- 8*d**2 + 7*d**2 - d**3 + 3*d**4. Let n = 0 - 1. Let o(x) = -5*x**4 - 3*x**3 - 3*x**2 - x. Let t(k) = n*o(k) + 4*w(k). Factor t(u).
u*(u - 1)**2*(u + 1)
Let h(d) = d + 1. Let g be h(-2). Let z be g/(-2)*(-4)/(-6). Factor z - t - 4/3*t**2.
-(t + 1)*(4*t - 1)/3
Suppose 6*p**3 + 0*p**2 + 3*p**2 + 2*p**2 - p**2 = 0. What is p?
-2/3, 0
Let o(h) = h**5 + 12*h**4 + 15*h**3 + 4*h**2 + 2*h + 2. Let t(m) = -4*m**5 - 60*m**4 - 75*m**3 - 19*m**2 - 11*m - 11. Let f(b) = 11*o(b) + 2*t(b). Factor f(g).
3*g**2*(g + 1)**2*(g + 2)
Suppose -4*i = -0*i + 64. Let u be i/24*9/(-12). Factor -2*q - u*q**4 - 1/2 - 3*q**2 - 2*q**3.
-(q + 1)**4/2
Let f(k) = -5*k**4 + 6*k**3 - 6*k - 3. Let p(y) = -y**3 + y**4 + 0*y + 3 + y - 2. Let b = -5 + 9. Let n(m) = b*p(m) + f(m). Let n(h) = 0. What is h?
-1, 1
Let m(k) be the first derivative of -k**4/16 + k**3/2 - 11*k**2/8 + 3*k/2 - 54. Factor m(r).
-(r - 3)*(r - 2)*(r - 1)/4
Let s(v) = -v**4 - 5*v**3 + v**2 + 5*v + 3. Let z(h) = h**4 + h**3 - h**2 - h - 1. Let g(w) = -s(w) - 3*z(w). Factor g(d).
-2*d*(d - 1)**2*(d + 1)
Let i(j) be the first derivative of -j**6/180 - j**5/30 + 5*j**3/3 + 3. Let s(y) be the third derivative of i(y). Factor s(l).
-2*l*(l + 2)
Let n = 4 + -6. Let c(w) = -w**3 - 2*w**2 - w. Let y be c(n). Factor d**4 - d**4 - d - d**5 + 0*d**4 + y*d**3.
-d*(d - 1)**2*(d + 1)**2
Let d(y) be the second derivative of -1/12*y**4 + 0*y**2 - y + 1/20*y**5 - 1/6*y**3 + 1/30*y**6 + 0. Factor d(l).
l*(l - 1)*(l + 1)**2
Let p be (50/(-18))/1 + 3. Let j(g) be the first derivative of 4/3*g + p*g**3 + 3 - g**2. Let j(o) = 0. Calculate o.
1, 2
Suppose -1/7*k - 1/7*k**2 + 0 = 0. Calculate k.
-1, 0
Determine l so that -2/7*l**4 + 2/7*l - 2/7*l**3 + 2/7*l**2 + 0 = 0.
-1, 0, 1
Let u(o) be the second derivative of -o**4/3 - 8*o**3/3 - 6*o**2 - 7*o. Determine l so that u(l) = 0.
-3, -1
Let w(b) = b**5 - b**4 + 1. Let n(o) = 8*o**5 - 2*o**4 + 2*o**3 + 6. Let s(u) = n(u) - 6*w(u). Factor s(h).
2*h**3*(h + 1)**2
Let i(n) = 2*n**4 + 6*n**2 - 4*n. Let m(s) = -s**4 + s**3 - s**2. Let y(z) = -i(z) - 4*m(z). Let y(f) = 0. What is f?
-1, 0, 1, 2
Let n be 6/(-15) + 17/5. Suppose 5*p = 7 + n. Factor 2/3*i**p + 2/3*i**3 - 2/3*i - 2/3.
2*(i - 1)*(i + 1)**2/3
Let q(t) be the first derivative of 5*t**3/3 - 5*t**2/2 - 10*t + 48. Factor q(w).
5*(w - 2)*(w + 1)
Let l be (-31)/(-7) + 3/(-7). Let o(w) be the first derivative of 2/3*w**3 + 1/3*w + 1/15*w**5 - 3 + 2/3*w**2 + 1/3*w**l. Factor o(i).
(i + 1)**4/3
Let u be (-133)/(-49) - 2/(-7). Let h be 3 + u/((-27)/21). Factor -h*l**2 + 2/3 + 0*l.
-2*(l - 1)*(l + 1)/3
Let l(k) be the first derivative of 2*k**6 + 9*k**5/5 - 3*k**4/4 + 18. Factor l(b).
3*b**3*(b + 1)*(4*b - 1)
Let d(l) = l**2 + 8*l. Let x be d(-4). Let q = -14 - x. Suppose -1/5*m**q + 2/5 + 1/5*m = 0. What is m?
-1, 2
Let o = 5 + 0. Suppose -11 = -5*i + s, 5*s - 5 = -0*i + o*i. Factor 9 + 4 - 2*p**i - 6*p**2 - 5.
-2*(p - 1)*(p + 2)**2
Let x = 93/10 + -79/10. Find y such that -2/5 + 16/5*y**4 - 11/5*y - 14/5*y**2 + x*y**5 + 4/5*y**3 = 0.
-1, -2/7, 1
Let k(z) be the first derivative of 1/20*z**5 - 1/6*z**3 + 1/4*z - 1/24*z**6 - 1/8*z**2 - 2 + 1/8*z**4. Find b, given that k(b) = 0.
-1, 1
Let a(m) be the third derivative of -1/24*m**4 + 0 - 1/3*m**3 + 0*m + 1/60*m**5 - 4*m**2. Determine o, given that a(o) = 0.
-1, 2
Let h = -7 - -7. Factor h + w**4 - 3*w**3 + w**2 + 3*w - 2 + 0*w**2.
(w - 2)*(w - 1)**2*(w + 1)
Let q(k) = k**2 - k. Suppose 4*z = 5*a - 6, 0*a - 2*z - 6 = -4*a. Let l be q(a). Factor 1/2*i**3 - 1/2*i**l + 0 + 0*i.
i**2*(i - 1)/2
Suppose -k + 9 = 4. Suppose 10 = k*x + 5*h, -x - 3*h - 6 = 2*h. What is j in j**4 + j**2 - x*j**2 + 3*j**3 + 0*j**4 - 2*j**4 + j = 0?
0, 1
Suppose 0*g + 4*g + 16 = 4*s, 5*s - 36 = -3*g. Let o be 10/(-25)*(-5)/s. Factor 1/3*u**3 + u - o - u**2.
(u - 1)**3/3
Let r(t) be the second derivative of 5*t + 0 + 1/26*t**5 + 4/13*t**3 - 3/13*t**4 + 8/13*t**2. Find n, given that r(n) = 0.
-2/5, 2
Let k(r) = 7*r - 4. Let u be k(3). Let z(f) = 4*f**2 - 10*f - 6. Let j(s) = 11*s**2 - 29*s - 17. Let o(c) = u*z(c) - 6*j(c). Factor o(t).
2*t*(t + 2)
Let f(b) be the first derivative of -b**6/720 + b**5/180 + 2*b**2 + 6. Let r(g) be the second derivative of f(g). What is l in r(l) = 0?
0, 2
Let u(n) = -2*n + 19. Let c be u(8). Suppose -5*y**2 + 2*y**2 + 3*y**3 + 0*y**c = 0. What is y?
0, 1
Let k(n) be the first derivative of -3*n**4/4 + 5*n**3 + 8*n**2 + 13*n - 6. Let c(o) = -2*o**3 + 8*o**2 + 8*o + 7. Let b(f) = -10*c(f) + 6*k(f). Solve b(l) = 0.
-2, -1
Let q(b) be the third derivative of -b**5/6 + b**4/6 - 5*b**2. Solve q(l) = 0.
0, 2/5
Find q such that -2*q**3 - 3*q**3 + q**4 + q**3 + 3*q**4 = 0.
0, 1
Let n = -11 - -8. Let m = n - -6. Find f, given that 5*f**3 + 7*f**4 + m*f**2 - 2*f + 3*f**3 + 4*f**3 = 0.
-1, 0, 2/7
Factor 1/5*l**4 - 1/5*l**3 + 0 - 1/5*l**2 + 1/5*l.
l*(l - 1)**2*(l + 1)/5
Suppose 0*g - 8/5*g**4 - 4/5*g**2 + 2/5*g**5 + 0 + 2*g**3 = 0. What is g?
0, 1, 2
Suppose 0*t + 2*t = 10. Factor -9*c**3 + 9*c**3 + 2*c**4 - 2*c**t.
-2*c**4*(c - 1)
Let f(s) be the first derivative of s**5/5 - 3*s**4/4 + 2*s**3/3 + 19. Solve f(q) = 0.
0, 1, 2
Let y(x) be the first derivative of 1/4*x**6 - 8 + 1/2*x**3 + 3/2*x**2 - 3/10*x**5 + 0*x - 9/8*x**4. Let y(l) = 0. Calculate l.
-1, 0, 1, 2
Let u(h) = 3*h - 15. Let m be u(6). Find d such that -2/7*d**m - 2/7*d**2 + 0 + 0*d = 0.
-1, 0
Suppose -3*y = -5 + 2. Let i = y + 5. Find p such that -25*p**3 + 20*p**2 - 4*p - 6 + i = 0.
0, 2/5
Let q(g) be the third derivative of g**8/10080 + g**7/6300 + g**5/20 + 2*g**2. Let r(a) be the third derivative of q(a). Suppose r(s) = 0. What is s?
-2/5, 0
Let l(t) = -882*t**2 - 168*t - 19. Let w(f) = 441*f**2 + 84*f + 10. Let u(r) = -6*l(r) - 11*w(r). Solve u(v) = 0.
-2/21
Let y(a) = -a - 5. Let c be y(-7). Suppose -3*k - 11 = -2*q, -4*k = -q + k + c. What is h in -h**2 + 2*h**2 + 2*h**4 - q*h**2 - 4*h + 0*h = 0?
-1, 0, 2
Let j(r) be the third derivative of -1/9*r**3 - 1/90*r**5 + 0 - 4*r**2 + 0*r + 1/18*r**4. Factor j(d).
-2*(d - 1)**2/3
Factor 2/15*c**4 + 8/15*c + 0*c**2 - 2/5*c**3 + 0.
2*c*(c - 2)**2*(c + 1)/15
Let y be (6 - 1)*(-3)/(-3). Factor 3*h + 0*h**3 - 6*h**2 - 2*h**3 + y*h**3.
3*h*(h - 1)**2
Let f(q) = -2*q + 12. Let g be f(6). Factor -8/5*a**3 + 8/5*a**2 + g - 2/5*a.
-2*a*(2*a - 1)**2/5
Let k = 9 + -5. Factor -2*s**2 - 6*s**4 - k*s**3 - 11 - 2*s**5 + 6*s + 6*s**2 + 13.
-2*(s - 1)*(s + 1)**4
Suppose 0 = 2*u - 7 - 3. Suppose 3*l**3 + u*l**4 + 4*l**4 - 3*l**4 - 3*l**4 = 0. What is l?
-1, 0
Let n = -12 + 8. Let z = -2 - n. Factor -45/4*w**4 - w**z + 0 + 0*w - 6*w**3 - 25/4*w**5.
-w**2*(w + 1)*(5*w + 2)**2/4
Suppose 2*y - 3*i - 24 = -y, -i = -3. Suppose -z - y = -4*s, -3*z - 11 = z - 5*s. Suppose 7 + 242*w**2 - 162*w**3 - 8*w**2 + z - 80*w = 0. What is w?
2/9, 1
Solve -15/2*m + 9/2 - 1/2*m**3 + 7/2*m**2 = 0.
1, 3
Let f(r) be the first derivative of -6 - 1/2*r - 1/3*r**3 - 1/4*r**4 + 3/10*r**5 + 3/4*r**2 - 1/12*r**6. Factor f(b).
-(b - 1)**4*(b + 1)/2
Find i, given that -36/7*i**2 - 192/7 - 3/7*i**3 - 144/7*i = 0.
-4
Let x(g) be the second derivative of -1/12*g**3 + 0 + 10*g + 0*g**2 - 3/80*g**5 - 5/48*g**4. Let x(j) = 0. Calculate j.
-1, -2/3, 0
Let w = -31 - -15. Let v = w - -18. Solve v*b**2 + 2/3*b + 2*b**3 + 0 + 2/3*b**4 = 0.
-1, 0
Let r(m) be the third derivative of -m**6/960 - m**5/240 + m**4/64 - 35*m**2. Factor r(t).
-t*(t - 1)*(t + 3)/8
Suppose -8 = 7*v - 22. Factor v*t**2 + 1/2*t + 0 + 3/2*t**3.
t*(t + 1)*(3*t + 1)/2
Factor 23 - 8*w - 4*w**2 + 7 + 2.
-4*(w - 2)*(w + 4)
Let h = 14 + -1. Let w be (-11)/13 + 13/h. Determine l so that -w*l**2 + 8/13*l**3 + 0 + 4/13*l**5 - 10/13*l**4 + 0*l = 0.
0, 1/2, 1
Let i(d) be the third derivative of d**8/3360 - d**7/1260 - d**6/360 + d**5/60 - 5*d**4/24 + 3*d**2. Let z(r) be the second derivative of i(r). Factor z(v).
2*(v - 1)**2*(v + 1)
Suppose -4*h - 7 = -27. Let j(p) be the second derivative of -1/20*p**h + 0*p**2 + 2*p + 0*p**4 + 0 + 0*p**3. What is i in j(i) = 0?
0
Let k(v) be the second derivative of 1/10*v**6 + 0*v**4 - v - 3/2*v**2 + 0 - v**3 + 3/10*v**5. Let k(n) = 0. Calculate n.
-1, 1
Suppose 2*q + 8 = 6*q. Factor 53*i**2 - q - 10 + 22*i**2.
3*(5*i - 2)*(5*i + 2)
Let k(g) be the second derivative of 2*g**6/15 - g**4/3 - 10*g. Factor k(d).
4*d**2*(d - 1)*(d + 1)
Let l(v) be the second d