4*k*(k - 1)**2
Let b = 1228/261 + -72/29. Find f such that -2/9 + 22/9*f**4 + 0*f**3 - b*f**2 + 4/3*f**5 - 4/3*f = 0.
-1, -1/2, -1/3, 1
Factor 3*u**3 + 2*u**4 + 10*u - 33 + 20*u**2 + 8*u**4 + 17*u**3 + 2*u**5 + 35.
2*(u + 1)**5
Let p(w) be the second derivative of -2*w**7/175 - w**6/200 + 2*w**2 - 2*w. Let k(o) be the first derivative of p(o). Factor k(g).
-3*g**3*(4*g + 1)/5
Let y be 6/(-9)*-3 - 0. Find h, given that 0*h**2 - 2 + y*h**2 - 4*h - 4*h**2 = 0.
-1
Let g(u) = -u**3 + u**2 + 1. Let y(z) = -2*z**3 + z + 2. Suppose 0 = -3*k - 4 - 2. Let w(t) = k*g(t) + 2*y(t). Find x, given that w(x) = 0.
-1, 1
Let r(g) = 4*g**5 - 14*g**4 + 2*g**3 + 14*g**2 - 6*g. Let j(v) = 4*v**5 - 13*v**4 + v**3 + 13*v**2 - 5*v. Let s(d) = 6*j(d) - 5*r(d). Factor s(m).
4*m**2*(m - 2)*(m - 1)*(m + 1)
Factor -l**5 - 7*l**5 + 0*l**2 - 2*l**2 + 2*l**4 - 2*l**3 + 10*l**5.
2*l**2*(l - 1)*(l + 1)**2
Let j(f) be the second derivative of -3*f**7/70 + f**6/20 + f**5/20 + f**2 - 4*f. Let x(l) be the first derivative of j(l). Find b, given that x(b) = 0.
-1/3, 0, 1
Suppose -4 = f - x - 5, -x + 5 = f. Let j(u) be the second derivative of -4*u + 0 - 3/8*u**4 - 1/2*u**f + 0*u**2. Suppose j(c) = 0. Calculate c.
-2/3, 0
Let x be ((-3)/135)/(16/(-10)). Let a(p) be the third derivative of -x*p**4 + 0*p + 0*p**3 + 0 - 2*p**2 + 1/180*p**5. Suppose a(j) = 0. Calculate j.
0, 1
Let i be (-8)/(-22)*(-660)/(-120). Find p such that -2/9*p**3 - 10/9*p**i - 16/9*p - 8/9 = 0.
-2, -1
Let i = 7 - 4. Let s = 7/22 - -2/11. Factor 1/2*b**i + 0 - b + s*b**2.
b*(b - 1)*(b + 2)/2
Suppose 2*g - 60 = -2*g. Let j be (-2 - g/(-9))*-6. Factor 3 - n**j - n - 3 + 2.
-(n - 1)*(n + 2)
Factor -4*n**2 + 56*n**3 - 15*n**5 + 18*n**4 + 2*n**4 - 51*n**3 - 6*n**2.
-5*n**2*(n - 1)**2*(3*n + 2)
Let n be 37/(-4)*(3 - -2). Let u = -46 - n. Find y, given that -1/4*y**5 + 1/2*y**3 - 1/4*y - u + 1/2*y**2 - 1/4*y**4 = 0.
-1, 1
Let f = 526 + -524. What is k in -1/3*k**f + 2/3*k**4 - 1/3 - k**3 + k = 0?
-1, 1/2, 1
Let l(x) be the second derivative of -x**7/14 + 11*x**6/10 - 51*x**5/10 - 2*x**4 + 80*x**3 - 192*x**2 + 17*x. Factor l(p).
-3*(p - 4)**3*(p - 1)*(p + 2)
Factor 1/3*u - 2/3*u**2 + 2/3 - 1/3*u**3.
-(u - 1)*(u + 1)*(u + 2)/3
Let o(t) be the second derivative of -t**5/5 + 2*t**3/3 + 7*t**2/2 + 7*t. Let d(a) = 2*a**3 - 2*a - 3. Let x(g) = 7*d(g) + 3*o(g). Suppose x(b) = 0. What is b?
-1, 0, 1
Suppose 0 = x - 2 - 2. Let u be 1 + (-10)/(-3) + 1. Factor u*k**3 + 0 - 10/3*k**x + 8/3*k**2 + 0*k.
-2*k**2*(k - 2)*(5*k + 2)/3
Suppose 4*d - 10 = -d. Determine t so that -5 - 3*t**3 + 5 + 3*t**5 + 3*t**2 - t**4 - d*t**4 = 0.
-1, 0, 1
Let m = -1/29157 - -36213001/204099. Let r = 178 - m. Factor 2/7 - r*h + 4/7*h**3 - 2/7*h**4 + 0*h**2.
-2*(h - 1)**3*(h + 1)/7
Let b(y) be the first derivative of y**4/42 - y**3/7 + 2*y**2/7 + 7*y + 7. Let h(v) be the first derivative of b(v). Solve h(x) = 0.
1, 2
Let y(f) be the second derivative of -f**7/42 + f**6/10 - f**5/20 - f**4/4 + f**3/3 - 15*f. Let y(u) = 0. What is u?
-1, 0, 1, 2
Let a = 1923/5 + -384. Determine h so that -1/5*h**3 + 0 - 2/5*h**2 + a*h**4 + 0*h = 0.
-2/3, 0, 1
Let j = 14 + -19. Let l be 6/j*40/(-16). Factor 0*x + 0*x**2 + 0*x**l + 0*x**4 + 2/5*x**5 + 0.
2*x**5/5
Suppose -2*s = 4*h + 3 + 3, 4*s - 4*h = 24. Let v(n) be the first derivative of 0*n + 0*n**2 - 2/3*n**s - 3 + 1/2*n**4. Solve v(d) = 0.
0, 1
Let g(d) = 8*d**4 + 13*d**3 - 3. Let w(m) = -m**4 - m**3 + 1. Let c(a) = g(a) + 3*w(a). Factor c(j).
5*j**3*(j + 2)
Solve 50/17 - 20/17*z + 2/17*z**2 = 0 for z.
5
Let v(f) be the third derivative of -1/180*f**6 + 0*f + 1/270*f**5 - 2*f**2 + 1/36*f**4 + 0 - 2/27*f**3 + 1/945*f**7. Factor v(s).
2*(s - 2)*(s - 1)**2*(s + 1)/9
Let x = -3 - -5. Let a(d) be the first derivative of -d**2 + 0*d + 2/3*d**3 - x. Suppose a(g) = 0. What is g?
0, 1
Let m = 16 - 14. Suppose -4*y + 4 = -j, 6*y - 8 = y + m*j. What is i in 0 + 2/5*i**5 - 2/5*i - 4/5*i**4 + 4/5*i**2 + y*i**3 = 0?
-1, 0, 1
Suppose 0 = -0*t + 5*t - 15. Suppose 7*o**3 + 6*o**3 - 2*o + 6*o**2 + t*o + 12*o**4 + 4*o**5 = 0. Calculate o.
-1, -1/2, 0
Let l(g) = 6*g**2 + g - 3. Let n(i) be the second derivative of i**4/12 + i**3/6 - i**2/2 - i. Let p(x) = -l(x) + 4*n(x). Let p(d) = 0. What is d?
1/2, 1
Let n be 2/(-6)*3/(-2). Factor 1/2*w**2 - n*w**3 - 1/2*w**4 + 0*w + 1/2*w**5 + 0.
w**2*(w - 1)**2*(w + 1)/2
Let h(a) = 3*a**2 - 17*a - 13. Let p(m) = 5*m**2 - 26*m - 19. Let u(b) = 8*h(b) - 5*p(b). Factor u(z).
-(z + 3)**2
Let s(n) = n**3 + 16*n**2 - 9*n - 9. Let g(k) = 2*k**2 - k - 1. Let w(o) = -18*g(o) + 2*s(o). Factor w(f).
2*f**2*(f - 2)
Find i such that 0 - 6/5*i**3 + 3/5*i**4 - 9/5*i**2 + 0*i = 0.
-1, 0, 3
Let k(v) be the third derivative of v**6/240 - v**5/40 + v**4/16 - v**3/12 + 4*v**2. Factor k(p).
(p - 1)**3/2
Let b(u) be the first derivative of -12*u**5/5 + 7*u**4 - 8*u**3/3 + 5. Solve b(t) = 0 for t.
0, 1/3, 2
Let o(p) = 19*p**4 + 10*p**3 - 11*p**2 - 14*p - 4. Let s(g) = 20*g**4 + 10*g**3 - 10*g**2 - 15*g - 5. Let y(b) = -5*o(b) + 4*s(b). Factor y(n).
-5*n*(n - 1)*(n + 1)*(3*n + 2)
Suppose 0*n = -5*n + 10. Suppose 5*x - 12 = -2. Factor -2*f**2 - x*f + 4*f**n + 4 + 5*f + 3*f.
2*(f + 1)*(f + 2)
Let 4*p**3 + 8/3 - 4*p - 8/3*p**2 = 0. What is p?
-1, 2/3, 1
Let z(r) be the third derivative of -1/9*r**3 + 3*r**2 + 0*r + 0*r**5 + 0 - 1/24*r**4 + 1/360*r**6. Factor z(j).
(j - 2)*(j + 1)**2/3
Let i(r) be the first derivative of 4*r**5/5 + r**4 - 8*r**3/3 + 5. Factor i(h).
4*h**2*(h - 1)*(h + 2)
Factor 0*y - 2/13 + 2/13*y**2.
2*(y - 1)*(y + 1)/13
Factor -5*v**2 + 25*v - 20 + 5*v - 25*v + 15*v.
-5*(v - 2)**2
Let d(n) = n**4 + n**3 + n**2 + n + 1. Let z(k) = -4*k**4 - 6*k**3 - 10*k**2 - 8*k - 7. Let c(x) = 21*d(x) + 3*z(x). Factor c(g).
3*g*(g - 1)*(g + 1)*(3*g + 1)
Let g = 9 + -5. Factor 11*r + 54 - 2*r**5 + 22*r**g + 180*r**2 - 92*r**3 - 88*r - 85*r.
-2*(r - 3)**3*(r - 1)**2
Factor -4*q**2 - 12 + 20*q + 3 - 15.
-4*(q - 3)*(q - 2)
Suppose 0 = -4*k + 3*t + 31, 0*k - 2*t - 22 = -3*k. Let o(j) be the first derivative of -1/2*j**k + 16*j - 12*j**2 + 4*j**3 + 2. Let o(f) = 0. Calculate f.
2
Suppose -3*g = 1 + 2. Let q be g - -5 - (-4)/(-5). Determine l, given that -q - 12/5*l**2 - 2/5*l**3 - 24/5*l = 0.
-2
Let w(m) = 21*m**2 + 210*m + 540. Let y(f) = -3*f**2 - 30*f - 77. Let v(b) = -2*w(b) - 15*y(b). Find p, given that v(p) = 0.
-5
Let l(x) be the first derivative of -x**3/9 + x**2/6 + 5. Let l(h) = 0. Calculate h.
0, 1
Let m(r) be the second derivative of -r**6/30 - r**5/5 - 8*r. Factor m(t).
-t**3*(t + 4)
Let h = -143 - -573/4. Factor -h*d**2 + 1/4 + 0*d.
-(d - 1)*(d + 1)/4
Suppose 0*j**4 + 1/4*j**5 - 1/2*j**3 + 0 + 1/4*j + 0*j**2 = 0. Calculate j.
-1, 0, 1
Let v(w) = -w**2 - 2*w + 1. Let d(k) be the first derivative of 3*k**2/2 + 1. Let s(a) = 2*d(a) + 3*v(a). Factor s(r).
-3*(r - 1)*(r + 1)
Factor 2/3*m**5 + 4/3*m**2 - 4/3*m**3 + 2/3*m - 2/3*m**4 - 2/3.
2*(m - 1)**3*(m + 1)**2/3
Suppose 0 = 5*s - 2 - 8. Suppose -y + s*y**3 - y**5 - 3*y + 3*y = 0. What is y?
-1, 0, 1
Suppose 0 = 11*a - 86 + 42. Suppose -n = 2*q - 5*n - 6, 0 = -2*n - 2. Factor 7/4*i**2 + a*i + q.
(i + 2)*(7*i + 2)/4
Let i(h) = -6*h**4 + 7*h**3 - 5*h**2 - 2*h + 6. Let m(s) = -2 + 3*s**4 - 3 + 5*s**3 - 11*s**3 + 4*s**2 + 2*s + 2*s**4. Let c(u) = -4*i(u) - 5*m(u). Factor c(b).
-(b - 1)**3*(b + 1)
Let c(f) be the third derivative of 0 - 8*f**2 - 1/210*f**5 - 1/84*f**4 + 0*f + 0*f**3. Factor c(h).
-2*h*(h + 1)/7
Let z(o) be the first derivative of o**3/5 - 3*o**2/10 + 21. Find r, given that z(r) = 0.
0, 1
Let z(w) be the second derivative of -3*w**5/20 - 17*w**4/12 - w**3/6 + 5*w**2/2 - 5*w. Let f(t) = t**3 + 6*t**2 - 2. Let u(r) = 8*f(r) + 3*z(r). Factor u(c).
-(c + 1)**3
Let z(p) be the third derivative of p**7/315 + p**6/45 + p**5/15 + p**4/9 + p**3/9 - 3*p**2. What is a in z(a) = 0?
-1
Let n(a) = -3*a + 4. Let h be n(-2). Let l(m) be the first derivative of -16/5*m**5 - 11*m**3 - m - h*m**4 + 4 - 5*m**2. Factor l(j).
-(j + 1)**2*(4*j + 1)**2
Let y(d) = -5*d - 1. Let j be y(-1). Let u(m) = j + 0 + 2*m + m. Let k(g) = g**2 + 2*g + 4. Let b(t) = -5*k(t) + 6*u(t). Suppose b(i) = 0. What is i?
-2/5, 2
Let p(v) = v**2 - 2*v. Let a(i) = i. Let y(s) = -5*a(s) + 5*p(s). Solve y(j) = 0 for j.
0, 3
Let a = 11 + -8. Suppose 21 = a*v + 3*w, 2*v + w = 4*w + 9. Factor c + c**2 - 4*c - c