. Factor g(f).
f*(f - 2)*(f - 1)/2
Let r(q) = -2*q**3 + 21*q**2 - 50*q - 5. Let d be r(4). Factor 1/4*s + 0*s**2 - 1/4*s**d + 0.
-s*(s - 1)*(s + 1)/4
Factor -640*m**2 + 321*m**2 + 320*m**2 - 1.
(m - 1)*(m + 1)
Let z = 1/9 + 2/9. Let f(a) = a**2 - 7*a - 74. Let v be f(-6). Factor -4/3*r**5 - 5*r**3 + 13/3*r**v + 0 + 7/3*r**2 - z*r.
-r*(r - 1)**3*(4*r - 1)/3
Let x = 8/35 - 9/40. Let z(c) be the third derivative of -1/1344*c**8 - 3*c**2 - 1/240*c**6 + 0*c**5 + 0*c**4 + 0*c + 0 + x*c**7 + 0*c**3. Factor z(s).
-s**3*(s - 2)*(s - 1)/4
Let g(i) be the third derivative of 32*i**7/105 + 4*i**6/3 - 31*i**5/15 - 11*i**4/3 - 2*i**3 + 2*i**2 - 396. Factor g(f).
4*(f - 1)*(f + 3)*(4*f + 1)**2
Let z(a) be the second derivative of -a**4/60 + 13*a**3/60 - 3*a**2/10 - 498*a. Determine h so that z(h) = 0.
1/2, 6
Determine p so that 32*p - 18*p**3 - 553*p**2 - 3*p**4 + 565*p**2 + 5*p**4 = 0.
-1, 0, 2, 8
Suppose 0 = 3*k - 5*f + 31, 14 = -2*k + f + f. Let w be 3/1*k*(-1)/4. Factor 3/2*s**2 - 3*s + w.
3*(s - 1)**2/2
Find g such that -35*g**4 - 31*g**3 - 14*g**3 + 5*g**5 + 21*g**2 + 40*g + 14*g**2 = 0.
-1, 0, 1, 8
Let d(v) be the third derivative of v**4/12 - 2*v**3/3 - 3*v**2. Let n be d(7). Determine c, given that -2*c**3 - 1 - c**4 + n*c**4 - 8*c**4 + 2*c = 0.
-1, 1
Let 79*v**5 - 191*v**5 + 8*v**3 - 48*v + 108*v**4 + 96*v**5 - 208*v**2 - 44*v**3 = 0. What is v?
-1, -1/4, 0, 2, 6
Let f(r) be the first derivative of 5*r**6/6 + 3*r**5 - 55*r**4/4 - 5*r**3 + 25*r**2 + 185. What is y in f(y) = 0?
-5, -1, 0, 1, 2
Factor -1/2 + 13/2*x + 143/4*x**3 - 213/8*x**2 - 121/8*x**4.
-(x - 1)**2*(11*x - 2)**2/8
Let q(w) be the second derivative of w**5/30 - 2*w**4/3 + 4*w**3 - 32*w**2/3 + 125*w. What is s in q(s) = 0?
2, 8
Solve -2/3*l**3 + 1/3*l**5 - 1 + 1/3*l - l**4 + 2*l**2 = 0.
-1, 1, 3
Let r be (0 - 3/4) + (36 - -49). Let a = -84 + r. Let 3/4*f + a*f**3 - 3/4*f**2 - 1/4 = 0. What is f?
1
Suppose -61 - 115 = z - 89*z. Factor -1/5*n**3 + 0 + 3/5*n**z + 4/5*n.
-n*(n - 4)*(n + 1)/5
Let w = 21296 + -63884/3. Factor 1/6*g**2 + w + g.
(g + 2)*(g + 4)/6
Find q, given that 11/4*q**3 - 1/2*q**4 - 9/4*q**2 + 0 + 0*q = 0.
0, 1, 9/2
Suppose -182*b - 161*b + 475 = -211. Solve 2/3 - 5/3*w + 2/3*w**b = 0 for w.
1/2, 2
Let x(g) be the second derivative of 3*g**5/95 + 25*g**4/114 + 28*g**3/57 + 4*g**2/19 - 214*g + 1. Suppose x(k) = 0. What is k?
-2, -1/6
Let b be 48/(-6)*(-2)/(-8)*-2. Let j(y) be the second derivative of 5*y + 0*y**2 + 1/50*y**5 - 4/15*y**3 + 0*y**b + 0. Let j(f) = 0. Calculate f.
-2, 0, 2
Let x(j) = 27*j**3 - 111*j**2 + 500*j. Let h(i) = 5*i**3 - 22*i**2 + 100*i. Let s(l) = -22*h(l) + 4*x(l). Let s(w) = 0. What is w?
0, 10
Factor 80*n**2 + 7 + 53 + 90*n - 179*n**2 + 30 + 3*n**3 + 102.
3*(n - 32)*(n - 2)*(n + 1)
Let w(s) be the first derivative of s**8/8400 - s**6/900 + s**4/120 - 14*s**3/3 - 14. Let u(i) be the third derivative of w(i). Factor u(q).
(q - 1)**2*(q + 1)**2/5
Let q(k) be the second derivative of -k**7/1680 + 5*k**3/3 - 7*k. Let t(c) be the second derivative of q(c). Factor t(o).
-o**3/2
Let o(n) be the third derivative of -n**5/12 - n**4/24 + 5*n**2. Let p(v) = 6*v**2. Let b(y) = 3*o(y) + 2*p(y). Factor b(i).
-3*i*(i + 1)
Solve -2*x**2 + 0*x - 2/5*x**3 + 0 = 0 for x.
-5, 0
Find z, given that 6*z + 5*z**2 + z**2 + 2*z**3 + 2*z**2 = 0.
-3, -1, 0
Let z(a) be the third derivative of -4*a**5/15 - 7*a**4/6 - 2*a**3 - 134*a**2. Let z(t) = 0. Calculate t.
-1, -3/4
Factor 0*g + 0 + 4/11*g**3 + 2/11*g**4 + 2/11*g**2.
2*g**2*(g + 1)**2/11
Let x(q) be the first derivative of -4*q + 1/20*q**5 + 0*q**2 + 3 + 1/12*q**4 + 0*q**3. Let c(p) be the first derivative of x(p). Factor c(h).
h**2*(h + 1)
Let b(g) be the second derivative of 2*g**7/63 - 4*g**6/45 - g**5/3 + 10*g**4/9 + 8*g**3/9 - 16*g**2/3 + 727*g. Find f, given that b(f) = 0.
-2, -1, 1, 2
Suppose 0 = 6*p - 3*p - 12. Suppose -o = -5*w - 15, -o = -p*o + 2*w + 19. Factor 10*i - 10*i + i**o - 2*i**4 + 2*i**3 + 5*i**4.
i**3*(i + 1)*(i + 2)
Let i be (-9)/(-2)*((-23)/138 - (-5)/18). Let 1/2*d**2 + 1/6 + i*d + 1/6*d**3 = 0. What is d?
-1
Let -505*s**5 - 16*s**2 - 7 + 504*s**5 + 4*s**3 + 3*s**4 + 23 = 0. What is s?
-2, -1, 2
Factor 0 + 17/4*p**4 + 15/4*p**2 + 1/4*p**5 + 0*p + 31/4*p**3.
p**2*(p + 1)**2*(p + 15)/4
Let v(r) be the first derivative of r**3/6 + 53*r**2/2 - 107*r/2 + 452. Factor v(l).
(l - 1)*(l + 107)/2
Let a(d) be the first derivative of -1 + 0*d**3 + 1/4*d**2 - 1/24*d**4 - 8*d. Let g(b) be the first derivative of a(b). Let g(o) = 0. What is o?
-1, 1
Find k, given that 2738/7 + 2/7*k**2 + 148/7*k = 0.
-37
Let u be (1/(5/(-30)))/(-2). Let m(j) be the third derivative of 0*j**u + 0*j + 0*j**5 + 0 + 1/120*j**6 - 1/24*j**4 - 3*j**2. Factor m(y).
y*(y - 1)*(y + 1)
Determine g so that -18/7*g + 162/7*g**3 - 2/7 + 18/7*g**2 = 0.
-1/3, -1/9, 1/3
Let o be 5/25 + 51/(-5). Let b = -8 - o. Suppose -5*v - 3*v**2 + 27 + b*v**2 + 4*v**2 - 13*v = 0. What is v?
3
Let v = -29 - -16. Let u = -38/3 - v. What is r in u*r**2 - 2*r + 3 = 0?
3
Let p(q) = 121*q**2 - 22*q + 56. Let u(o) = -5. Let c(l) = -4*p(l) - 44*u(l). Factor c(n).
-4*(11*n - 1)**2
Let x(y) = -5*y**4 + 10*y**3 + 51*y**2 + 11*y. Let r(l) = -l**4 + 2*l**3 + 10*l**2 + 2*l. Let w(m) = 11*r(m) - 2*x(m). Factor w(v).
-v**2*(v - 4)*(v + 2)
Let r be (-50)/(-16) - (-3)/(-24). Let p be (4/30)/((-4)/(-54)). What is f in -7/5*f - f**r + 2/5 + p*f**2 + 1/5*f**4 = 0?
1, 2
Let 11*i**3 + 8*i**3 + 50*i + 38*i + 56 + 34*i**2 - 17*i**3 = 0. What is i?
-14, -2, -1
Let s = -21/31 - -167/155. Suppose -3*j = 2*j. Factor s*y + j + 2/5*y**2.
2*y*(y + 1)/5
Let f be (18/(-12))/((-3)/(-4)) + -56 + 60. Factor -2 - 1/3*w**3 + 4/3*w**f - 1/3*w.
-(w - 3)*(w - 2)*(w + 1)/3
Let w(g) be the third derivative of 5*g**8/84 + g**7/21 + g**6/90 + 5*g**3/6 - 4*g**2. Let d(z) be the first derivative of w(z). Factor d(k).
4*k**2*(5*k + 1)**2
Let n(c) be the third derivative of c**7/14 + c**6/20 + 53*c**2. Suppose n(b) = 0. Calculate b.
-2/5, 0
Let l = -24 + 28. Suppose s = -l*a + 138, 0 = s - 4 + 2. Suppose 72*w**3 - a*w**2 + 2*w - w**2 + 11*w**2 = 0. What is w?
0, 1/6
Let m be ((-12)/8)/((-351)/13). Let h(q) be the third derivative of -1/270*q**5 + 0 - 1/3*q**3 - 3*q**2 + 0*q - m*q**4. Factor h(o).
-2*(o + 3)**2/9
Let d(j) be the second derivative of j**5/80 - 53*j**4/48 + 225*j**3/8 + 729*j**2/8 + 57*j - 4. Factor d(k).
(k - 27)**2*(k + 1)/4
Let f(u) = u**4 + 9*u**2 - 41*u - 54. Let q(c) = -c**3 - 2*c. Let m(b) = -4*f(b) + 28*q(b). Factor m(s).
-4*(s - 2)*(s + 3)**3
Let r(p) be the first derivative of -2/3*p**2 + 41 + 0*p + 8/9*p**3 + 1/15*p**5 - 5/12*p**4. Let r(m) = 0. Calculate m.
0, 1, 2
Determine w, given that -2225*w**2 + 2*w**3 + 0*w**3 - w**3 + 2320*w**2 + 240*w + 4*w**3 = 0.
-16, -3, 0
Let y(p) be the second derivative of p**5/4 + 355*p**4/12 - 725*p**3/6 + 365*p**2/2 - 191*p + 2. Factor y(c).
5*(c - 1)**2*(c + 73)
Let w(r) = 3*r**4 - 68*r**3 + 236*r**2 - 331*r + 7. Let n(x) = x**4 - 22*x**3 + 79*x**2 - 110*x + 2. Let j(t) = 7*n(t) - 2*w(t). Suppose j(h) = 0. What is h?
0, 3, 12
Let a be 2/(150/24 - 6) + -5. Factor 4/3*s - 2/3 - 4/3*s**a + 2/3*s**4 + 0*s**2.
2*(s - 1)**3*(s + 1)/3
Let c(r) be the first derivative of 5/6*r**6 - 5*r**3 + 5/4*r**4 - 5*r**2 + 0*r + 3*r**5 + 17. Factor c(w).
5*w*(w - 1)*(w + 1)**2*(w + 2)
Suppose 0 = -6*j + 3*j + 72. Suppose -s + 5*q = 3*s - 6, 0 = -4*s - 4*q + j. Suppose -15 + s*w**2 + 12*w + 6*w**2 - 2*w - 5*w**2 = 0. Calculate w.
-3, 1
Let l(m) be the second derivative of 1/40*m**6 + 1/168*m**7 + 0*m**3 - 53*m + 3/80*m**5 + 0 + 1/48*m**4 + 0*m**2. Determine t, given that l(t) = 0.
-1, 0
Factor 12*r**2 - 70*r**3 - 2*r**4 + 67*r**3 - r**4 + 12*r.
-3*r*(r - 2)*(r + 1)*(r + 2)
Let f(m) = 11*m**2 - 6 + 1 - m**3 - m**3 + 3*m. Let n(c) = 14*c**3 - 1 + c**2 - 26*c**3 + 11*c**3. Let p(r) = -f(r) + 5*n(r). Determine x, given that p(x) = 0.
-1, 0
Let u(s) be the first derivative of s**4/18 + 22*s**3/27 + 19*s**2/9 + 2*s + 116. Solve u(d) = 0 for d.
-9, -1
Factor -2*k + 3 + 25*k - 18*k + 2*k**2.
(k + 1)*(2*k + 3)
Let z(y) = -y**2 + 26*y + 29. Suppose 5*n - 126 = -3*q, 0*n - n = -2*q - 33. Let i be z(n). What is j in 2/3*j**3 - 10/9*j**i + 4/9*j + 0 = 0?
0, 2/3, 1
Let w(g) be the second derivative of -g**8/560 - g**7/45 - 17*g**6/180 - g**5/5 + g**4/3 + 18*g. Let n(x) be the th