ulate x.
-2, -1, 1
Let y(p) be the first derivative of p**6/3 + 8*p**5/5 + 2*p**4 + 8. Factor y(t).
2*t**3*(t + 2)**2
Let s(h) be the first derivative of 2*h**5/15 - 5*h**4/12 - 5*h**3/9 + 5*h**2/6 + h - 16. Determine x so that s(x) = 0.
-1, -1/2, 1, 3
Let l = 63061/40 - 1578. Let r = l - -15/8. Factor 0 + r*u**3 - 2/5*u**4 + 0*u**2 + 0*u.
-2*u**3*(u - 1)/5
Let k(v) = 4*v**5 + 11*v**4 - 14*v**3 - 5*v**2 + 5*v. Let u(d) = -5*d**5 - 12*d**4 + 15*d**3 + 6*d**2 - 6*d. Let y(s) = 6*k(s) + 5*u(s). Factor y(p).
-p**3*(p - 3)**2
Let i(r) = -3*r + 2. Let d be i(3). Let a = d - -9. Let -1 - s**2 + a*s + 6*s - 10*s = 0. What is s?
-1
Suppose 2*r**2 - 15*r + 13*r**3 + 13*r**3 - 6*r**3 + 3*r**2 = 0. Calculate r.
-1, 0, 3/4
Let v(m) be the third derivative of m**7/840 + m**6/240 - m**4/12 - 2*m**2. Let t(j) be the second derivative of v(j). Determine z so that t(z) = 0.
-1, 0
Factor 5*d**3 - 3*d**2 + 4 - d**2 + 4*d - 9*d**3.
-4*(d - 1)*(d + 1)**2
Let z = -442 + 5752/13. Factor -8/13 - z*k**2 - 16/13*k.
-2*(k + 2)*(3*k + 2)/13
Suppose 0 = 4*h - 2*h. Let s(r) be the second derivative of -r + 5/3*r**3 - r**2 + h - 25/24*r**4. Factor s(t).
-(5*t - 2)**2/2
Let a(o) = -5*o - 6. Let x be a(-4). Suppose -i = 4*v - 4, -3*v + x = 3*i + 2. Factor 2*y**2 - i - 1 + 3.
2*(y - 1)*(y + 1)
Let u(l) be the first derivative of -l**6/600 - l**5/150 + 3*l**2/2 - 2. Let v(s) be the second derivative of u(s). Factor v(b).
-b**2*(b + 2)/5
Let c(z) = z**4 - 3*z**3 - 2*z**2 + 6*z + 7. Let t(k) = 4*k**3 + 2*k**2 - 6*k - 6. Let p(v) = 2*c(v) + 3*t(v). Factor p(u).
2*(u - 1)*(u + 1)**2*(u + 2)
Let k(d) be the first derivative of 8*d**6/15 + 2*d**5/5 - 7*d**4/12 + d**3/6 + 4*d + 2. Let h(l) be the first derivative of k(l). Find m such that h(m) = 0.
-1, 0, 1/4
Let v be 2/(-6) + (-28)/(-12). Let y be 2 + (-1 - -1*v). Factor -1 - 2 - y*f**2 + 3*f + f**3 + 2.
(f - 1)**3
Suppose -5/3*i - 25/3*i**2 + 25/3 + 5/3*i**3 = 0. What is i?
-1, 1, 5
Let b(n) be the first derivative of n**3/3 - n + 6. Factor b(q).
(q - 1)*(q + 1)
Let k(d) be the second derivative of -d**4/6 + 2*d**3/3 - d**2 - 5*d. Determine o so that k(o) = 0.
1
Let i(f) be the third derivative of -f**5/20 + f**4/2 + 5*f**2. Factor i(t).
-3*t*(t - 4)
Factor 1/6*k - 1/6*k**3 + 1/3*k**4 - 1/3*k**2 + 0.
k*(k - 1)*(k + 1)*(2*k - 1)/6
Let -81 - 46*v**2 - v**4 - 62*v**2 - 162*v - 29*v**3 - 2*v**4 - v**3 = 0. Calculate v.
-3, -1
Let z(h) = 9*h**2 + 24*h + 15. Let b(p) = -p**2 + 1. Let v(d) = 6*b(d) + z(d). Find t such that v(t) = 0.
-7, -1
Let b(r) = 3 + 0 - r + 0*r**2 + 2*r**2 + r**2. Let m(j) = j**2 + 1. Let p(n) = -2*b(n) + 5*m(n). Factor p(f).
-(f - 1)**2
Solve 1/3*p**4 - 2*p**3 + 0 + 4*p**2 - 8/3*p = 0.
0, 2
Let f be 285/(-21) + 4/7. Let h be 4/6 + f/39. Factor 25/3*x**4 + h + 20*x**3 + 46/3*x**2 + 4*x.
(x + 1)**2*(5*x + 1)**2/3
Let c(h) be the third derivative of h**7/315 - h**5/45 + h**3/9 + 17*h**2. Suppose c(r) = 0. What is r?
-1, 1
Let k = 4 - 4. Suppose -3*g + 5 + 7 = k. Let 3 - i**2 - 2*i + 0*i - g = 0. What is i?
-1
Let f be (-36)/(-10) - (-4)/10. Factor 2*w**3 + w**2 - 3*w**2 - w**5 + f*w**4 - w + 1 - 3*w**4 + 0*w**2.
-(w - 1)**3*(w + 1)**2
Determine b so that -2*b - b + 9*b - 3*b**2 - 3 = 0.
1
Let g(h) = -3*h - 4. Let l be g(-2). Factor -4/3*w - 2/3 - 2/3*w**l.
-2*(w + 1)**2/3
Suppose -15 = 5*m - 9*r + 4*r, -3*m = -2*r + 5. Factor k**2 - m + 26*k - 26*k.
(k - 1)*(k + 1)
Let h(d) be the first derivative of d**6/240 + d**5/48 + d**4/24 - d**3/3 + 4. Let n(w) be the third derivative of h(w). Let n(g) = 0. Calculate g.
-1, -2/3
Let x(a) be the first derivative of a**5/110 + a**4/22 + 2*a**3/33 - 3*a - 3. Let h(z) be the first derivative of x(z). Factor h(i).
2*i*(i + 1)*(i + 2)/11
Let u = -5 - -8. Factor -2*o**2 - 3*o + 3*o**3 - 3*o**3 + 4*o**3 + u*o**4 - o - 1.
(o - 1)*(o + 1)**2*(3*o + 1)
Find f such that -2*f**2 - 405 + f**2 + 2*f**2 - 90*f - 6*f**2 = 0.
-9
Let m(s) be the second derivative of s**4/12 + s**3/6 - 3*s. Factor m(b).
b*(b + 1)
Factor -4/3*y**3 - 8*y**2 - 32/3 - 16*y.
-4*(y + 2)**3/3
Factor -5/3*z**4 - 10/3*z + 5/3*z**2 + 10/3*z**3 + 0.
-5*z*(z - 2)*(z - 1)*(z + 1)/3
Let k(b) be the second derivative of b**6/10 - 9*b**5/20 + 13*b**4/16 - 3*b**3/4 + 3*b**2/8 - 2*b. Factor k(w).
3*(w - 1)**2*(2*w - 1)**2/4
Let -3 - 3/4*h**2 + 3*h = 0. Calculate h.
2
Suppose -5*m + 18 = -4*x, -4*m + 0 = x - 6. Solve s**m - 1/3*s - s**3 + 1/3*s**4 + 0 = 0.
0, 1
Suppose 0 = -5*n + 3*n - 6. Let j(l) = 5*l**3 + 10*l**2 - l + 3. Let k(p) = 2*p**3 + 1 - 11*p**2 + 2*p - 7*p**3 - 5. Let y(x) = n*k(x) - 4*j(x). Factor y(w).
-w*(w + 1)*(5*w + 2)
Let f = -6/271 - -855/1897. Solve 0 + f*u**3 + 3/7*u**2 - 3/7*u**4 - 3/7*u = 0.
-1, 0, 1
Let n(a) = a**3 - a**2 - 3*a. Let b(u) = 2*u**3 - 3*u**2 - 7*u. Let x(g) = -3*b(g) + 7*n(g). Factor x(y).
y**2*(y + 2)
Find c, given that 120/7*c**5 - 4/7*c + 4/7*c**3 + 0 + 22/7*c**2 - 142/7*c**4 = 0.
-2/5, 0, 1/4, 1/3, 1
Suppose -2*c + v = 3*v + 2, 0 = -2*c + 2*v + 14. Find t, given that -2*t**2 + c*t**2 - 2*t**3 + 2*t - t**2 = 0.
-1, 0, 1
Let t(b) be the second derivative of -3/5*b**2 + 3/10*b**3 + 3*b + 0 - 1/20*b**4. Factor t(v).
-3*(v - 2)*(v - 1)/5
Let m(t) = 116*t**3 - 72*t**2 - 88*t + 16. Let n(l) = -21*l**3 + 13*l**2 + 16*l - 3. Let z(y) = 5*m(y) + 28*n(y). Factor z(d).
-4*(d - 1)*(d + 1)*(2*d - 1)
Let q(p) be the first derivative of 0*p**3 - 1/180*p**5 + 1/630*p**7 + 0*p**6 + 0*p + 2 - p**2 + 0*p**4. Let r(o) be the second derivative of q(o). Factor r(j).
j**2*(j - 1)*(j + 1)/3
Factor 0*r + 3/7*r**2 - 1/7*r**3 + 0.
-r**2*(r - 3)/7
Let z(s) be the third derivative of 0 + 0*s - 1/3*s**4 + 1/15*s**5 + 2/3*s**3 - 2*s**2. Suppose z(r) = 0. What is r?
1
Let x = -8793584074/12159 + 6508942/9. Let t = 2/579 - x. Factor -6/7*a**2 - 6/7*a - t*a**3 - 2/7.
-2*(a + 1)**3/7
Let o = 237/124 + -5/31. Let y(g) be the first derivative of -o*g**2 + g + 5/6*g**3 + 2. Factor y(c).
(c - 1)*(5*c - 2)/2
Let w be ((-16)/4)/(-20)*9. Solve -3/5 - 3/5*n**3 - w*n - 9/5*n**2 = 0.
-1
Determine r, given that 9*r**2 - 36*r + 9*r**4 + 15 - 22 + 30*r**3 - 5 = 0.
-2, -1/3, 1
Let c(a) be the first derivative of -1/3*a**6 + 2 + 10/3*a**3 - 2/5*a**5 + 0*a + 2*a**2 + 3/2*a**4. Factor c(b).
-2*b*(b - 2)*(b + 1)**3
Let c(j) = -j - 2. Let p be c(-4). Solve 3 - 3 + 3*n**2 - 4*n**2 - p*n = 0.
-2, 0
Determine c so that 9/5*c**3 + 11/5*c**4 + 1/5*c**2 + 0 - 1/5*c + 4/5*c**5 = 0.
-1, 0, 1/4
Let x(s) be the first derivative of -2/5*s**5 - 1/2*s**4 + 2/3*s**3 - 1 + 0*s + s**2. Factor x(v).
-2*v*(v - 1)*(v + 1)**2
Let z(y) = 5*y**2 + 16*y + 5. Let o(c) = 15*c**2 + 47*c + 15. Let t(f) = -6*o(f) + 17*z(f). Factor t(l).
-5*(l + 1)**2
Suppose -5*u - s = 62, 16 = -2*u - 3*s + 7*s. Let q be (-3)/u - 1/(-4). What is v in 0 - q*v**3 + 0*v - 1/2*v**2 = 0?
-1, 0
Let o = -1/21 + 17/210. Let y(p) be the third derivative of -o*p**6 + 0*p - 1/21*p**7 + 0*p**3 + 0 + 2*p**2 - 1/56*p**8 + 0*p**4 + 0*p**5. Factor y(m).
-2*m**3*(m + 1)*(3*m + 2)
Let o(t) be the first derivative of -t**4/4 - 3*t**3/2 - 3*t**2 - 6*t - 3. Let g(b) be the first derivative of o(b). Find h, given that g(h) = 0.
-2, -1
Let r(q) be the third derivative of q**9/3024 - q**7/420 + q**5/120 + q**3/6 + 3*q**2. Let k(h) be the first derivative of r(h). Factor k(s).
s*(s - 1)**2*(s + 1)**2
Suppose 5*t = 4*c - 33, 3*c - 5*c + 5*t = -29. Factor -2/3*r + 0 + 2/3*r**c.
2*r*(r - 1)/3
Let z(q) be the second derivative of -q**4/66 - q**3/66 + 63*q. Factor z(s).
-s*(2*s + 1)/11
Suppose 2*z + 2*f = -0*f - 6, 25 = -5*f. Let a(d) be the second derivative of 0 + 4/21*d**3 + 5/42*d**4 - 1/7*d**z + d. Factor a(p).
2*(p + 1)*(5*p - 1)/7
Let u(r) be the first derivative of r**4/28 + r**3/7 - 9*r**2/14 + 5*r/7 + 23. Determine n, given that u(n) = 0.
-5, 1
Let x be 2/(12/2)*9. Let r = -40 + 42. Find w, given that -2*w**4 + 4 + r*w**3 + w**5 - w**x - 4 = 0.
0, 1
Let d(v) = 13*v**4 - 3*v**2 - 5*v - 5. Let p(m) = -7*m**4 + m**2 + 3*m + 3. Let o(b) = -3*d(b) - 5*p(b). Factor o(u).
-4*u**2*(u - 1)*(u + 1)
Let z(w) be the third derivative of -w**6/200 + 3*w**5/100 + 16*w**2. Solve z(a) = 0.
0, 3
Suppose -3*a + 7 = z, 2*a - 3*z - 14 - 9 = 0. Let w be (4/6)/(a/12). Factor -3*x**3 - x**3 - 4*x + 0*x - 1 - 3*x**4 - 6*x**2 + w*x**4.
-(x + 1)**4
Let s(z) = -4*z**2 + z. Let i(o) = 2*o**2 - o. Let r(n) = -14*i(n) - 6*s(n). Determin