z**3 + 4*z**3 - 12*z**4 = 0.
-1, 0, 1
Factor -153*h**2 + 7*h**3 + 108 + 108*h + 189*h**2 - 3*h**3.
4*(h + 3)**3
Let k(z) be the first derivative of 2*z**3/15 + 2*z**2 + 10*z - 41. Factor k(g).
2*(g + 5)**2/5
Factor -9/5*r - 9/5*r**2 - 3/5*r**3 - 3/5.
-3*(r + 1)**3/5
Suppose 4*q = -5*m - 17, -m + 3*m + 16 = 3*q. Let g = 7 + m. Factor v - 10*v**3 - 3*v**5 - v - 3*v**g - 9*v**4 + v**3.
-3*v**2*(v + 1)**3
Suppose -35*x + 5*x + 90 = 0. Find f such that 0*f**4 + 0 + 0*f - 4/13*f**2 - 6/13*f**x + 2/13*f**5 = 0.
-1, 0, 2
Let b(h) be the third derivative of -h**6/480 + h**5/120 + h**4/24 - h**3/3 - 24*h**2. Solve b(a) = 0 for a.
-2, 2
Let v(m) = -m**4 - m**3 - m**2 - m - 1. Let a(r) = -10*r**4 + 20*r**3 - 12*r**2 - 6*r - 2. Let d(n) = a(n) - 2*v(n). Determine j, given that d(j) = 0.
-1/4, 0, 1, 2
Let v be 2*(-3)/(-24)*8. Let b(w) be the first derivative of -3/5*w**5 - 2 - 7/3*w**3 - w**2 + 0*w - v*w**4. Factor b(d).
-d*(d + 1)**2*(3*d + 2)
Let g(v) = 4*v**3 - 17*v**2 + 12*v - 4. Let t(p) = -2*p**3 + 8*p**2 - 6*p + 2. Let l(d) = 2*g(d) + 5*t(d). Factor l(u).
-2*(u - 1)**3
Suppose -7*v**3 - 21*v - 12*v**3 + 2*v**3 + 3 + 36*v**2 - 1 = 0. What is v?
2/17, 1
Let j = 54 - 54. Let k(n) be the third derivative of -1/60*n**6 + 1/30*n**5 - 1/3*n**3 + 3*n**2 + 1/12*n**4 + j + 0*n. Solve k(i) = 0.
-1, 1
Let k(p) be the third derivative of -1/15*p**4 - 1/50*p**5 + 2*p**2 + 1/525*p**7 + 4/15*p**3 + 0*p + 0 + 1/150*p**6. Factor k(b).
2*(b - 1)**2*(b + 2)**2/5
Let j(n) be the first derivative of -n**5/40 - n**4/4 - n**3 - 3*n**2/2 - 3. Let i(q) be the second derivative of j(q). Factor i(a).
-3*(a + 2)**2/2
Let v = 1409/2 + -703. Factor 9/4*u**3 + 0*u + 0 - 3/4*u**5 + 0*u**4 + v*u**2.
-3*u**2*(u - 2)*(u + 1)**2/4
Let x(r) be the third derivative of -r**5/240 - 13*r**4/96 + 5*r**2 - 3. Factor x(g).
-g*(g + 13)/4
Let n(u) = -u**2 + 5*u - 4. Let m be n(4). Let a(c) be the third derivative of 0 + m*c**3 + 0*c + 3*c**2 + 1/24*c**4 + 1/120*c**6 - 1/30*c**5. Factor a(r).
r*(r - 1)**2
Let m(n) be the second derivative of -3*n + 0*n**2 + 0 + 1/6*n**4 + 0*n**3. Factor m(u).
2*u**2
Let h(p) = -p**3 + 2*p**2 + 2. Let i be h(2). Factor -12*u**4 + 3*u**i - 3*u**5 - 3*u**5 + 3*u**4.
-3*u**2*(u + 1)**2*(2*u - 1)
Let v(d) be the first derivative of -2*d**5/85 + 13*d**4/34 - 70*d**3/51 - 49*d**2/17 + 51. What is x in v(x) = 0?
-1, 0, 7
Suppose 2*v + 8 = 4*h - 3*v, -h - 3*v + 2 = 0. Let 0 + 1/4*b - 1/4*b**h = 0. Calculate b.
0, 1
Find b, given that -8*b**2 - 40*b - b**2 - 9*b**2 - 80 + 13*b**2 = 0.
-4
Let q(b) = b**3 + b**2 + b - 1. Let z(o) = -28*o**4 - 67*o**3 - 47*o**2 - 11*o + 3. Let d(k) = 3*q(k) + z(k). Factor d(m).
-4*m*(m + 1)**2*(7*m + 2)
Let f be (3*(-5)/(-20))/27. Let d(z) be the third derivative of 0*z + 0 + 1/180*z**6 - z**2 + 1/9*z**3 - f*z**4 - 1/90*z**5. Suppose d(q) = 0. Calculate q.
-1, 1
Let k(v) = -2*v**3 - 3*v. Let r = -2 + -1. Let y(o) = 0*o**3 + o**3 - 4*o**3 - 5*o. Let m(b) = r*y(b) + 5*k(b). Find f, given that m(f) = 0.
0
Let g = 3 - 8. Let d = g + 7. Solve 1/4*o**3 + 0 - 1/4*o - 1/4*o**d + 1/4*o**4 = 0 for o.
-1, 0, 1
Let y(o) be the first derivative of -o**5/20 - o**4/8 + 7*o**3/12 - o**2/2 + 17. Factor y(v).
-v*(v - 1)**2*(v + 4)/4
Let y = -4 - -5. Let h be (-6)/(-15) + y/(-15). What is p in h*p**4 + 2/3*p**3 + 0 + 0*p + 1/3*p**2 = 0?
-1, 0
Let j(x) be the third derivative of -1/160*x**6 + 0 + 1/1344*x**8 + 1/48*x**4 + 1/840*x**7 + 0*x**3 - 1/240*x**5 - 5*x**2 + 0*x. Factor j(a).
a*(a - 1)**2*(a + 1)*(a + 2)/4
Let l be ((-6)/3)/(3/(-6)). Let o(p) be the third derivative of 0*p - 1/120*p**5 - 1/480*p**6 + 0*p**l + 0 + 1/280*p**7 + 2*p**2 + 0*p**3. Factor o(v).
v**2*(v - 1)*(3*v + 2)/4
Let s(j) be the second derivative of -1/8*j**4 - j - 3/4*j**2 + 0 - 1/2*j**3. Factor s(a).
-3*(a + 1)**2/2
Suppose -3 = -5*s + 3*z, -5*s = -6*s + 3*z + 3. Factor s*q - 3/2 + 3/2*q**2.
3*(q - 1)*(q + 1)/2
Let o(g) = 17*g - 525. Let t be o(31). Suppose -2/11 - 6/11*n**t - 8/11*n = 0. What is n?
-1, -1/3
Suppose -46*k + 8 = -48*k - 2*l, 3*k - 20 = 5*l. Solve -2/3*q**2 + k - 4/3*q = 0 for q.
-2, 0
Let c(p) be the first derivative of p**7/210 + p**6/45 + 7*p**3/3 + 3. Let k(q) be the third derivative of c(q). Factor k(a).
4*a**2*(a + 2)
Let v(u) be the third derivative of u**7/630 + u**6/180 - u**4/36 - u**3/18 + 3*u**2. Factor v(t).
(t - 1)*(t + 1)**3/3
Suppose -y + 0 = -1. Suppose 2*m - 5 = -y. Factor m*d**3 + 10*d + 4 + 0*d + 12*d**2 - 4*d**2.
2*(d + 1)**2*(d + 2)
Let p be 36/(-6)*(-4)/14. Let 50/7*u**4 - 72/7*u**2 + 0 + 18/7*u**5 - p*u**3 + 16/7*u = 0. What is u?
-2, 0, 2/9, 1
Let y be (3/(-2))/(9/(-24)). Factor -3*o**y + o**4 + o - 2 + o**3 + o**4 + 3*o**2 - 2*o.
-(o - 2)*(o - 1)*(o + 1)**2
Suppose -2*x + 4*b = x - 11, 4*x + 2*b = 22. Let f be x/(-2)*(-12)/10. Factor 2 + f*j**2 - j**2 - 3*j**2 - 4*j + 3*j**2.
2*(j - 1)**2
Let x be 2*1 + 4 + -3. Determine f so that 0*f**3 - 2*f + 67*f**4 - 2*f**5 - 59*f**4 - 8*f**x - 4*f**3 + 8*f**2 = 0.
0, 1
What is u in -135*u + 15*u**2 - 6*u**2 - 5*u**3 + 36*u**2 + 135 + 0*u**2 = 0?
3
Let j(g) = 2*g + 2. Let t be j(0). Factor 4/3 - 2/3*c + 2/3*c**3 - 4/3*c**t.
2*(c - 2)*(c - 1)*(c + 1)/3
Let a = 27 - 183/7. Factor -2/7 + 2/7*v**3 - 6/7*v**2 + a*v.
2*(v - 1)**3/7
What is k in -5*k**2 + 17*k**2 - 39*k**3 + 15*k**4 + 12*k + 0*k**3 = 0?
-2/5, 0, 1, 2
Let a = 54 + -49. Let k(p) be the first derivative of 3/2*p**3 + 2*p - 4 + 5/2*p**2 + 1/20*p**a + 7/16*p**4. Factor k(i).
(i + 1)*(i + 2)**3/4
Suppose 4/7*g**5 - 8/7*g**2 + 4/7*g**4 + 4/7 + 4/7*g - 8/7*g**3 = 0. What is g?
-1, 1
Let h(r) be the second derivative of r**6/40 - r**5/20 - r**3/6 - 7*r. Let u(a) be the second derivative of h(a). Let u(k) = 0. What is k?
0, 2/3
Let q(x) be the third derivative of x**6/60 + x**5/6 + 2*x**4/3 + 4*x**3/3 - 6*x**2. Find p such that q(p) = 0.
-2, -1
Let d = -3 + 9. Let w = -6 + d. Factor 4/9*c**4 + 0 - 2/9*c**5 + w*c**2 - 2/9*c**3 + 0*c.
-2*c**3*(c - 1)**2/9
Factor -1/4*m**3 + 1/2 + 3/4*m + 0*m**2.
-(m - 2)*(m + 1)**2/4
Solve -18/7*v**4 + 6/7*v**3 + 0 - 8/7*v + 16/7*v**2 = 0.
-1, 0, 2/3
Factor 0*m**2 - 2/9*m**3 + 0 + 2/9*m.
-2*m*(m - 1)*(m + 1)/9
Let t(l) be the second derivative of -25*l**4/12 - 5*l**3/3 - 2*l. Let t(k) = 0. Calculate k.
-2/5, 0
Let z(a) be the first derivative of -a**6/30 + a**5/5 - a**4/2 + 2*a**3/3 - a**2/2 + 3*a + 3. Let l(k) be the first derivative of z(k). Let l(w) = 0. What is w?
1
Let x be (-4)/16*-4 - 1. Factor -3*d**2 - 14*d**4 + x*d**2 + 17*d**4.
3*d**2*(d - 1)*(d + 1)
Let t(y) be the first derivative of 11*y**7/21 + 7*y**6/3 + 39*y**5/10 + 17*y**4/6 + 2*y**3/3 - 3*y + 2. Let d(v) be the first derivative of t(v). Factor d(p).
2*p*(p + 1)**3*(11*p + 2)
Let p(d) be the first derivative of d**8/56 - d**7/35 - 3*d**6/80 + d**5/20 + d**4/16 + 3*d**2/2 + 7. Let z(i) be the second derivative of p(i). Factor z(v).
3*v*(v - 1)**2*(2*v + 1)**2/2
Suppose 5 = 3*k + 4*b, b - 13 = -4*k + 2*b. Suppose -k*i - 5 = -17. Factor 0*f**i + 1/3*f**5 + 0 - 1/3*f**3 + 0*f + 0*f**2.
f**3*(f - 1)*(f + 1)/3
Let g(v) be the first derivative of 0*v**3 + 3 + 1/180*v**5 + 3/2*v**2 + 0*v**4 + 0*v. Let m(q) be the second derivative of g(q). Factor m(d).
d**2/3
Suppose -15 = 2*j + 21. Let i = -12 - j. Factor i*x - x**2 - 6*x + 2*x**2.
x**2
Let z(f) be the third derivative of 1/90*f**5 + 0 + 0*f**3 + 9*f**2 + 7/360*f**6 + 0*f + 0*f**4. What is p in z(p) = 0?
-2/7, 0
Factor 3*z**4 + 4*z - 5/3*z**2 - 4*z**3 - 4/3.
(z - 1)*(z + 1)*(3*z - 2)**2/3
Let o(m) = 4*m**2 + 5*m - 9. Let j(u) = u - 1. Let d(p) = -5*j(p) + o(p). Factor d(h).
4*(h - 1)*(h + 1)
Suppose 3*p = -0*o + o - 9, -3*o - p = 23. Let v be (6 + -3)*o/(-27). Factor 2*z**2 + v*z**3 + 2/3 + 2*z.
2*(z + 1)**3/3
Let l(o) be the third derivative of -o**8/2184 + 7*o**6/780 + o**5/65 + 53*o**2. Suppose l(v) = 0. What is v?
-2, -1, 0, 3
Let s(c) = c**2 - 2*c. Let q be s(-2). Solve 164*r**3 + 13*r**2 - q + 60*r - 84*r**4 - 137*r**2 + 16*r**5 - 24*r**2 = 0.
1/4, 1, 2
Let v = 1/20 - -11/180. Let c(u) be the second derivative of -2*u + 1/36*u**4 + 1/6*u**2 + 0 + v*u**3. Factor c(p).
(p + 1)**2/3
Let h(c) be the third derivative of 0 + 0*c - 1/112*c**8 + 0*c**5 + 0*c**3 + 2*c**2 + 1/20*c**6 - 1/8*c**4 + 0*c**7. Let h(o) = 0. Calculate o.
-1, 0, 1
Let j(f) = -4*f**5 + 6*f**4 + 8*f**3 - 12*f**2 - 8*f + 6. Let a(l) = l**3 + l