/12. Let a = -9 - x. Factor p**2 + p - 2 - a*p + 0*p**2.
(p - 2)*(p + 1)
Let n be ((-12)/27)/(10/(-5)). Let c(v) be the first derivative of -4/27*v**3 + 0*v + 1/6*v**4 + 0*v**2 + 2 + n*v**5. Factor c(x).
2*x**2*(x + 1)*(5*x - 2)/9
Let q be 15/6 - (-1)/(-6). Let m = -11/6 + q. Factor -1/2*a**2 + 0 - m*a.
-a*(a + 1)/2
Let y be 2*1/4*0. Let z = -50 + 203/4. Factor y - 1/4*m - 3/4*m**3 + z*m**2 + 1/4*m**4.
m*(m - 1)**3/4
Let j(g) be the first derivative of 2*g**5/5 + g**4 - 2*g**2 - 2*g - 16. Solve j(z) = 0.
-1, 1
Let j = -10 + 14. Let u = j + -1. Suppose -16/7*i**u - 2/7 - 4/7*i**5 + 4/7*i + 4/7*i**2 + 2*i**4 = 0. Calculate i.
-1/2, 1
Let g = -472 - -474. Suppose 2/9*r**3 + 2/9*r**g + 0*r + 0 = 0. Calculate r.
-1, 0
Let n(t) be the first derivative of -t**8/168 + t**7/84 + t**6/80 - t**5/24 + t**4/48 + t**2/2 - 4. Let j(q) be the second derivative of n(q). Solve j(w) = 0.
-1, 0, 1/4, 1
Let i(r) = -4*r**3 + 2*r**2 + r. Let b be i(-1). Suppose 0 = b*p - 2*p. Determine y so that p*y - 2/11*y**3 + 0 - 2/11*y**4 + 0*y**2 = 0.
-1, 0
Let z(c) be the first derivative of -c**3 + 9*c**2 + 8. Factor z(i).
-3*i*(i - 6)
Let u(m) be the second derivative of -49*m**4/24 + 7*m**3/12 - m**2/16 - 21*m. Factor u(b).
-(14*b - 1)**2/8
Let x(b) be the third derivative of b**7/35 + 2*b**6/15 + 7*b**5/30 + b**4/6 - b**2. Factor x(g).
2*g*(g + 1)**2*(3*g + 2)
Let w(o) be the third derivative of 2*o**7/175 + 2*o**6/75 + o**5/75 - 29*o**2. What is u in w(u) = 0?
-1, -1/3, 0
Factor -1/7 + 3/7*f**2 + 2/7*f.
(f + 1)*(3*f - 1)/7
Let j = 1/8 - -5/24. Let z(c) be the first derivative of j*c + 0*c**3 - 1/15*c**5 + 1 - 1/3*c**2 + 1/6*c**4. Suppose z(a) = 0. What is a?
-1, 1
Factor 0*m**2 + 1/3*m**3 - 2/3*m**4 + 0 + 1/3*m**5 + 0*m.
m**3*(m - 1)**2/3
Let u(o) be the second derivative of 0 + 2/9*o**7 + 11/18*o**6 - 5/36*o**4 - 7*o + 2/5*o**5 - 1/9*o**3 + 0*o**2. Determine p, given that u(p) = 0.
-1, -1/4, 0, 2/7
Let u be 4/(-14) - 100/(-105). Solve 2/3*h**2 - 2/3*h**4 + u*h - 2/3*h**3 + 0 = 0.
-1, 0, 1
Let u be ((-16)/(-12))/((-6)/(-9)). Factor 8/3*q + 2/3*q**4 - 8/3 + 2*q**u - 8/3*q**3.
2*(q - 2)**2*(q - 1)*(q + 1)/3
Suppose 3*s**3 - 4*s**5 - 4*s + 0*s + 5*s**3 = 0. What is s?
-1, 0, 1
Let b(s) be the third derivative of 0*s**3 + 0 + 1/60*s**6 + 0*s - 1/12*s**4 - 2*s**2 + 0*s**5. Factor b(j).
2*j*(j - 1)*(j + 1)
Let a(v) be the first derivative of v**7/560 - v**6/144 + v**5/120 + v**3/3 + 3. Let f(c) be the third derivative of a(c). Factor f(u).
u*(u - 1)*(3*u - 2)/2
Let v = 22 + -14. Let b be 4/2 - v/(-12). Factor 2/3*k**2 + b - 8/3*k.
2*(k - 2)**2/3
Let s = 1043/261 - 45/29. Factor 32/9*g**3 + 0 + 14/9*g**4 + 4/9*g + s*g**2.
2*g*(g + 1)**2*(7*g + 2)/9
Factor -2*n**2 - n**4 + n - 4*n**3 + 3*n + 12 - 9.
-(n - 1)*(n + 1)**2*(n + 3)
Factor 0 + 0*s - 2/13*s**4 + 12/13*s**2 + 2/13*s**3.
-2*s**2*(s - 3)*(s + 2)/13
Suppose 0 = -2*r + o + 9, 5*r - 8*r - 3*o = 0. Solve 3/4*y + 1/2 + 0*y**2 - 1/4*y**r = 0.
-1, 2
Let t(v) = 18*v**3 + 28*v**2 - 18*v + 4. Let b(j) = -6*j**3 - 9*j**2 + 6*j - 1. Let i(h) = 16*b(h) + 5*t(h). Let i(y) = 0. Calculate y.
-1, -2/3, 1
Let m(q) = q**5 + q**4 + q**3 + q. Let w(a) = -4*a**5 - 4*a**4 - 10*a**3 - 4*a**2 - 4*a + 2. Let i(j) = -6*m(j) - w(j). Factor i(s).
-2*(s - 1)**2*(s + 1)**3
Let x = 11 - 8. Solve 3*t + t**x - t - 4*t**3 + t = 0.
-1, 0, 1
Let n = -2145/4 + 537. Find b, given that 0 + 0*b - n*b**2 = 0.
0
Suppose c = 5 + 3. Let s(r) = r**4 - 11*r**3 - 11*r**2 - 3*r - 3. Let v(o) = 2*o**4 - 32*o**3 - 32*o**2 - 8*o - 8. Let j(z) = c*s(z) - 3*v(z). Factor j(f).
2*f**2*(f + 2)**2
Let w(b) be the third derivative of b**7/70 - b**6/20 + b**5/20 - 5*b**2. Let s(g) = 3*g**4 - 6*g**3 + 3*g**2. Let j(i) = 3*s(i) - 4*w(i). Factor j(h).
-3*h**2*(h - 1)**2
Find x, given that -16/3*x**2 - 2/3 - 4*x = 0.
-1/2, -1/4
Find b, given that -3*b**4 - 57*b**4 - 18*b**5 + 4*b**5 - 48*b**2 - 8*b - 143*b**3 + 57*b**3 = 0.
-2, -1, -2/7, 0
Let q(b) be the third derivative of -b**10/45360 + b**9/22680 + b**8/10080 - b**7/3780 - b**4/6 - b**2. Let f(l) be the second derivative of q(l). Factor f(u).
-2*u**2*(u - 1)**2*(u + 1)/3
Let u(l) be the first derivative of l**6/18 - l**5/5 + l**4/12 + l**3/3 - l**2/3 + 4. Solve u(s) = 0.
-1, 0, 1, 2
Let m be 5/((-450)/(-183)) + (-1 - 1). Let k(b) be the second derivative of 2/15*b**3 - b + m*b**4 + 1/5*b**2 + 0. Determine p, given that k(p) = 0.
-1
Let y(s) be the third derivative of 0*s**3 + 0*s**4 + 0*s**5 - 1/540*s**6 + 1/945*s**7 + 0*s + 0 + 9*s**2. Determine b so that y(b) = 0.
0, 1
Suppose 0*a - 9/2*a**3 - 5/2*a**5 - 6*a**4 - a**2 + 0 = 0. Calculate a.
-1, -2/5, 0
Let q(l) = 3*l**2 + 11*l + 4. Let r(f) = 3*f**2 + 12*f + 3. Let y(g) = -3*q(g) + 2*r(g). Let y(d) = 0. Calculate d.
-2, -1
Let r(t) be the third derivative of t**8/2184 - t**6/130 + 4*t**5/195 - t**4/52 + 12*t**2. Let r(j) = 0. What is j?
-3, 0, 1
What is g in 45*g**3 - 2*g**2 - 47*g**3 - 2 + 2 = 0?
-1, 0
Let x(q) = -q**4 + 6*q**3 + 8*q**2 - q - 7. Let h(z) = -z**4 + 5*z**3 + 7*z**2 - z - 6. Let v(f) = 5*h(f) - 4*x(f). Let v(g) = 0. Calculate g.
-1, 1, 2
Let p(j) be the second derivative of -j**6/360 - j**5/180 + j**4/36 + 3*j**2/2 + 3*j. Let s(z) be the first derivative of p(z). Factor s(r).
-r*(r - 1)*(r + 2)/3
Let n(y) be the third derivative of -1/600*y**6 - 1/300*y**5 + 0*y**4 + 1/1050*y**7 + 0 + 2*y**2 + 1/1680*y**8 + 0*y + 0*y**3. Factor n(j).
j**2*(j - 1)*(j + 1)**2/5
Factor -8/3 + 2/3*j**4 + 10/3*j - 10/3*j**3 + 2*j**2.
2*(j - 4)*(j - 1)**2*(j + 1)/3
Let t(c) be the third derivative of -c**6/540 - c**5/270 - 31*c**2. Factor t(r).
-2*r**2*(r + 1)/9
Let v(r) be the first derivative of r**6/900 + r**3 + 2. Let d(j) be the third derivative of v(j). Determine s, given that d(s) = 0.
0
Let o(l) = l**2 - 5*l + 5. Let k be o(4). Let -i**4 + 2*i + 4*i**2 - k - 4*i**2 - 2*i**3 + 2 = 0. Calculate i.
-1, 1
Factor -7/4*b + 1/4 + 3*b**2.
(3*b - 1)*(4*b - 1)/4
Suppose -k - 4*i - 16 = -5*k, -i + 20 = 2*k. Let s = k + -5. Factor -z**2 - 2*z**4 - z**3 - z**s + z**4.
-z**2*(z + 1)**2
Suppose -l = -4*k, k + 0*k = -l. Let j be -3 + l + (-91)/(-28). Factor j*z**2 + 1/2*z + 1/4.
(z + 1)**2/4
Suppose -4*w - 20 = -4*x, x - 3 - 2 = 2*w. Let z(t) be the first derivative of 1/2*t + 1/4*t**4 - 1/10*t**x + 2 - 1/2*t**2 + 0*t**3. Factor z(r).
-(r - 1)**3*(r + 1)/2
Determine j, given that 46*j + 12*j**2 - 11*j - 48 + 38*j - 9*j = 0.
-6, 2/3
Factor 0 + 1/5*v**3 + 0*v - 1/5*v**2.
v**2*(v - 1)/5
Suppose -2*z = 2*a, -5*a = -2*z + 3 + 25. Factor 16*n**4 + 3*n**2 + 24*n**2 - 4*n**z - 3*n - 23*n**3 - 10*n**3 - 3.
3*(n - 1)**3*(4*n + 1)
Let b(p) be the third derivative of 0*p + p**2 - 1/144*p**4 + 0 + 1/36*p**3 - 1/180*p**5. Factor b(n).
-(n + 1)*(2*n - 1)/6
Let x = 157/77 + -13/7. Factor -2/11*l**2 - 4/11*l - x.
-2*(l + 1)**2/11
Let z(t) = -28*t**2 + 110*t + 26. Let r(b) = -b + 1. Let c(n) = 6*r(n) + z(n). Factor c(l).
-4*(l - 4)*(7*l + 2)
Let o(r) = r**3 - r**2 - 1. Let t be 3/(-18) - (-14)/12. Let a(j) = -3*j**4 - 5*j**3 + 11*j**2 + 2. Let f(g) = t*a(g) + 5*o(g). Factor f(v).
-3*(v - 1)**2*(v + 1)**2
Let l(c) be the second derivative of -1/9*c**3 + 1/9*c**4 + 0 + 4*c - 1/30*c**5 + 0*c**2. Factor l(n).
-2*n*(n - 1)**2/3
Suppose 3*w = -2*w + 5. Suppose 3*g - 4 + w = 0. Factor 2*v**3 + 2*v**2 - 2*v**4 - 2*v - g + 0*v + 1.
-2*v*(v - 1)**2*(v + 1)
Let j(b) be the first derivative of -4*b**3/21 + 2*b**2/7 + 4. Suppose j(l) = 0. Calculate l.
0, 1
Let i(d) be the third derivative of -d**6/1020 + d**5/255 - d**4/204 - 8*d**2. Factor i(n).
-2*n*(n - 1)**2/17
Suppose -b + 5 = -2*b. Let z = b - -7. Factor -3*n**2 - 1 - n**z + 3 + 2*n**2.
-2*(n - 1)*(n + 1)
Suppose -12*l = -4*l. Factor 2/5 - 2/5*f**2 + l*f.
-2*(f - 1)*(f + 1)/5
Let i = 13/4 + -31/12. Factor -2/3*b**2 + i*b**4 + 2/3*b**3 - 2/3*b + 0.
2*b*(b - 1)*(b + 1)**2/3
Suppose -6 = -r - 2. Let p = r - 2. Let 0 - 4/5*b**p + 3/5*b**4 + 1/5*b**5 + 0*b + 0*b**3 = 0. What is b?
-2, 0, 1
What is q in 1/4*q**3 + 1/12*q + 1/3*q**2 + 0 = 0?
-1, -1/3, 0
Let t(b) be the first derivative of 4*b**3/3 - 10*b**2 - 24*b - 5. Factor t(i).
4*(i - 6)*(i + 1)
Let c(v) = 48*v**2 + 4*v - 4. Let m(o) = 144*o**2 + 12*o - 12. Let f(i) = 10*c(i) - 3*m(i). Factor f(b).
4*(3*b + 1)*(4*b - 1)
Suppose -5*d - 4 = -3*f - 64, 2*d + 5*f - 24 = 0. Suppose d*o = 8*o. Factor 2/7*l**2 + 0*l**3 - 2/7