 - y - 6. Let p be q(-8). Determine m, given that -3/5 + 9/5*m**4 - 6/5*m**p + 9/5*m - 3/5*m**5 - 6/5*m**3 = 0.
-1, 1
Let g(f) = -f**4 - f - 3. Let v(i) = i**4 + i**3 + i**2 + i + 2. Let n(k) = -2*g(k) - 3*v(k). Factor n(h).
-h*(h + 1)**3
Suppose 2*m + 4*w - 10 + 12 = 0, 22 = 4*m - 5*w. Factor -6/5*v**2 + 0*v + 0*v**4 + 9/5*v**m + 0 - 3/5*v**5.
-3*v**2*(v - 1)**2*(v + 2)/5
Let p(y) = -y**3 - 4*y - 2 + 4*y**2 - 3*y**2 - 3*y**2. Let o be p(-3). Let o*m**3 + 3*m - m - 6*m**4 - 5*m**3 - 10*m**2 = 0. Calculate m.
0, 1/3, 1
Suppose -12/5 + 12/5*a + 27/5*a**2 - 3/5*a**3 - 6/5*a**4 = 0. What is a?
-2, -1, 1/2, 2
Let i be (-2 - 8/(-3)) + 0. Let c(t) be the first derivative of -1 + i*t**3 + 0*t - t**2. Let c(k) = 0. Calculate k.
0, 1
Let a(i) = 18*i**2 + 30*i - 5. Let l(h) be the first derivative of 2*h**3 + 5*h**2 - 2*h - 5. Let x(b) = -2*a(b) + 7*l(b). Determine k, given that x(k) = 0.
-2, 1/3
Let m be (360/819)/1 + 2/(-13). Factor 4/7 + 8/7*h**2 - m*h**3 - 10/7*h.
-2*(h - 2)*(h - 1)**2/7
Let i(y) = 4*y**4 - 30*y**3 + 17*y**2 + 24*y. Let f(p) = -9*p**4 + 60*p**3 - 33*p**2 - 48*p. Let r(z) = 5*f(z) + 9*i(z). Factor r(j).
-3*j*(j - 2)**2*(3*j + 2)
Let c(l) be the third derivative of l**5/160 - l**4/32 - 18*l**2. Solve c(d) = 0.
0, 2
Let u = -8 - -12. Let q be 0*(3 - (-2 + u)). Factor 0 + q*i - 4/7*i**3 + 2/7*i**2 + 2/7*i**4.
2*i**2*(i - 1)**2/7
What is u in 0 - 3/7*u**2 - 6/7*u = 0?
-2, 0
Let x(z) be the second derivative of z**6/6 + z**5/4 - 25*z**4/12 + 5*z**3/2 + 2*z + 2. Factor x(l).
5*l*(l - 1)**2*(l + 3)
Let v(z) = z**3 + 6*z**2 + 5. Let o be v(-6). Solve o*p**3 + 0 - 4*p**3 + 0 = 0.
0
Factor -1 + 21/2*p**3 - 17*p**2 + 15/2*p.
(p - 1)*(3*p - 1)*(7*p - 2)/2
Let m be 3 + (-1)/1*1. Factor 4*j**2 - m*j**2 + 4*j**5 + 7*j - 6*j**4 - 7*j.
2*j**2*(j - 1)**2*(2*j + 1)
Let v be (-1)/4 + 2/8. Let m be (0 - -10)*33/110. Factor -2/5*y**m + 4/5*y**2 + v + 0*y.
-2*y**2*(y - 2)/5
Find t, given that -2*t**4 - 5/2*t**2 - 8*t**3 + 19/2*t - 3 = 0.
-3, -2, 1/2
Let v(n) be the first derivative of -n**3/4 + 3*n**2/2 + 15*n/4 - 47. Factor v(m).
-3*(m - 5)*(m + 1)/4
Let q(i) be the first derivative of -i**2 + 0*i + 1/20*i**5 + 0*i**3 + 2 - 1/12*i**4. Let w(f) be the second derivative of q(f). Solve w(v) = 0.
0, 2/3
Let y(p) = -9*p**4 + 7*p**3 - 2*p**2 - 4*p. Let j(l) = 18*l**4 - 14*l**3 + 3*l**2 + 7*l. Let v(h) = 4*j(h) + 7*y(h). Factor v(n).
n**2*(n - 1)*(9*n + 2)
Let d(j) = j**3 - 16*j**2 + 16*j - 15. Let x be d(15). Let h(p) be the second derivative of 0 + x*p**3 + 1/42*p**4 - 2*p - 1/7*p**2. What is i in h(i) = 0?
-1, 1
Suppose 5 = 5*m - 5. Let p = 0 + m. Let 2 + 0*b**2 - p*b**2 + b + 2 - 2 - b**3 = 0. Calculate b.
-2, -1, 1
Factor 0 + 4/3*a - 1/3*a**4 - 3*a**2 + 2*a**3.
-a*(a - 4)*(a - 1)**2/3
Factor -10/13*h**3 + 18/13*h**2 + 4/13 - 14/13*h + 2/13*h**4.
2*(h - 2)*(h - 1)**3/13
Let l(d) be the first derivative of -d**7/945 + d**5/9