6 - o. Factor 2*y**2 + j*y**3 + 1 + 5/2*y.
(y + 1)**2*(y + 2)/2
Factor -s + 5*s + 3 + s**2 + 2 - 2.
(s + 1)*(s + 3)
Let h(k) be the second derivative of 0*k**3 + 0 + 0*k**2 - 1/40*k**5 + 0*k**4 - 2*k. What is l in h(l) = 0?
0
Suppose 2*k = -2*k. Factor 2 + k - 10 - 4 - 3*m**2 - 12*m.
-3*(m + 2)**2
Let s = 144 - 142. Factor 2/11*o + 0 + 0*o**s - 2/11*o**3.
-2*o*(o - 1)*(o + 1)/11
Let s(g) be the first derivative of g**4 + 8*g**3/3 - 2*g**2 - 3*g - 5. Let z(b) = -6*b**3 - 12*b**2 + 6*b + 4. Let d(t) = -8*s(t) - 5*z(t). Factor d(r).
-2*(r - 1)*(r + 1)*(r + 2)
Let w(b) = -b**2 + 0*b + b - 3 + 8 + 3*b. Let f be w(5). Factor 0*u + 6/5*u**3 + f - 4/5*u**2 + 2*u**4.
2*u**2*(u + 1)*(5*u - 2)/5
Let k(v) be the first derivative of -2*v**6/105 + 3*v**5/70 - v**4/42 + 2*v + 3. Let z(o) be the first derivative of k(o). Solve z(s) = 0.
0, 1/2, 1
Factor 3/4*l**2 + 0*l - 3.
3*(l - 2)*(l + 2)/4
Let x(w) = -17*w**5 + 26*w**4 - 8*w**3 - 10*w**2 + w - 8. Let i(l) = -11*l**5 + 17*l**4 - 5*l**3 - 7*l**2 + l - 5. Let j(c) = 8*i(c) - 5*x(c). Factor j(d).
-3*d*(d - 1)**3*(d + 1)
Factor 6 - 3*q**3 - 7 + 4 + 9*q**2 - 9*q.
-3*(q - 1)**3
Let x = 1 - 1. Let t(i) be the first derivative of 2/9*i**3 + 0*i + x*i**2 - 1/9*i**6 - 2/15*i**5 - 3 + 1/6*i**4. Solve t(y) = 0.
-1, 0, 1
Let 3/5*f**2 - 3/5 + 12/5*f**3 - 12/5*f = 0. What is f?
-1, -1/4, 1
Suppose 38*l - 47 - 29 = 0. Let i = 284/35 - 54/7. Factor -i*k - 4/5 + 2/5*k**l.
2*(k - 2)*(k + 1)/5
Let x(l) be the second derivative of -2*l**3 + 0 + 2*l - 6*l**2 - 1/4*l**4. Let x(c) = 0. Calculate c.
-2
Factor 435 - 12*z - 7*z**2 + 3*z**2 - 443.
-4*(z + 1)*(z + 2)
Let q(d) be the first derivative of -d**4/14 - 2*d**3/21 + d**2/7 + d + 1. Let v(f) be the first derivative of q(f). Find y such that v(y) = 0.
-1, 1/3
Let a be (-1)/3 + 60/18. Suppose 5*o**3 - 5*o**3 + 6*o - 9*o**2 + a*o**3 = 0. Calculate o.
0, 1, 2
Let y(t) be the third derivative of -t**8/40320 - t**7/3780 - t**6/1080 + 11*t**4/24 + 10*t**2. Let q(z) be the second derivative of y(z). Factor q(d).
-d*(d + 2)**2/6
Let y be (-1)/(-2) - (-2)/8. Let o be (2/10)/((-104)/(-650)). Factor -o*s**2 - y*s + 1/2.
-(s + 1)*(5*s - 2)/4
Let r(u) = 4*u**4 + 6*u**3 - 30*u**2 + 20*u - 12. Let h = 17 + -18. Let b(m) = m**4 - m**3 - m**2 - 1. Let p(j) = h*r(j) + 6*b(j). Suppose p(o) = 0. What is o?
1, 3
Factor 10*a**3 - 12*a**5 - 5 + 0*a + 10*a**2 + 7*a**5 - 5*a**4 - 5*a.
-5*(a - 1)**2*(a + 1)**3
Solve -2*o**2 - 60*o**4 - 9*o - 6 + 103*o**3 + 48*o + 12*o**5 + 8*o**3 - 94*o**2 = 0 for o.
1/2, 1, 2
Let o be (-945)/(-55) - 4/22. Factor 17 - 4*t**3 - o + 8*t**2 - 4*t.
-4*t*(t - 1)**2
Suppose 12 = f - 4*j, -f + j + 45 = f. Let w = 24 - f. Factor -2/3*v**4 + 0 + 2/3*v**5 - 2/3*v**3 + 2/3*v**2 + w*v.
2*v**2*(v - 1)**2*(v + 1)/3
Let f(v) be the second derivative of v**5/90 + 7*v**4/27 + 49*v**3/27 + 37*v. Factor f(p).
2*p*(p + 7)**2/9
Let c(g) = -2*g**3 - g**2 - g + 1. Let s = 9 + -7. Let l = -1 - 5. Let v(o) = -o**3. Let t(i) = l*v(i) + s*c(i). Solve t(n) = 0.
-1, 1
Suppose 3*n - 6*n + 105 = 4*q, n = 2*q - 45. Suppose -5*h - q = -2*g, -3*h = -5*h - 8. Factor 3/2*k**g + 2 + 1/4*k**3 + 3*k.
(k + 2)**3/4
Let m(o) = -3*o**3 + 2*o + 1. Let t be m(-1). Determine a, given that -2*a + 4*a - 4*a**t + 8*a**2 + 6*a = 0.
-2, 0
Let w be (90/48)/((-9)/(-12)). Let w*i**4 - 1/2*i**2 + 7/2*i**3 - 4*i + 1/2*i**5 - 2 = 0. Calculate i.
-2, -1, 1
Let r(f) = -f**2 - 9*f + 2. Let v be r(-9). Suppose -b - 2*b**3 - v*b + 3*b - 2*b**2 = 0. What is b?
-1, 0
Let r(o) be the second derivative of 2*o**7/7 + 2*o**6/15 - 2*o**5/5 + 7*o. Let r(h) = 0. Calculate h.
-1, 0, 2/3
Let a(u) be the first derivative of 243/32*u**4 - 6*u**2 - 3/2*u - 7 - 45/8*u**3. Factor a(s).
3*(s - 1)*(9*s + 2)**2/8
Factor -12/5*i**2 - 56/15*i + 18/5*i**4 - 16/15 + 18/5*i**3.
2*(i - 1)*(3*i + 2)**3/15
Let x(r) = 32*r**4 - 49*r**3 + 36*r**2 - 13*r - 5. Let k(p) = p**4 + p**3 - p - 1. Let w(t) = 15*k(t) - 3*x(t). Factor w(a).
-3*a*(3*a - 2)**3
Factor 0 - 2/3*n**2 - 3*n**3 + 0*n - 5/3*n**5 - 4*n**4.
-n**2*(n + 1)**2*(5*n + 2)/3
Let x(v) be the second derivative of -v**5/54 + v**4/18 - v**3/27 - v**2/2 - 6*v. Let j(h) be the first derivative of x(h). Determine s so that j(s) = 0.
1/5, 1
Suppose 0*b = 2*b - 6. Find x, given that 9 - 2*x + 7*x + x - b*x**2 = 0.
-1, 3
Let l(w) = -7*w + 128. Let d be l(18). Factor 1/2*j**d - 1/4 - 1/4*j.
(j - 1)*(2*j + 1)/4
Let k = 1/12 + 17/84. Suppose -2/7*g**4 - 2/7*g + k*g**2 + 0 + 2/7*g**3 = 0. Calculate g.
-1, 0, 1
Let t = 6 - 0. Factor -t*n - 10*n**2 + 0*n + 4*n.
-2*n*(5*n + 1)
Let p(s) be the first derivative of -s**4/10 + 2*s**3/3 - 8*s**2/5 + 8*s/5 + 3. Solve p(q) = 0.
1, 2
Factor -18/5*j - 2/5*j**3 - 8/5 - 12/5*j**2.
-2*(j + 1)**2*(j + 4)/5
Let l = -2 + 4. Find d such that 2 + d + 5*d**2 - 9*d - 11*d**l + 6 = 0.
-2, 2/3
Let o(j) be the third derivative of j**5/480 - 3*j**2. Let o(k) = 0. Calculate k.
0
Suppose 5*k - 3 = -4*c, 2*c + 4*k - 4 = -2*c. Find x, given that 6*x + x - 4*x**c - 6*x**4 - 7*x + 10*x**3 = 0.
0, 2/3, 1
Suppose -3*z = -4*t + 23, t + 0*z = -2*z + 3. Let 1 + 2*k + 5*k**3 - 8*k - k**t + k**4 - 3*k**3 + 5*k - 2*k**2 = 0. Calculate k.
-1, 1
Find c such that 0*c + 0 - 2/15*c**2 + 2/15*c**4 - 2/15*c**5 + 2/15*c**3 = 0.
-1, 0, 1
Let f = 943/4 + -235. Factor -3/2*t + 3/4*t**4 + 0 + 3/2*t**3 - f*t**2.
3*t*(t - 1)*(t + 1)*(t + 2)/4
Let z = 3 - 0. Let b be (-4)/(-6)*(0 - -3). Factor -b - 10*y - z*y**2 + 4*y - 5*y**2 + 4*y**2.
-2*(y + 1)*(2*y + 1)
Suppose 0 = 3*l - 5*r - 19, -2*r = -2*l - r + 8. Suppose 2*b = b - 4*o + l, 2*o + 9 = 3*b. Determine t, given that -3/5*t**2 - 1/5 + 3/5*t + 1/5*t**b = 0.
1
Let y(x) be the second derivative of x**8/10080 + x**7/3780 - x**6/1080 - x**5/180 + x**4/4 + x. Let f(u) be the third derivative of y(u). Factor f(l).
2*(l - 1)*(l + 1)**2/3
Let s(l) = -l**4 + l**3 + l. Let r(d) = 6*d**4 - 8*d**3 - 2. Let p(y) = r(y) + 4*s(y). Factor p(b).
2*(b - 1)**3*(b + 1)
Find g, given that 312*g**3 + 21/4*g**5 + 0*g + 0 - 165/2*g**4 + 96*g**2 = 0.
-2/7, 0, 8
Let o = 6 - 4. Let i(u) be the first derivative of -3/7*u**o - 2/7*u**3 - 2/7*u + 1 - 1/14*u**4. Factor i(y).
-2*(y + 1)**3/7
Solve 8/9*y**2 + 2/3 + 2*y**4 - 28/9*y + 20/3*y**3 = 0 for y.
-3, -1, 1/3
Let m(i) be the first derivative of -3*i**4/4 - 3. Factor m(q).
-3*q**3
Suppose -22*t = -11*t. Suppose 1/2*z**2 + 1/2*z**3 + t + 0*z - 1/2*z**5 - 1/2*z**4 = 0. Calculate z.
-1, 0, 1
Let c(a) be the third derivative of 0 - 1/20*a**6 + 0*a + 2*a**2 - 4/15*a**5 - 1/3*a**4 + 0*a**3. Factor c(g).
-2*g*(g + 2)*(3*g + 2)
Let u = 59/468 - -5/52. Let l(a) be the first derivative of 0*a + u*a**3 - 1/6*a**2 - 1 - 1/12*a**4. Suppose l(j) = 0. What is j?
0, 1
Let a(n) = -n - 6. Let u be a(-8). Find f such that 3*f - 6 + 8*f**u + 2*f**2 - 7*f**2 = 0.
-2, 1
Suppose g + 3 - 6 = 0. Suppose -206 = -v + 4*i, -4*v + 979 = v - g*i. Factor -5*w**4 + 195*w**4 + 64*w + 12*w**5 + 8 + 280*w**3 + v*w**2 + 38*w**5 - 2*w**3.
2*(w + 1)**3*(5*w + 2)**2
Let t(a) = -a + 2*a - a**3 - 3*a**2 + 0*a**3 - 3*a. Let w be t(-2). Factor 0 - 1/4*v**3 + 1/4*v**2 + w*v.
-v**2*(v - 1)/4
Let 15/7*z**2 + 8/7*z**3 + 1/7*z**4 - 8/7*z - 16/7 = 0. Calculate z.
-4, -1, 1
Let w(d) = d**2 - d + 4. Let o be w(2). Let y be o + (-2 + 0)*2. Determine c, given that -2/5*c**y + 0*c + 0 = 0.
0
Let s = -13 + 13. Let m(x) be the first derivative of 1/4*x**4 - 1/3*x**3 + 0*x + s*x**2 - 1. Factor m(j).
j**2*(j - 1)
Factor 3 + 2*q**2 - 1 - 2*q - 2*q.
2*(q - 1)**2
Let g(q) be the first derivative of 0*q**3 + 5 + 1/2*q**4 + 0*q**2 - 1/5*q**5 - 1/6*q**6 + 0*q. Factor g(i).
-i**3*(i - 1)*(i + 2)
Find a such that -a**3 + 1/4 - a + 3/2*a**2 + 1/4*a**4 = 0.
1
Let b = 16 - 12. Let c(v) be the third derivative of 0 - 1/48*v**b + 0*v + 1/120*v**5 - 2*v**2 + 0*v**3. Let c(z) = 0. Calculate z.
0, 1
Let j = -1204/9 + 134. Find g such that -8/9*g + 8/9 + j*g**2 = 0.
2
Suppose 0 = 7*v - 4*v. Let n(h) be the first derivative of 1 + 0*h - 3/5*h**5 - 1/6*h**6 - 3/4*h**4 + v*h**2 - 1/3*h**3. Factor n(t).
-t**2*(t + 1)**3
Let n(z) be the first derivative of z**5/25 - 2*z**3/15 + z/5 + 4. Factor n(o).
(o - 1)**2*(o + 1)**2/5
Let j = 59 + -57. Suppose -4/9*l - 2/9*l**j - 2/9 = 0. What is l?
-1
Factor -14*j**3 + 4*j**4 + 8*j**2 - 8*j**2 - 6*j**2 + 4*j**3.
2*j**2*(j - 3)*(2*j + 1)
Suppose -5*z + 2*c - 1 = 4, -6 = -3*z + 3*c.