et n(m) be the first derivative of -m**3 + 27*m**2 - 51*m - 168. Factor n(k).
-3*(k - 17)*(k - 1)
Factor -6*t**2 - 4*t**2 - t**3 - 5*t**5 + 5*t**2 + 5*t**4 + 6*t**3.
-5*t**2*(t - 1)**2*(t + 1)
Suppose -186 = -109*y + 47*y. Let a(x) be the first derivative of 5*x**4 - 5 + 0*x + 4*x**5 + 5/3*x**y + 0*x**2. Factor a(j).
5*j**2*(2*j + 1)**2
Let u = 883/210 - 57/14. Let q(a) be the first derivative of 5 - 2/5*a - 3/20*a**4 + u*a**3 + 3/10*a**2. Factor q(k).
-(k - 1)*(k + 1)*(3*k - 2)/5
Let i(u) be the second derivative of -1/5*u**6 + 0*u**2 + 1/21*u**7 + 1/2*u**4 - 7*u - 2/3*u**3 + 1/10*u**5 + 0. Solve i(x) = 0.
-1, 0, 1, 2
Let f be 16/336*35*6/5. Let c(h) be the second derivative of -4/11*h**f + 1/33*h**4 - 7/33*h**3 + 0 + 8*h. Solve c(z) = 0 for z.
-1/2, 4
Let v(o) be the second derivative of 10*o + 0 - 5/48*o**3 + 1/48*o**4 + 1/8*o**2. Let v(m) = 0. What is m?
1/2, 2
Let a be (11 - (-188)/(-28))*(-28)/36*-2. Factor -25/3*q**2 + 0 - 5/3*q**3 - a*q.
-5*q*(q + 1)*(q + 4)/3
Let w(d) = -d + 8. Let f be (0 + 2)/((-13)/(-39)). Let i be w(f). Factor -4*t + 36*t**4 + 2 + 4*t**2 - i + 4*t**3 - 40*t**4.
-4*t*(t - 1)**2*(t + 1)
Let j be 4/(-18) + 30978/162. Factor -f**3 + 191*f - 2*f**2 - j*f - f**3.
-2*f**2*(f + 1)
Let d(r) be the second derivative of -32*r**5/45 - 104*r**4/27 + 61*r**3/9 - 4*r**2 - 390*r. Let d(l) = 0. What is l?
-4, 3/8
Let d(t) = t**2 - 7*t + 6. Let u be d(6). Let q(f) = f**2 - 3*f + 2. Let i be q(u). Let 205*j + 2*j**i - 205*j = 0. What is j?
0
Let q(k) be the third derivative of -5/18*k**4 + 0*k + 1/90*k**5 - 21*k**2 + 0 + 25/9*k**3. Determine b, given that q(b) = 0.
5
Find h, given that -31*h**4 - 28*h**4 + 40*h**3 - 2*h**5 + 95*h**4 - 30*h**4 - 8*h**5 - 24*h**2 = 0.
-2, 0, 3/5, 2
Suppose 2*f = f + 2. Let l(i) = 5*i - 3*i**f - i - 2 + 8 - i. Let q(w) = w + 1. Let c(p) = -l(p) + 12*q(p). Factor c(m).
3*(m + 1)*(m + 2)
Let w(c) be the second derivative of -2*c**6/15 + 9*c**5/5 - 2*c**4 - 112*c**3/3 - 4*c + 5. What is l in w(l) = 0?
-2, 0, 4, 7
Let n(m) be the third derivative of -m**6/360 + m**5/90 - m**4/72 + 54*m**2 + 3*m. Factor n(y).
-y*(y - 1)**2/3
Let b(m) be the second derivative of -m**7/105 + 3*m**5/25 + 4*m**4/15 + m**3/5 - 21*m - 1. Find v such that b(v) = 0.
-1, 0, 3
Let r(v) = 6*v**5 - 7*v**4 - 23*v**3 - 46*v**2 - 31*v. Let d(q) = -7*q**5 + 9*q**4 + 25*q**3 + 45*q**2 + 30*q. Let f(z) = 5*d(z) + 6*r(z). Solve f(g) = 0 for g.
-3, -1, 0, 4
Let i(k) = -k**2 - 6*k + 1. Let q be i(-7). Let h(c) = -c**2 - 7*c - 6. Let u be h(q). Determine f so that 6*f**2 - 8/3 + u*f = 0.
-2/3, 2/3
Let n(d) = -25*d**2 + 519*d + 9. Let z(v) = 6*v**2 - 130*v - 2. Let k(u) = -2*n(u) - 9*z(u). Factor k(i).
-4*i*(i - 33)
Let b(c) = -c**2 - 2*c - 1. Let j(i) = -5*i**2 - 7*i - 4. Let y(o) = -4*b(o) + j(o). Let x be y(1). Factor -63/5*w**3 + x - 24/5*w**2 + 12/5*w.
-3*w*(3*w + 2)*(7*w - 2)/5
Let g = 117 + -113. Solve -3*c**3 + 2*c**2 + c**g - 18 + 16 + 3*c - c**2 = 0.
-1, 1, 2
Let g be (-12)/16*12/(-3) + 0. Suppose 0 = 5*s - 16 + 6. Let 4/9*r**s + 2/9*r - 2/9*r**g - 4/9 = 0. What is r?
-1, 1, 2
Let t(h) = -4*h**5 - 11*h**4 - 15*h**3 - 7*h**2 - 3*h - 2. Let w(x) = -514 - 3*x + x**4 + 2*x + 513. Let i(d) = 5*t(d) - 10*w(d). Let i(q) = 0. Calculate q.
-1, -1/4, 0
Let d(q) = -8*q**3 - 55*q**2 + 52*q + 318. Let o be d(-7). Factor -8/23*a**2 + 6/23*a + 2/23*a**o + 0.
2*a*(a - 3)*(a - 1)/23
Let f(o) = 2*o + 32. Let d be f(-14). Factor d*n**3 - 27*n + 27*n - 8*n**2.
4*n**2*(n - 2)
Suppose -171 = 13*i + 271. Let x be i/(-8) - (91/(-28))/(-13). Find g, given that -1/5*g + 2/5*g**x - g**3 + 4/5*g**2 + 0 = 0.
0, 1/2, 1
Suppose -3*w + 65 - 56 = 0. Let m(k) be the first derivative of -1/16*k**4 - 1/8*k**2 - 1/6*k**w - 2 + 0*k. Factor m(n).
-n*(n + 1)**2/4
Factor 9/4 - 1/4*f**2 + 9/4*f - 1/4*f**3.
-(f - 3)*(f + 1)*(f + 3)/4
Suppose 5*h + 2 = 22. Find b such that -2*b + 24*b**2 - 19*b**3 + 0*b - 48*b**h - 2*b - b**3 = 0.
-1, 0, 1/4, 1/3
Let x(w) be the second derivative of 4/3*w**4 + 0 - 16*w + 1/6*w**6 - 2/3*w**3 - 17/20*w**5 + 0*w**2. Factor x(h).
h*(h - 2)*(h - 1)*(5*h - 2)
Let m(s) = 73*s**2 + 64*s + 21. Let o(f) = -72*f**2 - 68*f - 20. Let r(v) = 4*m(v) + 5*o(v). Factor r(h).
-4*(h + 1)*(17*h + 4)
Let j(d) be the third derivative of 0*d**5 + 0*d**4 + 0*d + 0 + 1/42*d**7 - 5/336*d**8 + 2*d**2 + 0*d**6 + 0*d**3. Factor j(n).
-5*n**4*(n - 1)
Let o(m) be the first derivative of -m**6/21 + 8*m**5/7 + 43*m**4/14 + 44*m**3/21 + 60. Suppose o(y) = 0. Calculate y.
-1, 0, 22
Suppose -4*n + 4*i = -16, 0 = 4*n - i - 2*i - 12. Let h(m) = -8*m + 16. Let u be h(2). Factor -6/5*g**3 + 0*g**4 + u*g + n - 4/5*g**2 + 2/5*g**5.
2*g**2*(g - 2)*(g + 1)**2/5
Let w(d) be the third derivative of -36*d**2 + 0*d**4 + 0*d + 0*d**3 + 0*d**6 + 0 + 1/360*d**5 - 1/1260*d**7. Factor w(q).
-q**2*(q - 1)*(q + 1)/6
Let o(q) be the third derivative of -q**5/180 - 7*q**4/36 - 20*q**3/9 + q**2 - 4*q. Determine d, given that o(d) = 0.
-10, -4
Let u(k) = -k**4 + k**3 - k**2 + k. Let a(t) = 20*t**5 + 23*t**4 - 107*t**3 - 133*t**2 + 133*t + 64. Let x(m) = -a(m) + 5*u(m). Determine w so that x(w) = 0.
-2, -2/5, 1, 2
Let v(o) be the first derivative of o**5/60 + o**4/36 + 14*o - 5. Let c(w) be the first derivative of v(w). Factor c(z).
z**2*(z + 1)/3
Let n(z) = -5 - 2*z**2 + z**2 + 0*z**2 - 24*z. Let q(b) = 2 - 20*b + 32*b + 7 - 1 + b**2 + 24*b. Let j(v) = -8*n(v) - 5*q(v). Factor j(h).
3*h*(h + 4)
Let v(b) = -2*b**3 - 80*b**2 - 8*b + 75. Let d(w) = -w**3 - w**2 - w. Let s(f) = 5*d(f) - v(f). Factor s(n).
-3*(n - 25)*(n - 1)*(n + 1)
Let i = 240/17 - 1423/102. Let m(b) be the third derivative of 0*b + 0 + i*b**3 - 4*b**2 - 1/16*b**4 + 1/120*b**5. Factor m(k).
(k - 2)*(k - 1)/2
Factor i**5 + 8*i + 70*i**4 + 3*i**3 - 2*i**5 - 130*i**4 - 14*i**2 + 64*i**4.
-i*(i - 4)*(i - 1)**2*(i + 2)
Let p = 132 + -128. Let h(a) be the second derivative of -a**3 + 9/2*a**2 + 0 + 1/12*a**p + 5*a. Suppose h(b) = 0. Calculate b.
3
Suppose 2 = 5*s + y, -4*s - y - 1 = -3. Let d(t) be the second derivative of s - t - 1/2*t**3 - 1/20*t**5 - 1/2*t**2 - 1/4*t**4. Factor d(r).
-(r + 1)**3
Factor 1/2*f**4 + 0 - 7/4*f**3 + 1/4*f**5 + 0*f + f**2.
f**2*(f - 1)**2*(f + 4)/4
Let w(g) be the third derivative of 1/60*g**6 - 2/15*g**5 + 0*g**3 + 0 + 1/3*g**4 + 0*g - 13*g**2. Factor w(m).
2*m*(m - 2)**2
Let n(j) be the first derivative of -j**4/8 - 41*j**3/3 - 1681*j**2/4 + 73. Find t, given that n(t) = 0.
-41, 0
Let h(m) be the first derivative of m**5/5 - 3*m**4/4 - m**3 + 7*m**2/2 + 6*m - 56. Factor h(s).
(s - 3)*(s - 2)*(s + 1)**2
Factor 289*v**5 - 650*v**3 + 39*v**4 + 29*v**4 + 654*v**3.
v**3*(17*v + 2)**2
Factor -1215*z - 212 - 5*z**3 + 34 - 3467 - 135*z**2.
-5*(z + 9)**3
Let t be -4 + -4 + 2 + 0. Let x = t - -9. Factor a**2 + 2*a**2 + 3*a**3 - 2*a + 2*a**4 - 9*a**3 + x*a**2.
2*a*(a - 1)**3
Let k(n) = n**2 + 2*n - 3. Let p(y) = 3*y**2 + 9*y - 12. Let m = 13 + -9. Suppose -3*s - 60 = 4*d + d, d - s = -m. Let x(v) = d*k(v) + 2*p(v). Factor x(b).
-3*(b - 1)*(b + 1)
Let r be 9/(-2)*46/(-69). What is k in -4/7*k**r + 2/7*k**4 + 0*k**2 + 0*k + 0 = 0?
0, 2
Suppose -3*a = 3*c - 2*a + 11, -13 = c + 5*a. Let j be (-2)/((c/(-9))/(3/(-9))). Solve 2/3*u**3 - 4/3*u + 2/3*u**j + 0 = 0 for u.
-2, 0, 1
Let a(f) be the second derivative of -f**5/4 - 5*f**4/4 + 25*f**3/3 + 60*f**2 - f + 14. Factor a(p).
-5*(p - 3)*(p + 2)*(p + 4)
Let r(b) be the first derivative of 0*b + 0*b**2 + 1/34*b**4 + 4/51*b**3 - 15. Suppose r(t) = 0. What is t?
-2, 0
Let l(w) be the third derivative of -w**6/240 + w**5/10 - 3*w**4/4 + 8*w**3/3 + 36*w**2. Factor l(v).
-(v - 8)*(v - 2)**2/2
Let h be (-4744)/(-420) + (-11)/(5445/(-22))*3. Determine k so that 16/7*k**4 + 12/7*k**3 - h*k**2 + 50/7*k + 2/7*k**5 + 0 = 0.
-5, 0, 1
Let q = 19463/5 - 3891. Factor 0*c + q*c**3 + 72/5*c**4 + 0*c**2 + 0 + 162/5*c**5.
2*c**3*(9*c + 2)**2/5
Factor z**3 + 3*z**3 - 4*z**2 + 11*z - 8*z - 2*z - 5*z + 4*z**4.
4*z*(z - 1)*(z + 1)**2
Suppose 5*m - 11 = -2*y, -9*m + 5 = -4*m. Let k = 44 + -40. Factor 8*d**2 - 37*d**4 + 33*d**4 + k*d**y + 0*d**2.
-4*d**2*(d - 2)*(d + 1)
Suppose -n = -5*n + 20. Let -25 - f**2 + n*f + 4*f + f + 0 = 0. Calculate f.
5
Let b(g) = 2*g**2 - 14*g + 17. Let s be b(5). Let y be (-1 + s)*(3 - -1)/(-36). Factor -2/9*c + 0 - 2/9*c**3 - y*c**2.
-2*c*(c + 1)**2/9
Factor 0 - 21/5*v - 3/