 + 2)/3
Let c(p) be the first derivative of 5*p**6/9 - 46*p**5/15 + 7*p**4 - 76*p**3/9 + 17*p**2/3 - 2*p + 24. Find x, given that c(x) = 0.
3/5, 1
Let j be (-13)/(-12) + 1/4. Let m be -4 - (0 - 3 - (7 + -3)). Factor 1/3 + v**4 + 2/3*v**m - j*v**2 - 2/3*v.
(v - 1)*(v + 1)**2*(3*v - 1)/3
Let v be 6/84*(4 - (1 + -1)). Let u(t) be the first derivative of 3/7*t**2 - 2/7*t**3 + 1 + 1/14*t**4 - v*t. Factor u(o).
2*(o - 1)**3/7
Let z = 319 - 2869/9. Let 2/9 + 4/9*b + z*b**2 = 0. What is b?
-1
Let y be (0/(-1))/(-23 + 24). Factor y - 2/7*p**2 + 2/7*p**3 + 0*p.
2*p**2*(p - 1)/7
Let p = -21 + 85/4. Factor 1/4*n - p*n**2 + 0.
-n*(n - 1)/4
Determine l, given that 4/3*l**2 + 1/3*l**3 - l - 6 = 0.
-3, 2
Let f(y) = -5*y**4 + 3*y**2 - 4*y + 2. Let w(a) = -11*a**4 - a**3 + 6*a**2 - 9*a + 5. Let c(o) = -5*f(o) + 2*w(o). Find z, given that c(z) = 0.
-1, 0, 2/3, 1
Let y(d) = 5*d**2 + 8. Let q(t) = t**3 - 14*t**2 + 12*t + 10. Let j be q(13). Let n(p) = 4*p**2 - p + 7. Let k(h) = j*y(h) + 4*n(h). Factor k(f).
(f - 2)**2
Let q = 12 + -10. Let y(s) be the second derivative of 0 + 1/12*s**4 + 1/2*s**2 + q*s + 1/3*s**3. Factor y(c).
(c + 1)**2
Let x(k) = -k**4 - 1. Let u(g) = 7*g**4 + 2*g**3 + g**2 + 6. Let s(m) = -u(m) - 6*x(m). Solve s(h) = 0.
-1, 0
Suppose -v = -3*v + 16. Let q be 1/4 + 22/v. Determine t so that -2*t**2 - q*t**3 + 5*t**4 - 2*t**3 - 5*t**4 + 7*t**4 = 0.
-2/7, 0, 1
Let n(k) be the first derivative of 14*k**5/95 + 22*k**4/19 + 178*k**3/57 + 64*k**2/19 + 24*k/19 - 14. Find w, given that n(w) = 0.
-3, -2, -1, -2/7
Let b be ((-5)/25)/(27/(-15) - -1). Determine u so that 3/4*u - 1/2 - b*u**2 = 0.
1, 2
Factor -15*n**2 + 3/2*n**3 - 12 + 51/2*n.
3*(n - 8)*(n - 1)**2/2
Suppose 5*l + 5 = 30. Factor 9/2*h**l + 23*h**3 - 33/2*h**4 + 9/2*h - 1/2 - 15*h**2.
(h - 1)**3*(3*h - 1)**2/2
Factor -1/4*r**4 - 3/4*r + 1/2 + 3/4*r**3 - 1/4*r**2.
-(r - 2)*(r - 1)**2*(r + 1)/4
Let s(c) be the third derivative of -c**6/360 + c**5/120 + c**3/3 + 3*c**2. Let g(i) be the first derivative of s(i). Factor g(u).
-u*(u - 1)
Let f(z) = -3*z**3 + z**2 - 2*z. Suppose -8*h = -3*h + 30. Let o(t) = t. Let q(g) = h*o(g) - 3*f(g). Find i such that q(i) = 0.
0, 1/3
Let p(f) be the second derivative of 1/30*f**5 + 3*f - 1/18*f**4 - 1/135*f**6 + 0*f**2 + 0 + 1/27*f**3. Suppose p(q) = 0. Calculate q.
0, 1
Factor -8/7*t + 2/7 + 12/7*t**2 + 2/7*t**4 - 8/7*t**3.
2*(t - 1)**4/7
Let w(p) be the second derivative of 0*p**2 + 0 + 0*p**5 - 3/55*p**6 + 7/66*p**4 + p - 2/33*p**3. Find q such that w(q) = 0.
-1, 0, 1/3, 2/3
Let y(b) = -b**2 + 7*b + 3. Let f be y(5). Let p be f/5 + (-12)/(-30). Factor -5 + 1 + 2*i**p + 6*i**2 - 2*i - 2*i**2 + 0.
2*(i - 1)*(i + 1)*(i + 2)
Factor -4*n**2 + 3*n**2 - 10*n**5 + 4*n**5 - 9*n**4 + 4*n**2.
-3*n**2*(n + 1)**2*(2*n - 1)
Suppose 0 = 5*f - 1 - 9. Let k be (-18)/(-24)*f/6. Factor -1/2*c + 0 + 1/4*c**3 + k*c**2.
c*(c - 1)*(c + 2)/4
Let h = 59 + -471/8. Let y(l) be the third derivative of -1/80*l**6 - 2*l**2 + l**3 + h*l**5 + 0*l - 1/2*l**4 + 0. Factor y(t).
-3*(t - 2)**2*(t - 1)/2
Suppose -8*w = -11*w. Let o be (-8)/6*9/(-2). Solve 3 + w - 7 - o*s - 2*s**2 = 0 for s.
-2, -1
Suppose 3*q = 5*c, -4*c + 12 = -q + 5. Suppose 2/3 + 2/3*k - 2/3*k**c - 2/3*k**2 = 0. What is k?
-1, 1
Let m be (-1)/((-1)/(-2)) - -21. Let p = -45 - -48. Factor 19 - m + a**p - a.
a*(a - 1)*(a + 1)
Let x = -13 + 7. Let z(l) = l**2 + 6*l + 5. Let t be z(x). Factor 2*s**3 + s**3 - s - s**3 - s**t.
-s*(s - 1)**2*(s + 1)**2
Let w(v) be the first derivative of -v**4/50 + 2*v**3/25 + 6. Factor w(r).
-2*r**2*(r - 3)/25
Let z be (0 - -10)/(-1 + 3). Let y(x) be the second derivative of -1/9*x**2 + 0*x**3 + x + 1/45*x**z + 0 + 1/18*x**4. Factor y(j).
2*(j + 1)**2*(2*j - 1)/9
Let 2/13*k - 6/13*k**2 + 6/13 - 2/13*k**3 = 0. What is k?
-3, -1, 1
Let s(z) be the third derivative of 0 + 0*z - 1/15*z**5 - 2/3*z**3 + 5/12*z**4 - z**2. Let s(b) = 0. Calculate b.
1/2, 2
Let d(b) be the first derivative of 1/3*b**3 + b**2 + b + 4. Find c, given that d(c) = 0.
-1
Suppose -3/4 + 1/4*s**3 - 5/4*s**2 + 7/4*s = 0. Calculate s.
1, 3
Let b(q) be the second derivative of q**9/13608 + q**8/2520 + q**7/1260 + q**6/1620 - q**3/6 - q. Let c(v) be the second derivative of b(v). Solve c(w) = 0.
-1, 0
Let j = 29/85 + 1/17. Factor j - 4/5*x**2 + 2/5*x.
-2*(x - 1)*(2*x + 1)/5
Let h(v) = -2*v**2 - 2*v + 4. Let u(b) = 7*b**2 + 9*b - 16. Let i(j) = 9*h(j) + 2*u(j). Suppose i(y) = 0. What is y?
-1, 1
Let u(s) = s**3 - s**2. Let h(q) = 14*q**3 - 5*q - 5. Let z(j) = 13*j**3 - j**2 - 4*j - 4. Let i(g) = 4*h(g) - 5*z(g). Let m(l) = i(l) + 6*u(l). Factor m(o).
-o**2*(3*o + 1)
Factor 2*r**4 + r**4 - 6*r**3 + 1 - 4*r + 10*r - 4.
3*(r - 1)**3*(r + 1)
Let j be (-2)/(-3) + ((-5)/15 - 0). Find p, given that 1/3*p + 0 - j*p**2 = 0.
0, 1
Let i(v) be the first derivative of -2*v**3/3 - 7*v**2 - 24*v - 16. Factor i(x).
-2*(x + 3)*(x + 4)
Let q(h) be the third derivative of -8*h**2 - 1/16*h**4 + 0*h + 0 - 1/240*h**6 - 1/40*h**5 - 1/12*h**3. Factor q(r).
-(r + 1)**3/2
Let o = -9 - -34. Determine v so that -4*v**2 + 15*v**4 + 4*v**5 + 27*v**3 - v**5 + o*v**2 + 6*v = 0.
-2, -1, 0
Let f(o) be the first derivative of 6*o**5/5 - 9*o**4/4 - o**3 + 9*o**2/2 - 3*o + 41. Find u such that f(u) = 0.
-1, 1/2, 1
Let m be ((-6)/2)/45*-3. Determine d so that 1/5*d + 0 - m*d**2 = 0.
0, 1
Suppose 1 - 5 = 4*w + 4*h, 0 = 5*h + 15. Let d be 1*(-2 - -2) + 3. Factor w*n + 2*n**4 + 2*n**2 - 4*n**d + 1 + 2*n**5 + 1 - 6*n**2.
2*(n - 1)**2*(n + 1)**3
Let b = 7 - 11. Let h be b/(-6) - (-20)/(-30). Suppose 0*f + 0*f**2 - 1/3*f**5 + h*f**3 + 1/3*f**4 + 0 = 0. Calculate f.
0, 1
Let p(a) = 5*a**5 - a**4 + a**3 + 7*a**2. Let n(m) = -4*m**3 + m**2 - 13*m**2 - 10*m**2 + 3*m**4 - 16*m**5 - m**4. Let z(g) = 3*n(g) + 10*p(g). Factor z(i).
2*i**2*(i - 2)*(i - 1)*(i + 1)
Let h(b) be the third derivative of -b**8/84 + b**7/21 - b**6/30 - 2*b**5/15 + b**4/3 - b**3/3 - 49*b**2. Suppose h(m) = 0. What is m?
-1, 1/2, 1
Let c = -21 + 27. Factor 3*s**2 - 3*s**2 + s**5 - 5*s**4 + c*s**4.
s**4*(s + 1)
Let c(p) = 4*p**4 - 2*p**2 - 2. Let g(x) = -9*x**4 + x**3 + 4*x**2 - x + 5. Let i(o) = 5*c(o) + 2*g(o). Solve i(q) = 0 for q.
-1, 0, 1
Let g = 5 - 14/3. Suppose -1/3*p**2 + 0 - g*p = 0. Calculate p.
-1, 0
Let j(m) be the first derivative of 7*m**4/16 + m**3/3 - 17*m**2/8 + 3*m/2 + 10. Let j(l) = 0. What is l?
-2, 3/7, 1
Let r(h) be the second derivative of -h**5/80 + h**4/24 + h**3/24 - h**2/4 + h. Solve r(j) = 0 for j.
-1, 1, 2
Let t(f) be the first derivative of -1/2*f**2 + 0*f**3 - 1/36*f**4 + 1/180*f**5 - 1 + 0*f. Let j(m) be the second derivative of t(m). Solve j(g) = 0 for g.
0, 2
Suppose 5*u + 5*y + 0*y - 10 = 0, y - 11 = 2*u. Let w be (1/(-2))/(u + 2). Factor -1/2*z + 0 - w*z**3 - z**2.
-z*(z + 1)**2/2
Factor 1/4*s**2 + 1/8*s**3 + 0*s + 0.
s**2*(s + 2)/8
Let l(v) be the second derivative of v**4/120 + v**3/12 + v**2/5 - 14*v. Find g such that l(g) = 0.
-4, -1
Let w be (1 + 2*-5)/(-1). Suppose w = q - 0. Let 2*g**2 - q*g - 3 - g**2 - 2*g**2 - 5*g**2 = 0. What is g?
-1, -1/2
Let p(u) be the first derivative of -1/8*u**4 - 1/6*u**3 + 2 + 0*u**2 + 0*u. Suppose p(i) = 0. What is i?
-1, 0
Let i(j) be the second derivative of j**7/126 - j**6/30 + j**5/20 - j**4/36 - 2*j. Find m, given that i(m) = 0.
0, 1
Factor 4/5*u - 12/5*u**3 - 8/5*u**2 + 0.
-4*u*(u + 1)*(3*u - 1)/5
Let l(k) be the third derivative of k**6/200 - k**5/50 + k**4/40 + 19*k**2. Let l(m) = 0. What is m?
0, 1
Let s(d) be the first derivative of 2*d**3/9 + 2*d**2/3 + 2*d/3 - 22. Let s(z) = 0. Calculate z.
-1
Let l(r) be the second derivative of -r**4/42 - 2*r**3/21 + 8*r**2/7 - 2*r. Factor l(h).
-2*(h - 2)*(h + 4)/7
Let m = -10 - -13. Factor -m + 6*t**3 - 4*t**2 - 4*t**3 + 3.
2*t**2*(t - 2)
Let i(y) = y**2 - 21*y + 23. Let d be i(20). Factor -3/2*x - 1/6 - 8/3*x**d - 4*x**2.
-(x + 1)*(4*x + 1)**2/6
Suppose -2*s + 3*p - 20 = 2*p, 3*s = 3*p - 24. Let m = s - -14. Factor 0*c - 1/2*c**m + 0.
-c**2/2
Suppose 0 - 1/7*u**4 + 3/7*u**3 - 3/7*u**2 + 1/7*u = 0. Calculate u.
0, 1
Suppose 2*o = -0*o - o. Let y(f) be the first derivative of -2/3*f**6 + 1/2*f**2 - 4/5*f**5 + 3/4*f**4 + o*f + 1 + 4/3*f**3. Suppose y(i) = 0. Calculate i.
-1, -1/2, 0, 1
Let w(i) be the third derivative of 0 + 1/4*i**4 - 1/35*i**7 - 1/30*i**6 + 2*i**2 + 0*i + 1/15*i**5 - 1/168*