 Let r(t) = 6*t**3 + 12*t**2 + 13*t + 7. Let g(p) = f*r(p) - 7*k(p). Factor g(v).
-3*v*(v + 1)**2
Factor -9*y**2 - y**2 + y**4 + 4*y**4 + 5.
5*(y - 1)**2*(y + 1)**2
Let m(p) = -p**2 + 7*p. Let h(o) = -3*o**2 + 15*o. Let k(c) = 4*h(c) - 9*m(c). Factor k(d).
-3*d*(d + 1)
Let v = 1/5 - -3/10. Find m, given that m**5 + 0 + 0*m + 2*m**3 + v*m**2 + 5/2*m**4 = 0.
-1, -1/2, 0
Let h(d) be the third derivative of 1/96*d**4 + 0*d**7 + 0*d**3 + d**2 + 1/1344*d**8 + 0 + 0*d - 1/240*d**6 + 0*d**5. Factor h(t).
t*(t - 1)**2*(t + 1)**2/4
Let q = -134 - -134. Solve 0*p + q*p**2 + 0 + 2/3*p**5 - 4/3*p**4 + 2/3*p**3 = 0.
0, 1
Let o(g) = -13*g**4 + 11*g**3 + 5*g**2. Let c(l) = -20*l**4 + 16*l**3 + 7*l**2. Let h(a) = 5*c(a) - 7*o(a). Factor h(p).
-3*p**3*(3*p - 1)
Let v(t) be the first derivative of -22*t**3/9 + 3*t**2 + 4*t/3 + 6. Factor v(n).
-2*(n - 1)*(11*n + 2)/3
Let v(y) be the third derivative of -2*y**2 - 1/5*y**5 + 3/8*y**4 + 0*y**3 + 1/40*y**6 + 0*y + 0. Factor v(u).
3*u*(u - 3)*(u - 1)
Let l(c) be the second derivative of c**4/15 - 2*c**2/5 - 11*c. Find g, given that l(g) = 0.
-1, 1
Let r(a) be the second derivative of 0 + 3/2*a**3 + 4*a + 0*a**2 - 1/2*a**4 + 1/20*a**5. Factor r(q).
q*(q - 3)**2
Let x(r) be the first derivative of -r**8/3360 - r**7/1680 + r**6/720 + r**5/240 - 5*r**3/3 - 4. Let g(n) be the third derivative of x(n). Factor g(j).
-j*(j - 1)*(j + 1)**2/2
Let p(k) = k**2 - 6*k + 3. Let x be p(6). Factor j + 3*j**x + j**3 + 3*j - 8*j**2.
4*j*(j - 1)**2
Let l(a) be the third derivative of -a**8/24 - 3*a**7/35 + a**6/12 + 3*a**5/10 + a**4/6 - 25*a**2. Suppose l(w) = 0. What is w?
-1, -2/7, 0, 1
Factor 14*f**4 - 25*f**4 + 45*f**3 - 24*f**4 - 3*f**2 - 7*f**2.
-5*f**2*(f - 1)*(7*f - 2)
Let z(i) = i**2 + 2*i + 1. Let d(w) = -1 + w + 2 - 3*w**2 + 4*w**2. Let f(u) = 4*d(u) - 3*z(u). Factor f(n).
(n - 1)**2
Let h(r) be the first derivative of 7*r**6/300 + r**5/75 - 7*r**4/60 - 2*r**3/15 + r**2/2 - 2. Let s(z) be the second derivative of h(z). Factor s(x).
2*(x - 1)*(x + 1)*(7*x + 2)/5
Suppose -d = 2*d + 4*o - 9, 0 = -4*d - 4*o + 12. Find c such that -2/3*c**d + 0*c + 2/3*c**5 + 4/3*c**4 - 4/3*c**2 + 0 = 0.
-2, -1, 0, 1
Let m be ((-4096)/168)/16*(-6)/4. Factor -4/7*v**5 - 20/7*v**3 + 8/7*v**2 + 0*v + m*v**4 + 0.
-4*v**2*(v - 2)*(v - 1)**2/7
Let o(n) be the first derivative of -2*n**5/35 + n**4/14 + 2*n**3/21 - n**2/7 + 8. Solve o(k) = 0 for k.
-1, 0, 1
Let -1024/13 - 48/13*r**2 - 384/13*r - 2/13*r**3 = 0. What is r?
-8
Let y(z) be the second derivative of z**4/28 + z**3/7 + 11*z. Factor y(r).
3*r*(r + 2)/7
Let a(p) be the second derivative of -2*p**7/189 - 4*p**6/135 - p**5/45 - 4*p. Factor a(l).
-4*l**3*(l + 1)**2/9
Let -5 - 11*f - 10 + 2*f - f + 5*f**2 = 0. What is f?
-1, 3
Factor 1/4*z**3 + 0*z + 3/2*z**2 + 0.
z**2*(z + 6)/4
Let n(z) = 7*z**5 + 3*z**4 + 17*z**3 + 13*z**2 + 7*z. Let a(m) = m**5 - m**4 + m**3 + m**2 + m. Let x(o) = -5*a(o) + n(o). Find p, given that x(p) = 0.
-1, 0
Let h = -1 + 7. Suppose 2*i = 6, -i - i = -4*d + h. Factor -3 - p + p**d + 3.
p*(p - 1)*(p + 1)
Let s(v) be the third derivative of -1/48*v**4 - 1/240*v**6 + 3*v**2 + 0 + 0*v**3 + 0*v + 1/60*v**5. Let s(r) = 0. What is r?
0, 1
Let g = -168 - -171. Suppose 3/4*z + 21/4*z**2 + 0 + 45/4*z**3 + g*z**5 + 39/4*z**4 = 0. What is z?
-1, -1/4, 0
Let m(j) = j - 3. Let g be m(5). Suppose -24 - 17 = -5*p - s, 4*p = 2*s + 30. Factor 3*k**g + p*k + 3*k**2 + 0*k**2 + 1 - 9.
2*(k + 2)*(3*k - 2)
Let m(g) be the first derivative of -g**5/20 + g**4/6 - g**3/6 + 4*g - 2. Let x(r) be the first derivative of m(r). Factor x(j).
-j*(j - 1)**2
Factor 0*d**4 + 0 + 0*d + 3/2*d**2 + 9/4*d**3 - 3/4*d**5.
-3*d**2*(d - 2)*(d + 1)**2/4
Let k(r) = -r**3 + 1. Let z(j) = -84*j**3 - 96*j**2 - 36*j + 16. Let m(c) = 20*k(c) - z(c). Solve m(y) = 0 for y.
-1, -1/4
Let b(k) be the third derivative of k**6/60 - k**5/30 - k**4/6 + 22*k**2. Factor b(c).
2*c*(c - 2)*(c + 1)
Let w = 70 - 48. Suppose 2*n - w = -3*x + 6*n, 0 = 3*n + 12. Factor 0*r - 1/5 + 1/5*r**x.
(r - 1)*(r + 1)/5
Let y(p) be the second derivative of -4*p + 1/9*p**4 + 1/3*p**2 + 1/3*p**3 + 0. Factor y(q).
2*(q + 1)*(2*q + 1)/3
Let m(o) be the third derivative of -21*o**6/160 + o**5/8 - o**4/32 - 9*o**2. Factor m(s).
-3*s*(3*s - 1)*(7*s - 1)/4
Let n(r) = -3*r**5 - 2*r**4 + 2*r**3 + 3*r. Let a(v) = -9*v**5 + 17*v**5 + v - v**2 + v**3 - 9*v**5. Let m(d) = -2*a(d) + n(d). Find g, given that m(g) = 0.
-1, 0, 1
Suppose 2*s - 3*l + 15 = -0*s, 0 = -3*s - 4*l + 20. Suppose s = 3*v - 9, 2*w + 2*w = v + 13. Solve 2*b**3 - b - 1 + 0*b + 2*b**2 + 3*b**w - 4*b**4 - b**5 = 0.
-1, 1
Suppose 4*a = -6*k + 5*k + 20, -5*k = -3*a + 15. Let n(f) be the second derivative of -f + k*f**2 - 1/15*f**3 + 0 + 1/30*f**4. Factor n(g).
2*g*(g - 1)/5
Let z(y) be the third derivative of y**6/1200 + 13*y**5/600 + y**4/5 + 3*y**3/5 + 11*y**2. Factor z(s).
(s + 1)*(s + 6)**2/10
Suppose 4*u = 3*w + 15, 8 = -3*u + 5*u - 2*w. Suppose -5*b - s = -23, -b - 5*s = u*b - 31. Determine y, given that b + 0*y**2 - 2 - 11*y - 2*y**2 + 11*y**3 = 0.
-1, 2/11, 1
Let u(y) = 10*y - 40. Let k be u(4). Factor 0 - 9/4*l**4 + 0*l**3 + k*l - 3/4*l**5 + 3*l**2.
-3*l**2*(l - 1)*(l + 2)**2/4
Let p be (6/7)/(2/(-14)). Let f = -2 - p. What is g in 6 + 0 - 2 - f*g + g**2 = 0?
2
Let y(i) = i**3 + 21*i**2 + 23*i + 11. Let n(o) = -7*o**2 - 8*o - 4. Let l = -17 + 9. Suppose -4*z - 8 - 4 = 0. Let q(g) = l*n(g) + z*y(g). Factor q(k).
-(k + 1)**2*(3*k + 1)
Let d(z) be the first derivative of z**7/1120 + z**6/480 - z**5/160 - z**4/32 - z**3/3 + 1. Let u(q) be the third derivative of d(q). What is t in u(t) = 0?
-1, 1
Let c(i) = 19*i**2 - 7*i + 11. Let g be c(-8). Let h = g - 5107/4. Factor 0 + h*k**5 - 11/4*k**3 + 15/2*k**4 - 3*k**2 + k.
k*(k + 1)**2*(5*k - 2)**2/4
Determine b so that 28 - 58 + 30 + 25*b**2 - 5*b**4 + 10*b - 5*b**5 + 15*b**3 = 0.
-1, 0, 2
Suppose -21*t = -29*t + 16. Factor -2*m**t + 0 + 1/2*m**3 + 3/2*m.
m*(m - 3)*(m - 1)/2
Let c be (97 - 98)/(2/(-6)). Suppose -1/4*u**4 + 1/4*u**2 + 0*u + 1/4*u**5 - 1/4*u**c + 0 = 0. Calculate u.
-1, 0, 1
Factor 2/3*q**2 + 0 - 2/3*q**3 + 2/9*q**4 - 2/9*q.
2*q*(q - 1)**3/9
Let r(l) = -l**4 + 4*l**3 + 2 - 2. Let w be (-4)/(-6) - 33/9. Let x(g) = -g**4 + 3*g**3. Let j(p) = w*x(p) + 2*r(p). Factor j(k).
k**3*(k - 1)
Let c(r) = -r**2 + 14*r + 3. Let g be c(14). Let n = 14 + -12. Factor 2/11*v**5 + 2/11*v**4 - 2/11*v**n - 2/11*v**g + 0*v + 0.
2*v**2*(v - 1)*(v + 1)**2/11
Let i be (1/(-45))/(52/(-65)). Let g(v) be the second derivative of 0 - i*v**4 + 4*v - 1/3*v**3 - 3/2*v**2. What is k in g(k) = 0?
-3
Let w be 14 - 0/((-12)/3). Let s be 16/2*w/252. Factor 0*l**3 + 2/9 + 2/9*l**4 - s*l**2 + 0*l.
2*(l - 1)**2*(l + 1)**2/9
Factor -1/4*o**3 + 1/2*o**2 + 0 + 0*o.
-o**2*(o - 2)/4
Let z(n) = -5*n + n**3 + 4 + 0*n - 5*n**2 + n**2. Let a be z(5). What is p in -5*p**3 - p**3 + p**3 + a*p**4 + p**2 = 0?
0, 1/4, 1
Let o = -690 + 693. Determine i so that 10/11*i - 8/11*i**2 - 4/11 + 2/11*i**o = 0.
1, 2
Let h = 38 - 38. Let c(o) be the third derivative of h*o - 1/150*o**5 + 0 - 2/15*o**3 + 1/20*o**4 - 4*o**2. Find g such that c(g) = 0.
1, 2
Let i(l) = 13 - 2*l + l - 2 - 1. Let a be i(6). Factor 0*k**3 + 0*k + 0 - 2/3*k**a + 2/3*k**2.
-2*k**2*(k - 1)*(k + 1)/3
Let q(p) be the second derivative of -p**6/165 - p**5/22 + 7*p**4/66 + 5*p**3/33 - 6*p**2/11 + 2*p + 10. What is s in q(s) = 0?
-6, -1, 1
Let x be (2 - 2) + -2 - -4. Find w, given that -2*w + 2*w**2 - 4*w - x + 6*w**2 = 0.
-1/4, 1
Let o(y) be the second derivative of y**8/112 - y**6/20 + y**4/8 - 2*y**2 + 4*y. Let u(d) be the first derivative of o(d). Factor u(i).
3*i*(i - 1)**2*(i + 1)**2
Let c(q) be the first derivative of q**3/3 + q**2 - 2. Factor c(p).
p*(p + 2)
Let z(i) = -2*i - 3. Let x be z(-3). Let l(u) be the first derivative of 0*u + 5 + 1/9*u**2 + 2/27*u**x. Factor l(k).
2*k*(k + 1)/9
Let v(f) be the first derivative of -f**2 + 1. Let l be v(-1). Determine o so that o**3 + o**3 + 0*o**2 - 2*o - 2*o**l + 2*o**4 = 0.
-1, 0, 1
Let f = -7 + 10. Let p be (f/4)/((-3)/(-12)). Factor -26*c**2 + 2*c**p + 3*c + 10*c**3 + 21*c - 2*c**4 - 8.
-2*(c - 2)**2*(c - 1)**2
Let d be 2/((-8)/(-10))*(-24)/(-15). Factor 1/2*l**2 - 1/2*l**d + 0 + 1/2*l**3 - 1/2*l.
-l*(l - 1)**2*(l + 1)/2
Solve 2/11*i**5 - 2/11*i**4 + 2/11*i**2 - 10/11*i**3 + 8/