p**5 + 4*p - 2*p**a - 3*p + 2*p**5.
p*(p - 1)**2*(p + 1)**2
Let j(k) be the first derivative of -k**5/5 - k**4/4 + k**3 + k**2/2 - 2. Let u(q) = -5*q**4 - 5*q**3 + 16*q**2 + 5*q. Let m(v) = 11*j(v) - 2*u(v). Factor m(z).
-z*(z - 1)*(z + 1)**2
Suppose -i = -4*p, 3*p = -3*i + 4*i. Suppose 5*k - k + 5*w = -9, i = k - 3*w - 19. Factor 0*a - 6/5*a**k - 16/5*a**3 - 12/5*a**2 + 2/5.
-2*(a + 1)**3*(3*a - 1)/5
Factor -1957 - 830*s + 57*s**2 - 253*s + 4*s**3 + 8816 - 5*s**3.
-(s - 19)**3
Let w = -1/1800 - -601/1800. Find u, given that 1/3*u**4 + w*u**2 + 0*u + 2/3*u**3 + 0 = 0.
-1, 0
Let l be 4 + -1 + 4 + -3 + 0. Factor 4/5*t**3 - 2/5 - 2/5*t**2 + 4/5*t**l + 1/5*t**5 - t.
(t - 1)*(t + 1)**3*(t + 2)/5
Let p(d) be the second derivative of d**4/16 + d**3/2 + 3*d**2/2 - d. Factor p(b).
3*(b + 2)**2/4
Let o(y) be the first derivative of 5*y**6/2 + 4*y**5 - 5*y**4 - 10*y**3 + 5*y**2/2 + 10*y + 9. Factor o(d).
5*(d - 1)*(d + 1)**3*(3*d - 2)
Let s = 452445187/8280 - 546429/10. Let w = s + -3/184. Solve 0 - 2/9*k**2 - w*k = 0.
-1, 0
Let c(g) = 13*g**2 - 43*g - 56. Let i(s) = 84*s**2 - 280*s - 364. Let d(m) = -32*c(m) + 5*i(m). Find h such that d(h) = 0.
-1, 7
Let k(c) be the first derivative of 0*c - 3/8*c**2 + 1/12*c**3 + 6. Factor k(r).
r*(r - 3)/4
Let t be (-46)/(-8) + -6 + (-26)/(-40). Factor 0 + 4/5*d + t*d**2.
2*d*(d + 2)/5
Let m(k) be the second derivative of 0*k**3 + 0*k**4 - k + 1/20*k**5 + 7/60*k**6 + 0 + 0*k**2 - 1/21*k**7. Factor m(w).
-w**3*(w - 2)*(4*w + 1)/2
Let p be (65/15 - 6)/((-10)/4). Suppose -p - 1/6*q**2 - 2/3*q = 0. Calculate q.
-2
Factor 0*b + 1/3*b**2 + 1/3*b**4 + 0 + 2/3*b**3.
b**2*(b + 1)**2/3
Let s = 133 + -128. Let c(f) be the third derivative of 0 + 3/16*f**4 - 1/4*f**3 + f**2 - 3/40*f**s + 1/80*f**6 + 0*f. Factor c(a).
3*(a - 1)**3/2
Determine d, given that 16/5 + 8*d - 2/5*d**3 - 2/5*d**5 - 8/5*d**4 + 28/5*d**2 = 0.
-2, -1, 2
Let l be -1 - 1084/(-360) - 2. Let f(h) be the third derivative of -2*h**2 - l*h**5 + 0 + 2/9*h**3 + 0*h + 1/36*h**4. Factor f(x).
-2*(x - 2)*(x + 1)/3
Suppose 1/2*o**3 - 1/2 - 3/2*o**2 + 3/2*o = 0. Calculate o.
1
Let a(h) be the second derivative of -h**4/36 - h**3/9 + h**2/2 + 7*h. Factor a(m).
-(m - 1)*(m + 3)/3
Factor -n**3 - 4*n - 3*n + 8*n**2 - 3*n**3 + 3*n.
-4*n*(n - 1)**2
Let k(q) be the second derivative of -q**6/10 + 3*q**5/20 + q**4/2 - 15*q. Factor k(b).
-3*b**2*(b - 2)*(b + 1)
Let c(w) be the third derivative of -5*w**8/1008 + w**6/36 - 5*w**4/72 - 4*w**2. Find x, given that c(x) = 0.
-1, 0, 1
Let c(w) be the second derivative of 3*w**6/35 - 43*w**5/70 + 53*w**4/42 - 13*w**3/21 - 6*w**2/7 + 9*w. Find s such that c(s) = 0.
-2/9, 1, 3
Let l = 47/6 - 15/2. Factor l*v**4 - 1/3*v**3 + 0 + 1/3*v - 1/3*v**2.
v*(v - 1)**2*(v + 1)/3
Factor -5*s**4 + s**3 - 30*s**2 - 59*s**3 + 33*s**3.
-5*s**2*(s + 2)*(s + 3)
Factor -3/7*z**2 + 18/7*z + 0.
-3*z*(z - 6)/7
Let q(w) be the second derivative of w**4/54 - 2*w**3/27 - 7*w. Find x such that q(x) = 0.
0, 2
Suppose -5*w = 5, -2*w + 43 = -f + 1. Let h be 3/(-21) - f/14. Solve -3/2*b**4 - 3*b + 9/2*b**2 + 0*b**h + 0 = 0.
-2, 0, 1
Let s(l) be the third derivative of l**8/112 + l**7/70 - l**6/20 - l**5/10 + l**4/8 + l**3/2 + 2*l**2. Factor s(b).
3*(b - 1)**2*(b + 1)**3
Solve 4*j**3 + 6*j**2 + 2*j**2 + 4*j**2 + 4 + 12*j = 0.
-1
Suppose 0 = -j - 2*o + 9, 5*j - 26 - 6 = 3*o. Let y = 9 - j. Factor 2*g**3 - 2*g**y - 2*g - 1 + 4*g**4 - 2*g**4 + 1.
2*g*(g - 1)*(g + 1)**2
Let f(h) = -4*h**2 + 8*h + 16. Let x(c) = -c**2 + 3*c + 5. Let j(d) = 5*f(d) - 16*x(d). Factor j(k).
-4*k*(k + 2)
Let i(l) be the third derivative of -7/15*l**5 + 1/3*l**4 - 5/84*l**8 + 2/15*l**7 + l**2 + 1/10*l**6 + 0*l**3 + 0*l + 0. Determine p, given that i(p) = 0.
-1, 0, 2/5, 1
Suppose 3*n - 11 = j, 0*j - 20 = -4*n - 4*j. Let g = 11 - 7. Factor -2*d**4 - 4*d**n + 0*d**4 + 5*d**g.
-d**4
Let w(z) be the first derivative of -z**3/3 + z**2/2 - 6. Suppose w(a) = 0. What is a?
0, 1
Let y be 6/(-1)*(-105)/126. Let k(u) be the second derivative of 0*u**2 + 0 - 2/45*u**6 + 1/18*u**3 - 1/6*u**4 - u + 3/20*u**y. Suppose k(h) = 0. Calculate h.
0, 1/4, 1
Let j(l) be the third derivative of 1/10*l**7 - 9/20*l**5 + 0*l + 5/8*l**4 + l**3 - 1/8*l**6 + 0 + l**2. Suppose j(i) = 0. What is i?
-1, -2/7, 1
Let j be ((-58)/48)/(30/(-8)). Let a = j + -1/10. Determine k so that a*k**5 - 2/9*k**3 + 0*k**2 + 0*k**4 + 0*k + 0 = 0.
-1, 0, 1
Let h(p) be the second derivative of p**5/20 + p**4/3 + 5*p**3/6 + p**2 - 8*p. Factor h(x).
(x + 1)**2*(x + 2)
Let u = -67589/90 - -751. Let p(s) be the third derivative of -s**2 + 1/90*s**6 + 0*s**3 + 0 + 1/315*s**7 + u*s**5 + 0*s + 0*s**4. Factor p(a).
2*a**2*(a + 1)**2/3
Factor 0 - 3/8*j**3 - 1/8*j**4 - 1/4*j**2 + 0*j.
-j**2*(j + 1)*(j + 2)/8
Find i, given that -18*i**3 - 9*i - 5*i - 3*i**5 + 12*i**2 + 12*i**4 + 11*i = 0.
0, 1
Factor -k**4 + 2*k**2 + 0*k - 2*k + k**2.
-k*(k - 1)**2*(k + 2)
Let t(j) be the third derivative of j**6/60 - j**4/4 - 2*j**3/3 + 25*j**2. Factor t(r).
2*(r - 2)*(r + 1)**2
Let m(k) be the second derivative of 5*k**7/42 - k**6/6 - k**5/2 + 5*k**4/6 + 5*k**3/6 - 5*k**2/2 - 8*k. Factor m(w).
5*(w - 1)**3*(w + 1)**2
Let c(o) be the first derivative of o**5/120 - o**4/12 + o**3/3 + o**2 + 3. Let t(a) be the second derivative of c(a). Determine w, given that t(w) = 0.
2
Let u(w) = 31*w**2 - 17*w - 5. Let n(d) = -9 - 18*d + 30*d**2 - 6 + 9. Let t(b) = 3*n(b) - 2*u(b). Factor t(k).
4*(k - 1)*(7*k + 2)
Suppose 0*y = 3*y - 9. Factor y*o**5 - 4*o + 2*o**5 - 2 - 4*o**3 + 0*o - 8*o**4 + 3*o + 10*o**2.
(o - 1)**3*(o + 1)*(5*o + 2)
Let -2/3*n**2 + 0 + 2/3*n**3 + 0*n = 0. Calculate n.
0, 1
Let z(v) be the third derivative of -v**6/180 - v**5/60 - 7*v**3/6 + 2*v**2. Let j(m) be the first derivative of z(m). Determine f, given that j(f) = 0.
-1, 0
Let -4/11*f + 2/11 + 2/11*f**2 = 0. What is f?
1
Let o(w) = -w**3 - w**2 + 4. Let h be o(0). Let q be h + 1 - (2 + 0). Factor -q*g - 2*g**2 - 3*g**2 - 4 + 3 + 3*g**2.
-(g + 1)*(2*g + 1)
Let g(d) be the third derivative of d**6/990 + d**5/220 + d**4/132 - d**3/3 - 6*d**2. Let v(z) be the first derivative of g(z). Factor v(s).
2*(s + 1)*(2*s + 1)/11
Let w(t) be the second derivative of 2*t**7/21 - 16*t**6/75 - 4*t**5/25 + 7*t. Factor w(g).
4*g**3*(g - 2)*(5*g + 2)/5
Let p(q) be the first derivative of q**6/360 - q**5/20 + 3*q**4/8 - q**3/3 - 4. Let c(n) be the third derivative of p(n). Factor c(j).
(j - 3)**2
Let c be ((-56)/6)/(3/(-9)). Let t be ((-24)/c)/(54/(-28)). Suppose t*d**3 + 0 - 2/9*d**2 + 2/9*d**4 + 0*d - 4/9*d**5 = 0. What is d?
-1, 0, 1/2, 1
Let c be 6 + (-3 + 2)*1. Factor -2*h**3 - 6*h + c*h - 2*h**4 + h.
-2*h**3*(h + 1)
Let m = 30 + -26. Let o(b) be the first derivative of -2/5*b**m - 9/5*b**2 - 4/5*b - 8/5*b**3 + 2. Factor o(r).
-2*(r + 2)*(2*r + 1)**2/5
Suppose 0 = -3*o - 2*p + 8, 2*p - 3*p = 5*o - 11. Factor 6/7*k - 6/7*k**2 + 4/7 - o*k**3 - 6/7*k**4.
-2*(k + 1)**3*(3*k - 2)/7
Let b be -1*9*(-1)/3. Suppose b = -3*g + 9. Factor -2/5*l**5 + 0 + 0*l - 8/5*l**g + 0*l**3 + 6/5*l**4.
-2*l**2*(l - 2)**2*(l + 1)/5
Let d(t) = -t**3 + t - 1. Let f(g) = -5*g**3 + 12*g**2 - 10*g - 2. Let z(n) = -2*d(n) + f(n). Factor z(w).
-3*w*(w - 2)**2
Let n = -5238/7 - -750. Factor -3*o**2 - 6/7*o + 3/7 - n*o**3.
-3*(o + 1)**2*(4*o - 1)/7
Let r(q) be the second derivative of -q**7/105 + q**6/25 - 3*q**5/50 + q**4/30 + 3*q. Determine l so that r(l) = 0.
0, 1
Let g(h) = h**4 + 5*h**3 + h**2 - h - 4. Let y(r) = -2*r**4 - 11*r**3 - 2*r**2 + r + 9. Let v(c) = 5*g(c) + 2*y(c). Determine z, given that v(z) = 0.
-2, -1, 1
Let n(b) be the second derivative of -3/5*b**2 - 1/20*b**4 + 5*b + 11/30*b**3 + 0. Suppose n(o) = 0. What is o?
2/3, 3
Let i(m) be the third derivative of m**6/80 - 3*m**5/40 + m**4/8 - 39*m**2. Factor i(x).
3*x*(x - 2)*(x - 1)/2
Let w = 3 - -1. Let f(r) = r**3 - 5*r**2 + 6*r - 6. Let b be f(w). Factor -2/3*o + 0 - 2/3*o**3 - 4/3*o**b.
-2*o*(o + 1)**2/3
Let b be -5 - -29 - (-1 - -1). Let l = b + -8. Suppose 5*x - 9*x**5 + 4*x**4 + 5*x**3 - x - l*x**4 + 12*x**2 = 0. What is x?
-1, -2/3, 0, 1
Let u(g) be the first derivative of -g**7/42 - 19*g**6/210 - 3*g**5/28 - g**4/84 + g**3/21 - g - 4. Let l(n) be the first derivative of u(n). Factor l(h).
-h*(h + 1)**3*(7*h - 2)/7
Let f(z) = -z**3 - z**2 + 2. Let c be f(-2). Suppose s - 3*s = -c. Facto