8 - 7 = 0. Suppose 4*j + 3*d + 12 = 6*j, 0 = -3*j + v*d + 20. Factor -2/7*h**5 + 0 - 6/7*h**4 - 6/7*h**3 + j*h - 2/7*h**2.
-2*h**2*(h + 1)**3/7
Let z(h) = -h**2 - 5*h - 5. Let s = 1 - 6. Let f(u) = -2*u + 6*u + 4*u + 2*u**2 + 8. Let v(a) = s*f(a) - 8*z(a). Determine g, given that v(g) = 0.
0
Let i(d) = 6*d**2 + 12*d + 3. Let x(v) = 13*v**2 + 25*v + 7. Let g(b) = -7*i(b) + 3*x(b). What is p in g(p) = 0?
-3, 0
Let c(i) be the second derivative of 4*i**4/3 - 10*i**3/3 + 2*i**2 + 6*i. Factor c(l).
4*(l - 1)*(4*l - 1)
Let s(o) be the first derivative of -1/54*o**4 + 0*o**2 + 0*o**5 + 0*o**3 - 2 + 1/135*o**6 - 3*o. Let p(n) be the first derivative of s(n). Factor p(g).
2*g**2*(g - 1)*(g + 1)/9
Suppose 4 + 11 = 5*j. Suppose g**j + 1 - g**2 - 1 + 2*g - 2*g**2 = 0. Calculate g.
0, 1, 2
Let n(m) = m**3 + 13*m**2 + 13*m + 14. Let o be n(-12). Let h be ((3 - 9) + o)/(-2). Determine x, given that 0 - x - 1/2*x**4 + 0*x**3 + 3/2*x**h = 0.
-2, 0, 1
Let s = -489 + 489. Solve -1/3*l**3 - 2/3*l - l**2 + s = 0 for l.
-2, -1, 0
Let y(t) be the second derivative of -t**7/168 - t**6/60 + t**4/24 + t**3/24 + 10*t. Factor y(a).
-a*(a - 1)*(a + 1)**3/4
Factor 4*a**4 - 8*a - 18 - 12*a**2 + 18.
4*a*(a - 2)*(a + 1)**2
Let m be 0 + (-2 - (0 - -2)). Let a be (-2 + m)/((-3)/2). Find k, given that 4*k**5 - 7*k**5 + 2*k**5 + 2*k**a = 0.
0, 2
Let g(z) be the third derivative of -z**6/360 - z**5/90 + z**4/72 + z**3/9 - 2*z**2. Factor g(j).
-(j - 1)*(j + 1)*(j + 2)/3
Factor 0*h + 3*h**3 + 0 + 2/3*h**2.
h**2*(9*h + 2)/3
Factor -3/4*h**4 + 0*h + 3/4*h**3 + 0*h**2 + 0.
-3*h**3*(h - 1)/4
Let j(k) = k - 5. Let u be j(8). Suppose s - 3 = -q - 4, 3*q = -u. Suppose -3/2*c**3 - c**2 + c**4 + 3/2*c**5 + s + 0*c = 0. What is c?
-1, -2/3, 0, 1
Factor 4*f**3 - 12*f**3 + 4*f**5 - f + 5*f.
4*f*(f - 1)**2*(f + 1)**2
Let s(t) be the first derivative of -1/60*t**6 + 0*t**3 - 4 + 0*t**4 + 1/30*t**5 + 0*t + 5/2*t**2. Let a(y) be the second derivative of s(y). Factor a(c).
-2*c**2*(c - 1)
Solve -8/19*g**3 + 2/19*g**2 + 0 + 0*g = 0.
0, 1/4
Let k = 4 - 2. Suppose 0*r - k = -r. What is b in 0 - 1 - r*b**2 + 0*b**2 + 3*b**2 = 0?
-1, 1
Let a(r) be the first derivative of 1/2*r**2 - 3 - 2/3*r + 0*r**3 - 1/12*r**4. Let a(n) = 0. What is n?
-2, 1
Let v(r) be the third derivative of -r**5/510 + r**4/34 - 3*r**3/17 + 35*r**2. Determine d, given that v(d) = 0.
3
Let j be (-32)/20*5/(-1). Factor 4*b**3 + j*b**4 - 19*b**3 - 3*b**5 - 3*b**4 + 7*b**4 + 6*b**2.
-3*b**2*(b - 2)*(b - 1)**2
Let l(r) be the third derivative of r**8/84 + 13*r**7/210 + r**6/8 + 7*r**5/60 + r**4/24 - 19*r**2. Suppose l(b) = 0. What is b?
-1, -1/4, 0
Let c(r) be the third derivative of r**9/75600 - r**4/4 + 2*r**2. Let p(o) be the second derivative of c(o). Factor p(l).
l**4/5
Let a(z) be the second derivative of 147*z**5/160 + 77*z**4/32 + 2*z**3 + 3*z**2/4 - z - 1. Factor a(p).
3*(p + 1)*(7*p + 2)**2/8
Let j(a) be the third derivative of 2*a**5/15 + a**4/2 - a**2. Factor j(i).
4*i*(2*i + 3)
Let k(q) = -q**2 - q. Let t(h) = -6*h - 7*h**2 + 3*h**2 + 4 + 4. Let l(j) = -2*k(j) - t(j). Factor l(v).
2*(v + 2)*(3*v - 2)
Factor 1/3*y - 1/3*y**2 + 2/3.
-(y - 2)*(y + 1)/3
Factor 60*s - 3*s**5 + 2*s**5 - 62*s + 5*s**4 - 9*s**3 + 7*s**2.
-s*(s - 2)*(s - 1)**3
Let j = 6 + -2. Suppose -j*t = 4 + 8. Let w(h) = -3*h**3 + h**2 + 2. Let v(a) = -4*a**3 + a**2 + 3. Let k(p) = t*w(p) + 2*v(p). Determine r so that k(r) = 0.
0, 1
Let l(b) be the first derivative of 0*b + 0*b**2 + 4/5*b**4 + 8/15*b**3 + 1/15*b**6 + 2/5*b**5 - 2. Factor l(g).
2*g**2*(g + 1)*(g + 2)**2/5
Let u(d) be the second derivative of -7*d**7/3 + 91*d**6/15 - d**5/5 - 41*d**4/3 + 17*d**3 - 9*d**2 - 23*d. What is m in u(m) = 0?
-1, 3/7, 1
Factor 2*i**2 + 0*i**2 + 14 + 985*i - 1001*i.
2*(i - 7)*(i - 1)
Let w = 315 + -1253/4. Factor -r**3 + r**2 + 1/2 + w*r.
-(r - 2)*(2*r + 1)**2/4
Let j(t) = -t**2 - 8*t - 9. Let k be j(-6). Solve -k*q**3 - 3*q**3 - 1 - 9*q**2 + 4*q**3 - 2*q**3 - 6*q = 0 for q.
-1, -1/4
Let z = 69 - 69. Let h(n) be the third derivative of -1/6*n**3 - 1/24*n**4 + n**2 + 0 - 1/240*n**5 + z*n. Let h(w) = 0. Calculate w.
-2
Suppose -7/3*h**4 + 2/3*h - 2/3*h**3 + 7/3*h**2 + 0 = 0. What is h?
-1, -2/7, 0, 1
Let a(w) be the first derivative of -w**4/10 + 4*w**3/5 - 12*w**2/5 + 16*w/5 + 47. Determine m so that a(m) = 0.
2
Factor -35 - 3*p**2 + 35 + 3*p.
-3*p*(p - 1)
Let v = -4 + 4. Factor -4*h + 5*h - 3*h + 2*h**2 + v*h.
2*h*(h - 1)
Suppose 0 - 1/3*i**3 - i**2 + 4/3*i = 0. What is i?
-4, 0, 1
Factor -50 - 2*a**2 - 3*a - 3*a**2 + 2*a - 34*a.
-5*(a + 2)*(a + 5)
Let y(v) be the second derivative of 0 + 1/110*v**5 - v + 0*v**3 + 0*v**2 + 1/66*v**4. Factor y(r).
2*r**2*(r + 1)/11
Let y(n) = -n**2 + n + 2. Let t be y(-4). Let k = t + 20. Factor 1/2*w**k + w + 0.
w*(w + 2)/2
Suppose 5*c = -l + 10, -4*c - 6*l + 2*l = 8. Let a(x) be the second derivative of -1/8*x**2 + 1/12*x**c - 1/48*x**4 + 0 - x. Solve a(q) = 0 for q.
1
Find y, given that 0 - 12/11*y**3 - 2/11*y**5 - 2/11*y - 8/11*y**4 - 8/11*y**2 = 0.
-1, 0
Let r(m) be the first derivative of m**6/18 - 2*m**5/15 + 2*m**3/9 - m**2/6 - 6. Factor r(n).
n*(n - 1)**3*(n + 1)/3
Let k(c) = 16 - 2*c - 5*c**2 - 16. Suppose 0 = u + 3*u + 108. Let g(r) = -66*r**2 - 27*r. Let n(a) = u*k(a) + 2*g(a). Suppose n(z) = 0. Calculate z.
0
Suppose 0*q = -2*v + 4*q + 8, 11 = 4*v - 3*q. Solve 2/9*o**3 + 10/9*o**v - 2 + 2/3*o = 0.
-3, 1
Solve 0 + 2/5*r - 1/5*r**2 - 2/5*r**4 - r**3 = 0 for r.
-2, -1, 0, 1/2
Let b(v) be the second derivative of v**4/108 + v**3/18 - 46*v. Factor b(z).
z*(z + 3)/9
Determine n so that 72/5*n**2 + 48/5 + 3/5*n**4 - 24/5*n**3 - 96/5*n = 0.
2
Let p(x) = -x**3 + 5*x**2 - 3*x + 4. Let r be p(4). Suppose -5*a = -3*a - r. Let 0*j**3 + 2*j**a + 2*j**3 - j**2 - j**2 - 2*j = 0. Calculate j.
-1, 0, 1
Let f = 20 + -28. Let i be ((-2)/(-4))/((-6)/f). Suppose -1/3*b**2 + i*b + 0 - 1/3*b**3 = 0. Calculate b.
-2, 0, 1
Suppose 3*w + n + 1 = -1, 4*w - 5*n - 29 = 0. Let z be 1*(1 - w*-2). Factor h + h**3 - h + z*h**2 - 4.
(h - 1)*(h + 2)**2
Find a, given that -7*a**4 + 8*a - 2*a**3 + 10*a**4 + a**4 - 8*a**2 - 2*a**4 = 0.
-2, 0, 1, 2
Let o(i) = 11*i**3 + 5*i**2 - 49*i + 19. Let g(m) = -4*m**3 - 2*m**2 + 16*m - 6. Let t(v) = 14*g(v) + 4*o(v). Factor t(f).
-4*(f - 1)*(f + 2)*(3*f - 1)
Factor 149*k + 2 + 0 - 139*k - k**2 + 9.
-(k - 11)*(k + 1)
Let i(r) be the third derivative of -r**6/30 + r**5/15 + r**4/3 + r**2. Factor i(n).
-4*n*(n - 2)*(n + 1)
Suppose -2*z + 34 + 0 = 4*t, 2*z = t + 9. Suppose -3 - 1 + 5*u - z*u + 2*u**2 = 0. Calculate u.
-1, 2
Let b(y) be the second derivative of -y**7/168 + y**6/60 + 3*y**5/80 - y**4/12 - y**3/6 - 7*y. Suppose b(u) = 0. Calculate u.
-1, 0, 2
Suppose 4*c + 5*j = -13, 2*c = 5*j + 12 + 19. Determine z so that 1 - 8*z**3 - 3 - 9*z - 12*z**2 + 2*z**3 + z**c = 0.
-1, -2/5
Let x = -11/8 - -15/8. Suppose -d + 12 = -4*d, k - 5*d - 23 = 0. Find i such that x*i**5 + 1/2*i**4 + 0 + 0*i + 0*i**k + 0*i**2 = 0.
-1, 0
Let m(k) be the third derivative of k**5/20 - 5*k**4/2 + 50*k**3 + 38*k**2. What is r in m(r) = 0?
10
Let d(q) = -9*q**3 - 13*q**2 - 5*q - 5. Let f(t) = 14*t**3 + 20*t**2 + 8*t + 8. Let g(p) = 8*d(p) + 5*f(p). Factor g(b).
-2*b**2*(b + 2)
Let b = 6 + -4. Suppose 0*f + 2*f = 5*x - 17, 0 = -3*x + b*f + 11. Factor 2/5*o**5 - 2/5*o**2 + 0 + 0*o + 2/5*o**4 - 2/5*o**x.
2*o**2*(o - 1)*(o + 1)**2/5
Let d be 1352/(-845) + 24/10. Factor -2/5*h - d + 2/5*h**2.
2*(h - 2)*(h + 1)/5
Let w = -71 - -71. Suppose -1/3*u**4 + 0*u - 1/3*u**3 + 2/3*u**2 + w = 0. Calculate u.
-2, 0, 1
Let q(o) be the second derivative of 0 - 1/36*o**4 + 1/90*o**6 + 1/18*o**3 - 6*o - 1/60*o**5 + 0*o**2. Find v such that q(v) = 0.
-1, 0, 1
Let r(c) = -24*c**2 - 14*c - 14. Let u(s) = -5*s**2 - 3*s - 3. Let m(a) = 3*r(a) - 14*u(a). Factor m(w).
-2*w**2
Suppose 2*r = -3*r + 3*r. Suppose -1/2*d + r + 1/2*d**2 = 0. Calculate d.
0, 1
Suppose -6 = f - 4*f. Let v = -2 + f. Solve -3 + 6*z + 7 - 2*z**3 + v = 0.
-1, 2
Let v(u) = 0*u + 9 + 0*u - u. Let h be v(4). Let 0*n**2 + 0*n - 2/7*n**h + 0*n**4 + 0 + 2/7*n**3 = 0. What is n?
-1, 0, 1
Suppose -33*w**3 - 9*w**3 + 2*w**2 + 10*w**2 + 18*w**4 + 15*w**3 - 3*w**5 = 0. What is w?
0, 1, 4
Suppose 26 = 338*k - 325*k. Factor 4*p + 1/2*p**3 - 5/2*p**2 - k.
(p - 2)**2*(p - 1)/2
Let c = 23 - 38. Let j = c - -17. Factor 2/5 + 