Factor s(g).
-(g - 1)**2*(g + 1)**2/2
Let i(b) be the third derivative of -b**6/60 + b**5/10 + b**4/3 - 4*b**3 + 7*b**2. Factor i(t).
-2*(t - 3)*(t - 2)*(t + 2)
Factor 45*h**3 - h + 3*h**2 - 42*h**3 - 5*h.
3*h*(h - 1)*(h + 2)
Let k = -12 + 17. Suppose -p = -0*p - 1, 3*p = k*t - 7. Suppose -w**4 - 4*w**3 + 4*w**t + 0*w - 3*w**2 - w + 5*w**3 = 0. Calculate w.
-1, 0, 1
Let v(h) be the third derivative of -h**7/105 + h**6/60 + h**5/5 - h**4/3 - 8*h**3/3 - 36*h**2. Factor v(k).
-2*(k - 2)**2*(k + 1)*(k + 2)
Suppose 7*c = 3*c + 40. Suppose 4*o + 7 = n - 13, 3*n - 2*o - c = 0. What is q in 0*q + 9/2*q**5 + 0*q**2 - q**3 - 7/2*q**4 + n = 0?
-2/9, 0, 1
Factor 22*o + 6*o**2 - 1 + 11 + 2.
2*(o + 3)*(3*o + 2)
Let x(g) be the first derivative of -g**3 - 3*g**2/2 + 1. Suppose x(l) = 0. What is l?
-1, 0
Suppose 0 = -x + 4*x - 54. Let g = x - 16. Find j such that 0*j + 0 - 2/11*j**g + 2/11*j**3 = 0.
0, 1
Suppose 6*j + 10 = 11*j. Let s(b) be the second derivative of 1/10*b**6 + 0*b**3 - b + 1/2*b**4 + 0*b**j + 9/20*b**5 + 0. Solve s(o) = 0 for o.
-2, -1, 0
Let b(s) be the second derivative of -s**5/15 + 2*s**4/27 - 6*s + 6. Factor b(z).
-4*z**2*(3*z - 2)/9
Factor 27*v**2 - 27*v**2 + 0*v**3 - 12*v + 3*v**3.
3*v*(v - 2)*(v + 2)
Let p(b) be the second derivative of -b**4/8 - 3*b**3/4 - 3*b**2/2 + 3*b. Factor p(x).
-3*(x + 1)*(x + 2)/2
Let m = -6 + 8. Suppose m*p = p. Factor p - 1/4*u**2 + 1/4*u.
-u*(u - 1)/4
Factor 27*c**3 - 3*c + 5*c**2 - 7*c**3 - 17*c**2 - 5*c.
4*c*(c - 1)*(5*c + 2)
Let u(x) be the third derivative of -1/350*x**7 + 0 - 2*x**2 + 0*x**3 + 0*x**6 + 0*x**4 + 0*x + 1/100*x**5. Factor u(k).
-3*k**2*(k - 1)*(k + 1)/5
Suppose -r = -0*r. Let w(u) be the second derivative of r + 0*u**2 - 1/3*u**3 - 2*u + 1/6*u**4. Solve w(f) = 0 for f.
0, 1
Let o = 13 - 10. Let i(q) be the first derivative of -3*q**4 + 2 + q - 2/3*q**o + 9/5*q**5 + 2*q**2. Factor i(p).
(p - 1)**2*(3*p + 1)**2
Let j(v) be the first derivative of -v**8/80 - 2*v**7/35 - 11*v**6/120 - v**5/20 + v**3 - 4. Let g(c) be the third derivative of j(c). Factor g(a).
-3*a*(a + 1)**2*(7*a + 2)
Suppose 0 = -21*l + 17*l - 4. Let p = 3/2 + l. Find d, given that p - 1/2*d**3 + 3/2*d**2 - 3/2*d = 0.
1
Let y be (6/(-16))/1 - 113/(-88). Suppose -16/11*o + 8/11 - y*o**2 = 0. What is o?
-2, 2/5
Let z be 9/(-15) - (-140)/25. Let -z*c + 5*c + 3 - 3*c**2 = 0. Calculate c.
-1, 1
Let d(x) be the second derivative of 0 + 0*x**5 + 0*x**3 - 3*x - 1/36*x**4 + 1/90*x**6 + 0*x**2. Factor d(n).
n**2*(n - 1)*(n + 1)/3
Suppose 0 = -5*f - 2*s + 14 - 5, -2*f - 3*s - 3 = 0. Factor -4*n**3 - 3*n**5 - 3*n**3 - 3 + 9*n + 9*n**4 - 6*n**2 - n**3 + 2*n**f.
-3*(n - 1)**4*(n + 1)
Factor 18/5*i - 3/5*i**2 - 27/5.
-3*(i - 3)**2/5
Let r = -14 - -20. Let k(i) = -i**3 + i**2. Let a(q) = -12*q**3 + 12*q**2. Let m(t) = r*a(t) - 68*k(t). Factor m(j).
-4*j**2*(j - 1)
Let a(w) = -w**3 - w. Let s(m) = 4*m**3 + 4*m**2 + 8*m - 4. Let q(c) = -6*a(c) - s(c). Factor q(z).
2*(z - 2)*(z - 1)*(z + 1)
Let f(s) be the first derivative of 5*s**4/4 + 10*s**3/3 + 5*s**2/2 - 12. Factor f(q).
5*q*(q + 1)**2
Let c = -33 + 33. Factor 2/3*t**5 + 2/9*t**3 + 2/9*t**2 + 0 - 10/9*t**4 + c*t.
2*t**2*(t - 1)**2*(3*t + 1)/9
Let c = -36606365/255591 - -6/28399. Let r = -143 - c. Factor 2/9*z**3 - r*z**5 - 2/9*z**4 + 2/9*z**2 + 0 + 0*z.
-2*z**2*(z - 1)*(z + 1)**2/9
Suppose -3*m + 5*f + 48 = 0, f = -m + 4*f + 20. Let w = -1 - -4. Factor -2*t**w - 11 + 2*t + m.
-2*t*(t - 1)*(t + 1)
Let s(k) be the second derivative of k**7/420 - k**6/90 + k**5/60 + k**3/2 + k. Let n(i) be the second derivative of s(i). Find r such that n(r) = 0.
0, 1
Suppose 4*y = 3*v + 2*y, 3*v + 2*y = 0. Factor -2/7*z**2 + 4/7*z + v.
-2*z*(z - 2)/7
Factor 3*w + 3/8*w**3 + 21/8*w**2 - 6.
3*(w - 1)*(w + 4)**2/8
Factor -3/4*d**4 - 3/4*d**3 - 9/4*d + 15/4*d**2 + 0.
-3*d*(d - 1)**2*(d + 3)/4
Suppose 10 = 4*k - 2*v - 64, 3*v = 5*k - 95. Let w = -14 + k. Factor -2/7*d**4 + 4/7*d**w + 0*d + 0*d**3 - 2/7.
-2*(d - 1)**2*(d + 1)**2/7
Find j, given that -52*j**3 - 2800*j - 415*j**2 - 51*j**3 + 88*j**3 + 980 = 0.
-14, 1/3
Suppose 5*d = -99 + 39. Let j = d - -48. Factor -2*t**2 + j*t - 36*t + t**3.
t**2*(t - 2)
Let d(j) be the third derivative of -j**7/168 + j**6/48 + j**5/48 - 5*j**4/48 - 3*j**2. Factor d(t).
-5*t*(t - 2)*(t - 1)*(t + 1)/4
Let s(p) be the first derivative of -2 + 1/15*p**3 + 1/5*p - 1/5*p**2. Find m such that s(m) = 0.
1
Let f(k) be the third derivative of 7*k**5/180 - 5*k**4/72 - k**3/9 + 6*k**2. What is d in f(d) = 0?
-2/7, 1
Let a(g) be the first derivative of g**5/20 - g**4/3 + 5*g**3/6 - g**2 + g - 1. Let t(w) be the first derivative of a(w). Factor t(c).
(c - 2)*(c - 1)**2
Let n(u) be the second derivative of 0 + 3*u + 4/3*u**3 + 9/2*u**4 - 3/2*u**2 + 81/10*u**5 + 243/40*u**6. Let s(w) be the first derivative of n(w). Factor s(q).
(9*q + 2)**3
Let 0 + 3/2*o**2 + 3/2*o = 0. Calculate o.
-1, 0
Let u(x) be the second derivative of 1/30*x**3 + 0 + 0*x**2 - 1/50*x**5 + 0*x**6 + 1/210*x**7 + 0*x**4 + 3*x. Factor u(w).
w*(w - 1)**2*(w + 1)**2/5
Let t(f) be the second derivative of 2*f**6/45 - f**5/5 + f**4/9 + 2*f**3/3 - 4*f**2/3 + 3*f. Factor t(c).
4*(c - 2)*(c - 1)**2*(c + 1)/3
Solve -10/11*v + 10/11*v**3 - 4/11 + 4/11*v**2 = 0.
-1, -2/5, 1
Let d(k) be the first derivative of 0*k**4 + 0*k - k**2 - 1/120*k**5 - 2 + 1/12*k**3. Let x(f) be the second derivative of d(f). Factor x(n).
-(n - 1)*(n + 1)/2
Let b(q) = -q**2 + 4*q + 5. Let x be -1*(-4 - (3 - 2)). Let a be b(x). Factor 0*y + 0*y**2 - 16/3*y**4 + a - 5*y**5 - 4/3*y**3.
-y**3*(3*y + 2)*(5*y + 2)/3
Factor 1/2 - 3/2*p**5 - 7*p**3 - 11/2*p**4 - 3*p**2 + 1/2*p.
-(p + 1)**4*(3*p - 1)/2
Let o(h) be the second derivative of h**8/3360 + h**7/504 + h**6/180 + h**5/120 - h**4/12 - 4*h. Let w(z) be the third derivative of o(z). Factor w(i).
(i + 1)**2*(2*i + 1)
Let x(a) be the first derivative of 14*a**3/3 - 68*a**2 - 40*a + 2. Let x(r) = 0. What is r?
-2/7, 10
Factor -4*v**2 + v - 11*v - 4 - 6*v - 8.
-4*(v + 1)*(v + 3)
Let o be (-32)/(-180) - (-20)/90. Factor 4/5*y - 2/5*y**3 - o*y**2 + 0.
-2*y*(y - 1)*(y + 2)/5
Let z(w) be the second derivative of 1/10*w**3 + 1/50*w**6 + 3*w - 3/100*w**5 - 1/20*w**4 + 0 + 0*w**2. Suppose z(v) = 0. Calculate v.
-1, 0, 1
Suppose 2*h = -h. Let x = h + 2. Factor 5*u**2 + 0*u**2 - u**2 + x*u**3.
2*u**2*(u + 2)
Solve -4/3*j**2 + 1/3*j + 0 + 1/3*j**5 + 2*j**3 - 4/3*j**4 = 0 for j.
0, 1
Suppose -3*h - 5 = -2*y, 0 = 4*h + 4 - 0. Let p(x) be the first derivative of 2/5*x**4 + y - 4/5*x**2 - 2/5*x - 4/15*x**3 + 6/25*x**5. Solve p(a) = 0.
-1, -1/3, 1
Let b(u) be the first derivative of -2*u**5/45 - 5*u**4/18 + 10. Factor b(o).
-2*o**3*(o + 5)/9
Let k(j) = 2*j**2 - 4*j + 3. Let z be k(2). Let x(q) be the first derivative of -1/2*q**4 - 20/7*q**2 - 12/7*q**z - 3 - 2/35*q**5 - 16/7*q. Factor x(p).
-2*(p + 1)*(p + 2)**3/7
Let f = 34 + -34. Let p(o) be the second derivative of -o**2 + o + f - 2*o**3 + 4/21*o**7 - 4/3*o**4 + 1/5*o**5 + 3/5*o**6. Let p(l) = 0. Calculate l.
-1, -1/4, 1
Let o(l) = -l + 1. Let a be o(-1). Let q(k) be the first derivative of a*k + 3*k**2 + 1/2*k**4 - 2 + 2*k**3. Solve q(g) = 0 for g.
-1
Let v(t) be the third derivative of -1/60*t**5 - 1/630*t**7 + 1/120*t**6 + 2*t**2 + 0 + 0*t**3 + 0*t + 1/72*t**4. Suppose v(k) = 0. Calculate k.
0, 1
Let -6/5*l**4 + 0 + 0*l**2 + 3/5*l**5 + 0*l + 3/5*l**3 = 0. What is l?
0, 1
Suppose -10 + 0 = -2*d. Let j(m) = -3*m**2 + 5*m - 2. Let x(s) = -3*s**2 + 6*s - 3. Let h(o) = d*x(o) - 6*j(o). Factor h(z).
3*(z - 1)*(z + 1)
Let x(w) = 5*w**3 - 14*w**2 + w - 4. Let l be 14*((-3)/2 - -1). Let d(o) = 5*o**3 - 15*o**2 + o - 5. Let y(c) = l*x(c) + 6*d(c). Factor y(i).
-(i - 1)**2*(5*i + 2)
Suppose 0 = 2*a - 0*a. Factor -y**3 - 2*y**2 + 0*y**3 - 2*y + 2 + 3*y**3 + a*y.
2*(y - 1)**2*(y + 1)
Factor 6/13*p**2 + 0 - 2/13*p**4 - 4/13*p + 0*p**3.
-2*p*(p - 1)**2*(p + 2)/13
Let u(y) be the first derivative of -y**4/2 + 4*y**3/3 - y**2 - 8. Determine i so that u(i) = 0.
0, 1
Suppose 4*v = 2*v. Let b(j) be the first derivative of v*j + 0*j**3 + 0*j**2 - 2 - 1/10*j**4. Let b(z) = 0. Calculate z.
0
Let t(v) be the first derivative of v**6/1080 + 4*v**3/3 + 2. Let r(w) be the third derivative of t(w). Factor r(h).
h**2/3
Let z(c) be the first derivative of c**4/48 + c**3/24 - c**2/4 - 7*c + 3. Let s