**5 - 2*i**3 + 0*i**2 - 2*i**4.
-i**3*(i + 2)**2/2
Let j(t) be the second derivative of 0 + 1/45*t**5 + 2*t + 0*t**4 - 2/27*t**3 - 1/9*t**2 + 1/135*t**6. Factor j(n).
2*(n - 1)*(n + 1)**3/9
Let w be ((-44)/12 + 3)/((-2)/6). Factor 9/7*c**3 + 0*c**w + 0 - 3/7*c + 6/7*c**4.
3*c*(c + 1)**2*(2*c - 1)/7
Let u be -2 - (-3 - (3 - 2)). Let h(t) be the second derivative of 0*t**5 - t + 1/36*t**4 + 0*t**3 + 0 - 1/90*t**6 + 0*t**u. Determine j, given that h(j) = 0.
-1, 0, 1
Let p be -3 - (-4*2 + 3). Let a(c) be the first derivative of -p*c**2 + 0*c + 2/3*c**3 - 2 + 1/2*c**4. Factor a(q).
2*q*(q - 1)*(q + 2)
Let 941 - f**4 + 4*f - 941 + 0*f**4 - 8*f**2 + 5*f**3 = 0. What is f?
0, 1, 2
Let f be 4 + -1 + 1 + -1. Suppose -3*k + 9 = -f. Factor -2/3*o**3 - 1/3*o**k + 0*o + 0 - 1/3*o**2.
-o**2*(o + 1)**2/3
Let w be (-20 + 18)*(2 - (-19)/(-9)). What is d in -2/9*d**3 + w + 2/9*d - 2/9*d**2 = 0?
-1, 1
Let b(n) be the second derivative of n**7/6300 + n**6/900 + n**5/300 + n**4/12 - 6*n. Let y(f) be the third derivative of b(f). Suppose y(z) = 0. What is z?
-1
Let m = 104/21 + -30/7. Factor 4/3*i**2 - 4/3 + m*i**3 - 2/3*i.
2*(i - 1)*(i + 1)*(i + 2)/3
Factor 0 + c**2 + 1/2*c + 1/2*c**3.
c*(c + 1)**2/2
Let m be 2/5 - 88/(-30). Let j be 0 + -3 + (130/15)/2. Factor m*d - 4/3 - 10/3*d**3 + j*d**2.
-2*(d - 1)*(d + 1)*(5*d - 2)/3
Factor 4/9*t**2 + 0*t + 0 + 2/9*t**3.
2*t**2*(t + 2)/9
Let c(m) = -m**3 - 10*m**2 - 8*m - 16. Let w be c(-11). Let v = -1349/7 + w. Determine b, given that 0*b - v*b**2 + 0 = 0.
0
Solve 64/3*t**4 + 4/9*t - 4/3*t**2 + 0 - 80/9*t**3 + 256/9*t**5 = 0 for t.
-1, -1/4, 0, 1/4
Let d be 4/35*5*1. Find z, given that 0 + 6/7*z**2 - 2/7*z**3 - d*z = 0.
0, 1, 2
Let g(d) = -2*d**2 - 10*d + 5. Let n(s) = s**2 + 9*s - 6. Let u(y) = -2*g(y) - 3*n(y). Let o be u(6). Factor 2/3*v**o - 8/3*v + 8/3.
2*(v - 2)**2/3
Let i(q) be the first derivative of 3*q**4/8 - 11*q**3/2 + 15*q**2/2 - 11. Factor i(l).
3*l*(l - 10)*(l - 1)/2
Let f = -116 - -2785/24. Let l(o) be the second derivative of 0 + 0*o**2 + o - 1/80*o**5 + f*o**4 - 1/24*o**3. Factor l(y).
-y*(y - 1)**2/4
Suppose 0 = 9*t - 11*t + 84. Let j = t - 40. Let -1/3*u + 1/3*u**j + 0 = 0. What is u?
0, 1
Let c(n) = 3*n**2 - n + 6. Let k(s) = 0*s**2 - 5 + 3 - s**2. Let j(o) = -3*c(o) - 8*k(o). Solve j(v) = 0 for v.
1, 2
Suppose 3*c + 5*r = 14, -2 = -c - 3*r + 4. Suppose 0 = c*h + h. Factor 1/4*d**2 + h - 1/2*d + 3/4*d**3.
d*(d + 1)*(3*d - 2)/4
Factor -2 + 0*f + 3/2*f**2 - 1/2*f**3.
-(f - 2)**2*(f + 1)/2
Let g = 3/4 + -5/12. Factor -1/3*f**2 - 1/3*f**3 + g*f + 1/3.
-(f - 1)*(f + 1)**2/3
Let -10 + 3*m - 2*m**3 - 2*m**4 + 12 + 14*m**2 + 10 + 23*m = 0. What is m?
-2, -1, 3
Let r(j) be the second derivative of -j**4/72 + j**2/12 - 4*j. Factor r(h).
-(h - 1)*(h + 1)/6
Suppose -u + 4*x + 10 = 0, 2*x - 16 = -4*u + 6*x. Suppose 5*d - 10 = -5*f, -f = 2*f + 5*d - 6. Factor -2/5 - 6/5*b**3 - u*b - 14/5*b**f.
-2*(b + 1)**2*(3*b + 1)/5
Let b(l) be the third derivative of -l**7/1575 + l**6/900 + l**5/90 + l**4/60 + 4*l**2. Factor b(u).
-2*u*(u - 3)*(u + 1)**2/15
What is y in 1/3*y + 0 + 1/3*y**3 - 2/3*y**5 + y**4 - y**2 = 0?
-1, 0, 1/2, 1
Let y be (17 - 0)*2/(-2). Let a(p) = -23*p**2 - 29*p - 6. Let m(z) = -7*z - 7 - 8*z**2 + 6*z + 5 - 9*z. Let k(i) = y*m(i) + 6*a(i). Let k(r) = 0. What is r?
-1
Let g be (-1086)/(-39) - (-12)/78. Let j = g - 83/3. Factor -2/3*x**2 + 0 + 1/3*x + j*x**3.
x*(x - 1)**2/3
Let k(x) be the first derivative of -x**6/3 + 2*x**4 + 4*x**3/3 - 3*x**2 - 4*x + 15. Let k(c) = 0. Calculate c.
-1, 1, 2
Let a(v) be the third derivative of -3/20*v**5 - 1/40*v**6 + 3/2*v**3 + 0*v + 8*v**2 + 0 + 1/8*v**4. Factor a(t).
-3*(t - 1)*(t + 1)*(t + 3)
Factor 0*k**2 - 1/2*k**3 + 1/2*k + 0.
-k*(k - 1)*(k + 1)/2
Factor -2/5*z**2 + 0 + 14/5*z.
-2*z*(z - 7)/5
Suppose 26 + 14 = 4*f. Let a(c) = -c**3 + 9*c**2 + 11*c - 6. Let t be a(f). Determine y, given that 3*y**t + 3*y**2 - 5*y**2 - y**4 = 0.
-1, 0, 1
Suppose 4*u + 4*a - 20 = 0, 5 + 11 = 2*u + 4*a. Suppose 3*m + 5*o = 13, -5*m - o = -5 - 2. Factor u*g + 3*g + m - 19*g**2 + 23*g**2.
(g + 1)*(4*g + 1)
Let w(i) be the first derivative of 0*i**2 - i - 1 - 1/15*i**3 - 1/30*i**4. Let b(c) be the first derivative of w(c). Suppose b(g) = 0. Calculate g.
-1, 0
Let n(o) be the third derivative of -o**8/23520 - o**7/8820 - o**4/24 - 4*o**2. Let p(s) be the second derivative of n(s). Factor p(y).
-2*y**2*(y + 1)/7
Let r(f) = f**3 - 9*f**2 - f + 12. Let y be r(9). Suppose 9*a**2 + 3*a + 7*a**2 - 3*a**y - 13*a**2 - 3*a**4 = 0. Calculate a.
-1, 0, 1
Let v(r) = r**2 - 5*r + 4. Let z be v(6). Suppose -2*o - 3*o + z = 0. Factor -o*a**2 + 3*a**2 + 0*a - a.
a*(a - 1)
What is c in 2*c + 2*c**2 + 5 - 11*c - 7*c + 27 = 0?
4
Let r(d) be the first derivative of -2*d**5/25 - 3*d**4/5 - 14*d**3/15 + 6*d**2/5 + 16*d/5 - 11. Determine p, given that r(p) = 0.
-4, -2, -1, 1
Suppose 4*u = -u + 20. Suppose 0 = -a - 4*q - 0*q - 7, u*a = 5*q + 35. Factor -2*l**3 + 5*l**3 + 0*l**4 + 6*l**4 + 2*l**2 + a*l**3.
2*l**2*(l + 1)*(3*l + 1)
Let l be 12/15*(-1 + 11). Suppose 0*y = 3*y - 4*f - 18, -2*y - f = -1. Factor k**2 - 6 - k + l - y*k.
(k - 2)*(k - 1)
Let c = -431/387 - 19/43. Let b = c + 106/45. Determine r so that 0 + b*r**4 - 6/5*r**3 + 0*r + 2/5*r**2 = 0.
0, 1/2, 1
Let m(o) = -6*o**4 - 6*o**3 + 14*o**2 - 2*o - 8. Let w(l) = 6*l - 4*l**4 - 7*l - 1 - 4 - 4*l**3 + 0*l + 9*l**2. Let g(j) = -5*m(j) + 8*w(j). Solve g(t) = 0.
-1, 0, 1
Let y(p) = p**2 - 5*p - 2. Let h be y(6). Let z(q) = -q**3 + 4*q**2 + 2*q - 6. Let n be z(h). Factor -2*m**n + 8*m + 2 - 8*m.
-2*(m - 1)*(m + 1)
Let b(r) be the third derivative of -r**6/540 - r**5/135 - r**4/108 + 21*r**2. Suppose b(w) = 0. What is w?
-1, 0
Let c = 5199/20828 - -2/5207. Factor -2*s + 4 + c*s**2.
(s - 4)**2/4
Let j(s) = -4*s**3 - 4*s**2 - 2*s. Let w(a) = -5*a**3 - 5*a**2 - 2*a. Let o(t) = 4*j(t) - 3*w(t). Let b(r) = -r. Let c(g) = 2*b(g) - o(g). Factor c(u).
u**2*(u + 1)
Let s(p) be the first derivative of 8*p**7/7 - 4*p**6 + 99*p**5/20 - 5*p**4/2 + p**3/2 - 11*p - 7. Let f(t) be the first derivative of s(t). Factor f(c).
3*c*(c - 1)**2*(4*c - 1)**2
Let g(m) = -30*m - 118. Let u be g(-4). Factor 0 + 1/3*p**u + 1/3*p.
p*(p + 1)/3
Let g(a) be the first derivative of 1/5*a**5 + 1/2*a**2 - 1/4*a**4 - 1/3*a**3 + 0*a + 1. Let g(r) = 0. Calculate r.
-1, 0, 1
Let p(d) be the first derivative of d**6/30 + 3*d**5/40 - d**3/12 - 4*d - 3. Let u(v) be the first derivative of p(v). Factor u(r).
r*(r + 1)**2*(2*r - 1)/2
Let l(x) be the first derivative of 1/40*x**6 - 1/12*x**4 + 4 - 1/12*x**3 - 1/120*x**5 + x**2 + 0*x. Let y(w) be the second derivative of l(w). Solve y(a) = 0.
-1/2, -1/3, 1
Let w be (-2 - -3)/(3/(-27)). Let o be (-18)/w + (-2)/(-3). Determine j so that -2/3*j**4 - 16/3*j**3 + o*j**5 + 8/3*j + 4/3*j**2 - 2/3 = 0.
-1, 1/4, 1
Let f(a) be the third derivative of 7/300*a**6 + 2/15*a**3 - 1/75*a**5 + 0 + 5*a**2 + 0*a - 7/60*a**4. Factor f(w).
2*(w - 1)*(w + 1)*(7*w - 2)/5
Let n = 197 - 2165/11. Suppose 0 - 2/11*b**2 - n*b = 0. Calculate b.
-1, 0
Let h(q) be the third derivative of q**6/300 + q**5/75 - q**4/12 - 2*q**3/5 - 8*q**2. Solve h(f) = 0 for f.
-3, -1, 2
Let n = -44 + 46. Let z(f) be the third derivative of 0*f**3 + 0*f + 0*f**6 + 1/105*f**7 + 0*f**4 + 0 - 1/30*f**5 + 3*f**n. Factor z(x).
2*x**2*(x - 1)*(x + 1)
Suppose -8 = -2*z - 0*z. Suppose -2*c - b + 20 = -3*b, 3*c - z*b - 35 = 0. Suppose 7 + 4*i**3 + i**c - 3*i**5 - 2*i - 4*i**2 + 2*i**4 - 5 = 0. Calculate i.
-1, 1
Let q = -2037 - -2040. Let i = 65/42 - 1/21. Factor 0 - q*z + 3/2*z**3 + i*z**2.
3*z*(z - 1)*(z + 2)/2
Suppose 8*l = 3*l + 15. Let r be 3*(3 - 4) + l. Factor r + 0*d**2 - 1/4*d**3 + 0*d.
-d**3/4
Let g(d) be the first derivative of -d**3/12 - 7*d**2/16 - 3*d/8 + 3. Factor g(v).
-(v + 3)*(2*v + 1)/8
Suppose -2*x = 2*m - 1 - 1, -5*x + 3*m + 29 = 0. Solve 2*o - 2*o + 4 + x*o**2 + 8*o = 0 for o.
-1
Let v(y) be the second derivative of -3*y**5/100 - y**4/4 - 7*y**3/10 - 9*y**2/10 + 7*y. Factor v(z).
-3*(z + 1)**2*(z + 3)/5
Suppose 0 - 4/3*l**4 - 5/3*l**2 + 2/3*l - 11/3*l**3 = 0. What is l?
-2, -1, 0, 1/4
Factor -3/2*q + 1/2*q**4 + 1/2*q**2 + 3/2*q**3 - 1.
(q - 1)*(q + 1)**2*(q + 2)/2
Let y(f) be the third derivative of 0*f + 0 - 1/16*f**4 + 0*f**3 - 3*f**2 - 1/80*f**5. Find t such that y(t) = 0.
-2, 0
Let m(q