12. Let c(b) = 1. Let s = 0 - -1. Let w(i) = p*c(i) + s*z(i). Factor w(y).
-2*(y - 1)**2
Factor 99/2*t**2 + 19/2*t + 81/2*t**3 + 1/2.
(t + 1)*(9*t + 1)**2/2
Let h = -126 - -117. Let n be (17738/231)/7 + (-6)/h. Factor -2/11*y**3 + 24/11*y**2 - 96/11*y + n.
-2*(y - 4)**3/11
Let q be (32/(-18) + 2)*4/(-8). Let g = 5/36 - q. Factor g*l**2 - 1/2*l + 1/4.
(l - 1)**2/4
Let g(t) = 9*t**3 + 156*t**2 + 8112*t + 140612. Let l(q) = -20*q**3 - 312*q**2 - 16224*q - 281225. Let w(k) = -9*g(k) - 4*l(k). Solve w(o) = 0 for o.
-52
Let p(h) = 15*h**2 + 11*h. Let t(z) = z**2. Let k(v) = 39*v**2 + 32*v. Let c(y) = k(y) + 6*t(y). Let i(b) = 6*c(b) - 17*p(b). Factor i(m).
5*m*(3*m + 1)
Let w(i) be the first derivative of 1/18*i**4 + 0*i + 4/9*i**2 - 8/27*i**3 - 11. Determine m so that w(m) = 0.
0, 2
Let b(n) be the first derivative of n**4 - 6*n**2 + 8*n + 165. Factor b(v).
4*(v - 1)**2*(v + 2)
Let c(s) be the second derivative of 2*s**6/45 + 41*s**5/15 + 40*s**4/9 - 2*s + 20. Suppose c(j) = 0. Calculate j.
-40, -1, 0
What is r in 2*r**3 + 33*r + 6*r**4 - 61*r**3 + 6 - 12*r**2 - 7*r**3 + 33*r**5 + 0*r**4 = 0?
-1, -2/11, 1
Let x(v) be the first derivative of -v**3/30 + 9*v**2/10 - 16*v/5 + 189. Find j such that x(j) = 0.
2, 16
Factor -270*q**3 - 44*q**4 + 138*q**2 - 671*q**2 - 424*q - 48 + 2 - 2 - 31*q**2.
-2*(q + 2)**3*(22*q + 3)
Suppose 0 = -48*d - 1459 + 1651. Determine b so that 28/5*b**d - 174/5*b + 124/5*b**2 + 36/5 + 146/5*b**3 = 0.
-3, 2/7, 1/2
Let f be 0 + (-10)/(-4)*-4. Let a be (-28)/f + 4/20. What is v in -2*v**5 + 3*v**4 + 5*v + v + 4*v**5 + v**5 - 9*v**a - 3*v**2 = 0?
-2, -1, 0, 1
Let h = 58 + -54. Suppose r + h*r = 2*r. Factor 0 - 2/5*c**2 - 3/5*c**3 + r*c - 1/5*c**4.
-c**2*(c + 1)*(c + 2)/5
Let w(z) be the second derivative of 38*z - 7/4*z**4 + 11/2*z**3 - 15/2*z**2 + 3/20*z**5 + 0. Factor w(v).
3*(v - 5)*(v - 1)**2
Solve 53 - 15 + 3*s**2 - 2*s**4 + 3*s**2 + 18*s**2 + 80*s + 26 - 4*s**3 = 0 for s.
-2, 4
Let g(y) be the second derivative of 0*y**3 - 1/6*y**4 + 1/3*y**6 + 41*y + 0 + 0*y**2 - 1/20*y**5. Let g(h) = 0. Calculate h.
-2/5, 0, 1/2
Let y = 122 + -120. Let n(u) be the first derivative of -8/11*u + 2 + 0*u**y - 1/22*u**4 + 2/11*u**3. Determine l so that n(l) = 0.
-1, 2
Let s(r) = -10*r - 28. Let b be s(-6). Let v be 1/3*24/b. Factor v*l + 1/2 - 1/4*l**2.
-(l - 2)*(l + 1)/4
Let g(q) be the first derivative of q**5/20 + 4*q**2 - 1. Let t(v) be the second derivative of g(v). Let t(y) = 0. What is y?
0
Let u(x) be the third derivative of 1/570*x**5 + 0*x + 0 - 17*x**2 + 1/57*x**4 + 4/57*x**3. Solve u(t) = 0 for t.
-2
Let n = 6/1877 - -5583/15016. Factor n*v**2 + 0*v + 0 + 5/8*v**3 - 1/8*v**5 + 1/8*v**4.
-v**2*(v - 3)*(v + 1)**2/8
Let t(z) be the third derivative of -z**5/12 + 335*z**4/24 - 55*z**3 + 573*z**2. What is j in t(j) = 0?
1, 66
Factor 0 + 0*w + 4/7*w**3 - 164/7*w**4 + 0*w**2 + 1681/7*w**5.
w**3*(41*w - 2)**2/7
Let j be (9 + -7)*(-4)/(-2). Let g be 2*(16/17)/j. Factor g*o**3 + 10/17*o**2 + 4/17*o + 2/17*o**4 + 0.
2*o*(o + 1)**2*(o + 2)/17
Let s(y) be the first derivative of y**6/15 - 2*y**5/5 + 7*y**4/8 - 11*y**3/12 + y**2/2 + 13*y - 20. Let f(n) be the first derivative of s(n). Factor f(t).
(t - 2)*(t - 1)*(2*t - 1)**2/2
Let l(w) be the second derivative of w**7/84 - 3*w**5/10 - 2*w**4/3 - 2*w - 70. What is k in l(k) = 0?
-2, 0, 4
Factor -6*z - 6*z - 9*z**2 - 6*z**3 + 7*z + 3*z**4 + 5*z.
3*z**2*(z - 3)*(z + 1)
Let c(h) be the third derivative of h**9/20160 - h**8/4032 + h**7/2520 - 11*h**5/30 + 20*h**2. Let m(w) be the third derivative of c(w). Factor m(n).
n*(n - 1)*(3*n - 2)
Let r(b) be the third derivative of -b**6/90 + 17*b**5/15 - 289*b**4/6 + 9826*b**3/9 + 88*b**2. Factor r(p).
-4*(p - 17)**3/3
Suppose -17*f + 6 = -14*f. Solve 0*r**4 - 6*r**3 - f*r**4 - 8 - 30*r**2 - 26*r - 8*r**3 = 0.
-4, -1
Let 6/5*s**3 - 12 + 36/5*s**2 + 18/5*s = 0. What is s?
-5, -2, 1
Let w(c) be the second derivative of -2/3*c**2 - 1/6*c**3 + 1/36*c**4 + 0 + 13*c. Determine f, given that w(f) = 0.
-1, 4
Suppose 5 = -2*y + 15. Let 4/3*x**2 + 4*x**4 + 0*x + 4/3*x**y + 4*x**3 + 0 = 0. What is x?
-1, 0
Suppose 0 = 277*h - 164 - 390. Suppose -6/7*v + 3/7*v**h - 9/7 = 0. Calculate v.
-1, 3
Let h(r) be the third derivative of -3/220*r**6 + 0*r + 8/165*r**5 - 2/33*r**3 + 0 - 16*r**2 - 5/132*r**4. Solve h(w) = 0.
-2/9, 1
Let d(i) be the second derivative of -1/36*i**3 + 1/120*i**5 + 1/9*i**4 + 0 + 16*i - 2/3*i**2. Factor d(k).
(k - 1)*(k + 1)*(k + 8)/6
Let p be (15 - (-304)/(-20))*-10. Determine w, given that 1/2*w**p + 0 + 1/2*w**3 - w = 0.
-2, 0, 1
Suppose -6*i + 7*i + 6 = 0. Let q be (-25)/i + 7/(-42). Determine s so that -s**4 - 7*s**2 + 4*s**2 - 9*s**3 - 8*s**q - 3*s**5 = 0.
-1, 0
Let y(b) = -8*b**2 + 85*b + 13. Let r(n) = 4*n**2 - 42*n - 6. Let m(o) = -13*r(o) - 6*y(o). Find d, given that m(d) = 0.
0, 9
Suppose 5*l = c - 264, c - 19 - 245 = -l. Factor 133*i**5 + 3*i + 66*i**3 + 158*i**5 - c*i**5 + 24*i**2 + 72*i**4.
3*i*(i + 1)**2*(3*i + 1)**2
Let s be 7 - (-9 - (-22 + 6)). Let y(w) be the second derivative of s + 9/2*w**2 - w - 2*w**3 + 1/4*w**4. Solve y(j) = 0 for j.
1, 3
Let c(a) be the first derivative of 486*a**5/5 - 279*a**4/2 + 224*a**3/9 - 4*a**2/3 + 84. Factor c(b).
2*b*(b - 1)*(27*b - 2)**2/3
Let l(r) = 36*r**3 - 14*r**2 + 44*r + 44. Let g(j) = 5*j**3 - 2*j**2 + 6*j + 6. Let b(c) = 44*g(c) - 6*l(c). Factor b(u).
4*u**2*(u - 1)
Let j be (5/15)/(4/9). Let t(w) be the first derivative of j*w**4 + 0*w + 2*w**3 + 7 + 0*w**2. Solve t(i) = 0.
-2, 0
Let b be 0/19 + 50 + 0 + 1. Factor 5*f**5 + 56*f**3 - b*f**3 + 10*f**4 - f**2 + f**2.
5*f**3*(f + 1)**2
Solve 0 - 27/4*b**4 + 51/4*b**3 + 27/4*b**2 - 27/2*b + 3/4*b**5 = 0.
-1, 0, 1, 3, 6
Let a(k) be the second derivative of -k**6/6 - k**5/2 + 15*k**4 - 220*k**3/3 + 160*k**2 - 241*k. Factor a(y).
-5*(y - 2)**3*(y + 8)
Solve 4/5*m + 2/5*m**2 - 6/5 = 0.
-3, 1
Let x(z) be the second derivative of -5*z**7/42 - 5*z**6/6 + 8*z**5 - 15*z**4 + 7*z + 5. Factor x(p).
-5*p**2*(p - 2)**2*(p + 9)
Factor 1 + 9*i - 7*i - i**2 + 0*i - 17 + 6*i.
-(i - 4)**2
Let g(t) be the third derivative of -t**8/2520 - t**7/630 + t**5/90 + t**4/36 - t**3/2 + 9*t**2. Let f(a) be the first derivative of g(a). Factor f(l).
-2*(l - 1)*(l + 1)**3/3
Let b(l) be the third derivative of -l**7/105 - l**6/15 - l**5/10 + l**4/3 + 4*l**3/3 - 239*l**2. Factor b(x).
-2*(x - 1)*(x + 1)*(x + 2)**2
Factor 5/4*p**4 + 10*p**3 + 55/2*p + 10 + 105/4*p**2.
5*(p + 1)**2*(p + 2)*(p + 4)/4
Let h be (2 - 3*8/12)*1. Let d(v) be the second derivative of h*v**5 + 0 - 1/10*v**6 - 3/2*v**2 - 4*v + 0*v**3 + 1/2*v**4. Factor d(m).
-3*(m - 1)**2*(m + 1)**2
Let j(s) be the second derivative of -s**10/10080 + s**9/2520 - s**8/2240 + s**4/6 - 9*s. Let m(t) be the third derivative of j(t). Solve m(l) = 0 for l.
0, 1
Suppose 3*y = 4*l, 4*y + 4*l + 28 = -0*y. Let c be (16/y)/(4/(-8)). Factor -7*h**3 + 5*h - c - 25*h - 21*h**2 + 3*h**2 + 0*h**4 - h**4.
-(h + 1)*(h + 2)**3
Let j(w) = 5*w**3 - 369*w**2 - 74*w + 4. Let f be j(74). Factor 12/7*o**3 - 4/7*o**f + 0*o + 0*o**2 + 0.
-4*o**3*(o - 3)/7
Let v(y) be the first derivative of 5*y**2 - 5/2*y**4 - 5*y - 17 + y**5 + 0*y**3. Factor v(b).
5*(b - 1)**3*(b + 1)
Let c(n) = -n**3 - 7*n**2 - 7*n - 6. Let s be c(-6). Suppose s*g + 15 = g - 4*o, g - 2*o = 9. Factor -1 - g*m**2 + 7 - 4*m + m.
-3*(m - 1)*(m + 2)
Let 24/13*k**3 - 18/13*k**2 - 2/13*k**4 - 44/13*k + 0 = 0. What is k?
-1, 0, 2, 11
Let y(u) = -u**3 + u**2 - u - 7. Let v be y(0). Let k = 10 + v. Let 6*h**k + 2*h**3 - 7*h**5 - 4*h + 3*h**5 = 0. Calculate h.
-1, 0, 1
Let z(w) be the third derivative of 5*w**9/48384 - w**8/896 + w**7/576 + w**6/96 + w**5/15 - 5*w**2. Let s(b) be the third derivative of z(b). Factor s(g).
5*(g - 3)*(g - 1)*(5*g + 2)/4
Let v(y) be the first derivative of -2*y**3/21 - 3*y**2/7 - 4*y/7 + 48. Factor v(g).
-2*(g + 1)*(g + 2)/7
Let q(l) = 476*l + 1909. Let v be q(-4). Find m such that 176/3*m + 308/3*m**3 - 344/3*m**2 + 20/3*m**v - 32/3 - 128/3*m**4 = 0.
2/5, 1, 2
Let d be ((-27)/81 + (-10)/(-12))*1. Find m, given that 4*m**2 + 4*m + 1/4*m**5 - 8 - d*m**4 - 2*m**3 = 0.
-2, 2
Let t be (-832)/(-1092)*(-6 - 153/(-24)). What is p in -2/7*p + 2/7*p**2 + 0 - t*p**4 + 2/7*p**3 = 0?
-1, 0, 1
Let q = -9 + 12. Suppose q*s = 6*s - 6. Factor 17*g**2 + 9*g - 2 + 0*g - 6*g