n - 2)*(n + 1)/4
Let d(i) = -i**2 + i. Let w(x) = 4*x**3 + 16*x**2 - 4*x - 16. Let b(r) = 4*d(r) + w(r). Factor b(p).
4*(p - 1)*(p + 2)**2
Suppose 6*h + 4 = 10*h. Let o be (-3)/81*-33 - h. Determine i, given that 2/9*i**4 + 2/9 + 4/9*i**3 - 4/9*i**2 - 2/9*i - o*i**5 = 0.
-1, 1
Let f(x) be the second derivative of 3/5*x**5 + 0 - 8*x**2 - 16/3*x**3 - 7*x - 1/3*x**4. Determine b so that f(b) = 0.
-1, -2/3, 2
Determine w, given that 4/11 + 2/11*w - 2/11*w**2 = 0.
-1, 2
Factor -2/3*j**5 - 6*j**4 - 14*j**3 - 38/3*j**2 - 4*j + 0.
-2*j*(j + 1)**3*(j + 6)/3
Let w(x) be the first derivative of x**5/15 - x**4/12 - x**3/9 + x**2/6 + 2. Factor w(l).
l*(l - 1)**2*(l + 1)/3
Suppose -112 - 13 = -5*f. Let w = -73/3 + f. Find q, given that 0 - 2/3*q**2 - w*q = 0.
-1, 0
Let d(o) = -20*o**4 - 36*o**3 - 20*o**2 - 4*o - 5. Let a(h) = -19*h**4 - 35*h**3 - 21*h**2 - 5*h - 4. Let w(n) = 4*a(n) - 3*d(n). Let w(z) = 0. Calculate z.
-1/2
Let u(o) be the second derivative of 2*o**6/45 - 4*o**5/5 + 4*o**4 + 22*o. Find j, given that u(j) = 0.
0, 6
Let j(r) = 4*r**3 - 8*r**2 + 56*r + 56. Let n(f) = -f**3 + f**2 - f + 1. Let p(u) = j(u) + 8*n(u). Factor p(z).
-4*(z - 4)*(z + 2)**2
Let p = -28 - -32. Let f(j) be the second derivative of 3*j - 1/40*j**5 + 0*j**2 - 1/120*j**6 - 1/48*j**p + 0*j**3 + 0. Determine g, given that f(g) = 0.
-1, 0
Let p be (-42)/(-10) - (-1)/(-5). Find t, given that -2*t - 2 - p*t**2 + 5*t**2 + t = 0.
-1, 2
Let x(v) be the first derivative of 2*v - 1/10*v**5 + 2 + 1/3*v**3 + 0*v**4 + 0*v**2. Let z(d) be the first derivative of x(d). Factor z(g).
-2*g*(g - 1)*(g + 1)
Let y(j) be the third derivative of -1/8*j**4 + 1/40*j**5 + 1/4*j**3 + j**2 + 0*j + 0. Factor y(a).
3*(a - 1)**2/2
Let 2*q - 4*q**2 + 0*q**2 + 2*q**2 = 0. What is q?
0, 1
Let r(h) be the second derivative of -8*h - 1/3*h**3 + 1/2*h**2 + 1/12*h**4 + 0. What is i in r(i) = 0?
1
Let l(r) = r**3 + 4*r**2 + 2*r - 1. Let y be l(-3). Solve 15 + 24*i - 3 + y*i**3 + 4 + 12*i**2 = 0 for i.
-2
Let a be ((-1)/(-2))/((-5)/10). Let d be a - (-1)/((-8)/(-10)). Suppose 1/4*f**2 + d - 1/2*f = 0. Calculate f.
1
Let h = 2 + -7. Let j be ((-6)/10 - 0)*h. Factor 3*s**5 - 2*s**j - s**5 - s**2 + 2*s**4 - s**2.
2*s**2*(s - 1)*(s + 1)**2
Let p(z) = z. Let i(a) = a**2 - 6*a + 1. Let x(j) = -5*i(j) - 20*p(j). Find k, given that x(k) = 0.
1
Suppose -5*r - 8 = -4*r. Let l(j) = -9*j**3 - 11*j**2 - 20*j - 8. Let t(u) = 14*u**3 + 16*u**2 + 30*u + 12. Let h(n) = r*l(n) - 5*t(n). Factor h(s).
2*(s + 1)**2*(s + 2)
Let z(j) be the first derivative of -2*j**5/25 - 2*j**4/5 - 2*j**3/3 - 2*j**2/5 - 7. Determine a, given that z(a) = 0.
-2, -1, 0
Let -15*n**3 - 16*n**3 - n - 4*n**5 - 12*n**2 - 19*n**4 - 7*n**2 + 2 = 0. Calculate n.
-2, -1, 1/4
Suppose -2*x - 3*o = 2*x + 1, 0 = -o - 3. Factor j - 1/2*j**x - 1/2.
-(j - 1)**2/2
Factor 2/9*g**4 - 2/9*g**2 + 2/9*g**3 + 0 - 2/9*g.
2*g*(g - 1)*(g + 1)**2/9
Let u(i) be the first derivative of i**7/210 - i**6/150 + 4*i - 3. Let a(g) be the first derivative of u(g). Find t such that a(t) = 0.
0, 1
Let m(u) be the first derivative of 2*u**3 - u**2 - 17. Factor m(p).
2*p*(3*p - 1)
Find x, given that -16*x**2 + 6*x**2 - 4*x + 6*x**2 + 4*x**4 + 4*x**3 + 0*x**3 = 0.
-1, 0, 1
Factor 2/3*h**2 + 8/3 - 8/3*h.
2*(h - 2)**2/3
Suppose 4*w + 2*d + d = -10, 5*w = -d - 7. Let o(h) = h**2 - 2*h + 5. Let s(q) = 1. Let p(u) = w*o(u) + 5*s(u). Let p(n) = 0. Calculate n.
0, 2
Determine r so that 0*r**3 + 9 - 6*r**3 - 8*r**2 + 4*r + 2*r - 2*r**4 + r**4 = 0.
-3, -1, 1
Let 6/5*r - 8/5 + 2/5*r**2 = 0. Calculate r.
-4, 1
Let f(w) = -w**2 + 3. Let d(l) = 12*l**2 - 39. Let n = -18 + -9. Let z(s) = n*f(s) - 2*d(s). Solve z(y) = 0.
-1, 1
Let f(n) be the second derivative of -1/6*n**4 - n + 0*n**2 + 0 + 0*n**3. Factor f(y).
-2*y**2
Let d(p) = -p**4 + p**3 + p**2 + p + 1. Let n(y) = 6*y**4 - 15*y**3 - 6*y**2 - 3*y - 9. Let i(o) = 9*d(o) + n(o). Determine z so that i(z) = 0.
-2, -1, 0, 1
Let v(j) be the first derivative of -98/39*j**3 - 8/13*j + 28/13*j**2 + 9. Factor v(h).
-2*(7*h - 2)**2/13
Suppose -5*u = -3*b - 14, -4*u + 30 = 5*b + u. Let a be (-4)/b + 10/4. Determine q so that q + 0 + a*q**2 = 0.
-2, 0
Let w(f) be the third derivative of 3/70*f**5 + 7*f**2 - 4/21*f**3 - 1/735*f**7 + 1/21*f**4 + 0*f + 0 - 11/420*f**6 + 1/392*f**8. Solve w(o) = 0.
-2, -2/3, 1
Let g = -188189/270 + 697. Let x(w) be the third derivative of -2*w**2 + 0*w**4 + 0*w**3 + 1/540*w**6 - g*w**5 + 0 + 0*w. Determine p, given that x(p) = 0.
0, 1
Factor 0 + 0*o - 1/7*o**2 + 1/7*o**3.
o**2*(o - 1)/7
Let z(m) be the third derivative of 0 + 1/15*m**5 + 1/4*m**4 - 3*m**2 - 1/60*m**6 + 0*m**3 + 0*m. Suppose z(y) = 0. What is y?
-1, 0, 3
Factor 8*b - 32 - 1/2*b**2.
-(b - 8)**2/2
Let y(n) be the second derivative of -n**7/14 + 7*n**6/30 - 3*n**5/20 - n**4/4 + n**3/3 + 5*n. Factor y(x).
-x*(x - 1)**3*(3*x + 2)
Let l(j) be the third derivative of 0*j + 0 + 3/4*j**4 + 6*j**2 - 1/20*j**5 - 9/2*j**3. Factor l(a).
-3*(a - 3)**2
Let b(u) be the first derivative of u**4/4 - 2*u**3/3 + u**2/2 - 3. Suppose b(m) = 0. What is m?
0, 1
Let n(a) be the second derivative of a**7/126 - a**6/90 - a**5/60 + a**4/36 + 7*a. Factor n(p).
p**2*(p - 1)**2*(p + 1)/3
Let b(o) be the second derivative of 6*o - 1/6*o**4 + 0*o**3 + 4*o**2 + 0. Solve b(f) = 0 for f.
-2, 2
Let a(u) be the first derivative of -u**3/3 + 2*u**2 - 1. Factor a(b).
-b*(b - 4)
Let y(i) be the second derivative of i**8/840 + i**7/105 + i**6/36 + i**5/30 + i**3/2 + 2*i. Let a(q) be the second derivative of y(q). Solve a(d) = 0.
-2, -1, 0
Let u(r) be the third derivative of r**8/3360 - r**7/840 + r**3/2 + 2*r**2. Let d(p) be the first derivative of u(p). Factor d(y).
y**3*(y - 2)/2
Factor -33*h**2 - 2*h**5 - 26*h**3 - 16*h**4 + 9*h**2 - 8*h + 4*h**4.
-2*h*(h + 1)**2*(h + 2)**2
Let c(u) be the second derivative of -u**4/6 + u**3 - 2*u**2 - 43*u. Factor c(v).
-2*(v - 2)*(v - 1)
Let n(g) be the second derivative of -g**7/42 - 2*g**6/15 - 3*g**5/10 - g**4/3 - g**3/6 - 5*g. Factor n(i).
-i*(i + 1)**4
Let o(t) = -5*t**3 + 2*t**2. Let n(m) = -4*m**3 + m**2. Let y(h) = 4*n(h) - 3*o(h). Solve y(f) = 0.
-2, 0
Factor -85*a**2 - 35*a**4 + 5*a**5 + 44*a**3 - 16*a**3 + 57*a**3 + 30*a.
5*a*(a - 3)*(a - 2)*(a - 1)**2
Let p(s) be the third derivative of -s**6/120 - s**5/20 - s**4/12 + 38*s**2. Find u such that p(u) = 0.
-2, -1, 0
Suppose 15*q**2 - 9*q + 12*q**3 + 5*q + 7*q = 0. Calculate q.
-1, -1/4, 0
Suppose -3*l - 3*x + 5*x + 36 = 0, 3*l + 3*x = 36. Let i be l/30 - (1 + -1). Factor 1/5*w + 0 + 1/5*w**3 - i*w**2.
w*(w - 1)**2/5
Let c = -1436/3 - -520. Let p = c + -41. Suppose 1/3*m**2 - 1/3 + p*m**3 - 1/3*m = 0. What is m?
-1, 1
What is b in 0*b**3 + 0 + 1/5*b**2 + 0*b - 1/5*b**4 = 0?
-1, 0, 1
Let r(z) be the first derivative of -2*z**5/115 - 5*z**4/46 - 4*z**3/23 + 4*z**2/23 + 16*z/23 + 39. Factor r(d).
-2*(d - 1)*(d + 2)**3/23
Let l(u) = 2*u**4 + 3*u**3 - 2*u**2 + 3. Let i(q) = 9*q**4 + 12*q**3 - 8*q**2 + 13. Let y(h) = 6*i(h) - 26*l(h). What is s in y(s) = 0?
0, 1, 2
Let z(t) be the third derivative of -1/280*t**7 + 0*t**3 - 3*t**2 + 0*t**4 + 1/240*t**5 + 0 - 1/240*t**6 + 0*t. Find h, given that z(h) = 0.
-1, 0, 1/3
Suppose -4 = m - 3*m. Find a such that -4 + 18*a - 1 - 5*a**2 + 1 - 3*a**m = 0.
1/4, 2
Let m(z) = 2*z + 6. Let f be m(-3). Suppose -v + 3*v = f. Solve 0*i + v + 1/2*i**3 + 1/2*i**2 = 0 for i.
-1, 0
Suppose 6*k - 5*k - 3 = 0. Solve -27*u + 18*u**4 + 6*u**3 + 4*u**5 + 10*u**3 - u**5 + 8*u**k - 18*u**2 = 0.
-3, -1, 0, 1
Let l = 173 + -40. Let h = l + -1461/11. Factor 2/11*a**4 + 0 + h*a**3 - 2/11*a**2 - 2/11*a.
2*a*(a - 1)*(a + 1)**2/11
Find w such that 0 - 2/5*w**2 - 2*w = 0.
-5, 0
Let x(t) be the second derivative of t**4/48 - t**3/6 + 3*t**2/8 + 3*t. Factor x(o).
(o - 3)*(o - 1)/4
Let -5/3*a - 20/3*a**2 + 5/3*a**3 + 20/3 = 0. Calculate a.
-1, 1, 4
Let t be (132/30 - 4)*1/18. Let q(o) be the second derivative of 0 + 0*o**2 + 1/18*o**4 + t*o**6 + 0*o**3 + 2*o - 1/15*o**5. Factor q(w).
2*w**2*(w - 1)**2/3
Let w(c) be the second derivative of 2*c**4/9 + 19*c**3/9 - 5*c**2/3 + 7*c. Factor w(y).
2*(y + 5)*(4*y - 1)/3
Suppose -a = 41 - 14. Let k = a - -27. Suppose 1/2*o**2 - 1/2*o**4 - 1/2*o + k + 1/2*o**3 = 0. What is o?
-1, 0, 1
Let a(t) be the first derivative of -7*t**4/2 - 4*t**3/3 + 5*t**2/2 + 4*t + 4. Let u