p + 2*p**3 - p**3.
-3*p*(p + 1)**2*(2*p - 1)
Let t(y) be the third derivative of -y**9/75600 + y**7/12600 - 7*y**4/24 - 7*y**2. Let z(l) be the second derivative of t(l). Factor z(w).
-w**2*(w - 1)*(w + 1)/5
Let i(b) = 2*b**2 + 4*b + 3. Let g be i(-2). Suppose 5*v - 13 = -g. Suppose 0*x**2 - 4 - 3*x**2 + 4*x + v*x**2 = 0. Calculate x.
2
Let a(n) be the third derivative of n**8/1176 + n**7/105 + 3*n**6/70 + 11*n**5/105 + 13*n**4/84 + n**3/7 - 14*n**2. Suppose a(m) = 0. Calculate m.
-3, -1
Let g = 3/290 - -1091/6670. Let d = 82/207 - g. Factor 2/9*i**4 + 2/3*i**2 + 0 + d*i + 2/3*i**3.
2*i*(i + 1)**3/9
Let k(w) be the second derivative of -32*w**6/3 - 72*w**5/5 + 19*w**4/3 + 6*w**3 - 4*w**2 + 10*w. Determine x, given that k(x) = 0.
-1, -2/5, 1/4
Factor 2/3*y - 2/15*y**2 - 2/5 - 2/15*y**3.
-2*(y - 1)**2*(y + 3)/15
Let x(w) be the first derivative of 1/8*w**2 - 1/20*w**5 - 1 + 1/12*w**3 + 0*w - 1/16*w**4. Factor x(t).
-t*(t - 1)*(t + 1)**2/4
Let k(n) be the second derivative of n**7/490 - n**6/280 - 5*n**2/2 + 2*n. Let o(a) be the first derivative of k(a). Factor o(d).
3*d**3*(d - 1)/7
Let c(s) = s + 4. Let k be c(-4). Factor -3*j**3 + 2*j + 3*j**3 - 4 + 4*j**2 + k*j - 2*j**3.
-2*(j - 2)*(j - 1)*(j + 1)
Let q(c) be the third derivative of -c**5/270 - c**4/36 - 31*c**2. Factor q(t).
-2*t*(t + 3)/9
Let p(a) be the third derivative of -a**8/336 - a**7/70 - a**6/40 - a**5/60 - 6*a**2. Determine l so that p(l) = 0.
-1, 0
Suppose -775*z + 773*z = -10. What is l in -1/2*l**z + 0*l + 1/2*l**3 + 0*l**2 + 0*l**4 + 0 = 0?
-1, 0, 1
Factor 0*h + 8/7*h**4 + 6/7*h**3 + 2/7*h**5 + 0*h**2 + 0.
2*h**3*(h + 1)*(h + 3)/7
Suppose 4*p - 10 = 6. Let q(t) = 2*t**2 + 8*t - 6. Let r(g) = 5*g**2 + 17*g - 13. Let u(i) = p*r(i) - 9*q(i). Factor u(l).
2*(l - 1)**2
Suppose 0 = -4*b - 61 + 73. Let h(y) be the first derivative of 2/3*y**3 - 2/5*y**5 + 0*y - y**2 + b + 1/2*y**4. What is k in h(k) = 0?
-1, 0, 1
Let j be 1/(-2*2/36). Let h(v) = 13*v**4 - 11*v**3 + 7*v**2 - 9. Let q(u) = 6*u**4 - 5*u**3 + 3*u**2 - 4. Let g(x) = j*q(x) + 4*h(x). Factor g(w).
-w**2*(w - 1)*(2*w + 1)
Factor -6 + k**2 + 29*k - 31*k - 2.
(k - 4)*(k + 2)
Let z be 3 - -3*(-2)/6. Suppose -3*y + 2*y**3 + 2*y**2 - 2*y**2 + y - 2*y**2 + z = 0. What is y?
-1, 1
Let u = 8 + -4. Suppose 8 + 12 = u*s. Solve 1/3*q + 1/3*q**4 + 1/3 - 2/3*q**2 + 1/3*q**s - 2/3*q**3 = 0.
-1, 1
Solve 8/3*s**2 - 4/3*s + 0 - 8/3*s**4 + 12*s**3 - 32/3*s**5 = 0.
-1, -1/2, 0, 1/4, 1
Let v(x) be the third derivative of x**5/180 - x**3/18 + 17*x**2. Factor v(r).
(r - 1)*(r + 1)/3
Let s be -3 - (-3 + 0) - -2. Factor -8*d**3 + 3 + 9*d**s + 5*d**3 - 9*d + 0*d.
-3*(d - 1)**3
Suppose 3*h + 8 = -4*p, -5*h - 13 + 43 = -2*p. Factor 5*u - h*u**2 - 3*u**3 - 6*u**4 + 10*u**2 + u - 3*u.
-3*u*(u - 1)*(u + 1)*(2*u + 1)
Let c(b) be the first derivative of -b**4/10 - 4*b**3/15 + 3*b**2/5 - 10. Determine x so that c(x) = 0.
-3, 0, 1
Let r(b) = -b**3 - 6*b**2 - 8*b - 6. Let x be r(-5). Factor -3*p**5 + p**3 - x*p - 1 - 2 + 6*p**2 - 3 + 11*p**3.
-3*(p - 2)*(p - 1)*(p + 1)**3
Let r(x) be the first derivative of 1/3*x**3 + 0*x + 1/4*x**4 + 0*x**2 - 1. Suppose r(y) = 0. Calculate y.
-1, 0
Let s(m) be the first derivative of 7 - 2/27*m**3 - 2/9*m**2 - 2/9*m. Find u, given that s(u) = 0.
-1
Let r(b) be the third derivative of b**2 + 0*b**3 - 1/240*b**6 + 0*b + 1/48*b**4 + 0 + 0*b**5. Factor r(p).
-p*(p - 1)*(p + 1)/2
Let x(o) be the third derivative of -1/135*o**6 + 0*o**3 + o**2 + 1/378*o**8 - 1/945*o**7 + 0*o + 0*o**4 + 1/270*o**5 + 0. Determine p so that x(p) = 0.
-1, 0, 1/4, 1
Let q be (-1)/54*5644/(-91). Let k = q - 2/351. Factor -8/7*h + 0 - k*h**2 - 2/7*h**3.
-2*h*(h + 2)**2/7
Suppose 5*b**2 + 0 + 5/2*b**3 - 70*b**4 + 0*b = 0. Calculate b.
-1/4, 0, 2/7
Suppose -4*d + 2 = t, -2*d - 5*t + 10 = 3*d. Suppose d = -2*h - 1 + 5. Find o, given that -6*o**h - 4/3*o - 2/3*o**3 + 14*o**4 + 0 - 6*o**5 = 0.
-1/3, 0, 1, 2
Let w(a) be the third derivative of -a**5/12 - 25*a**4/24 - 10*a**3/3 - 34*a**2. Factor w(h).
-5*(h + 1)*(h + 4)
Let j(g) be the first derivative of g**6/40 - 2*g - 5. Let o(a) be the first derivative of j(a). Determine d, given that o(d) = 0.
0
Let y(o) be the third derivative of -7*o**6/30 - o**5/3 + o**4/3 - 38*o**2. Suppose y(v) = 0. What is v?
-1, 0, 2/7
Let j(w) be the second derivative of w**7/3360 + w**6/1440 - w**5/480 - w**4/96 - w**3/3 - 2*w. Let q(d) be the second derivative of j(d). Factor q(l).
(l - 1)*(l + 1)**2/4
Suppose 2*w - 5*b = 26, -17 = -0*w - 3*w + 2*b. Determine r, given that 2/7*r**w + 2/7*r**5 + 0*r**2 - 4/7*r**4 + 0*r + 0 = 0.
0, 1
Let 2/7*z**2 + 6/7*z + 4/7 = 0. What is z?
-2, -1
Let h(c) = -2*c**2 + 9*c - 7. Let y(a) = 4*a**2 + a**2 - 2*a**2 + 6*a - 20*a + 11. Let k(p) = -8*h(p) - 5*y(p). Factor k(t).
(t - 1)**2
Suppose -8/13*h - 10/13 + 2/13*h**2 = 0. What is h?
-1, 5
Let m(y) = -4*y**3 - 2*y**2 + 4*y + 2. Let u(j) = 5*j**3 + 3*j**2 - 5*j - 3. Let v = 12 - 8. Let t(d) = v*m(d) + 3*u(d). Find f, given that t(f) = 0.
-1, 1
Let h(x) = x**3 + 17*x + 8. Let f(w) = 16*w + 8. Let a(u) = 5*f(u) - 4*h(u). Factor a(z).
-4*(z - 2)*(z + 1)**2
Let x(q) = 3*q**2 - 9. Let c(r) = -3*r**2 + 10. Let m(u) = -3*c(u) - 2*x(u). Factor m(o).
3*(o - 2)*(o + 2)
Let l = -13 + 14. Solve l + 86*p**2 + 1 - 85*p**2 + 3*p = 0.
-2, -1
Let d be (-32)/(-12)*9/(-2). Let b be 2/8 - 33/d. Factor -2 - 2*s**b - 4*s**4 - 12*s**2 - 8*s + 2*s**4 - 6*s**3.
-2*(s + 1)**4
Let f(o) = -1. Let s(z) = z**3 - 2*z**2 - 4*z + 3. Let i(b) = 5*f(b) - s(b). Factor i(h).
-(h - 2)**2*(h + 2)
Let z be ((-38)/14 - -1) + 2. Let k = 3/8 - 5/56. Suppose -z*x - k*x**2 + 0 = 0. What is x?
-1, 0
Let k(j) be the second derivative of j**9/75600 - j**7/12600 + j**4/6 + 4*j. Let x(q) be the third derivative of k(q). Factor x(d).
d**2*(d - 1)*(d + 1)/5
Let j be 448/4*6/(-4). Let z be (-1)/4 + (-234)/j. Determine g, given that z*g**2 - 10/7*g - 2/7*g**3 + 4/7 = 0.
1, 2
What is c in 0 + 0*c**2 + 2/9*c**3 - 2/9*c = 0?
-1, 0, 1
Suppose -7*g**3 - 27*g**2 + 2 + 9*g - 5 - 9*g + 6*g**4 - 17*g = 0. Calculate g.
-1, -1/2, -1/3, 3
Let b(w) be the third derivative of 6*w**2 + 0*w**3 + 0 - 1/1050*w**7 - 1/150*w**6 - 1/75*w**5 + 0*w**4 + 0*w. Solve b(r) = 0.
-2, 0
Let d(b) = -2*b - 8. Let i be d(-5). Let y(x) be the second derivative of 0 - i*x + 0*x**3 + 0*x**2 + 1/6*x**4. Factor y(q).
2*q**2
Let k(p) be the first derivative of 1/2*p**6 - 1 - 9/5*p**5 + 0*p**2 - p**3 + 0*p + 9/4*p**4. What is u in k(u) = 0?
0, 1
Let p = 123 + -121. Let 1/2*s + 1/4*s**p + 1/4 = 0. What is s?
-1
Suppose 7 = -0*q - q. Let u be (-4)/14 + (-23)/q. Factor 2*s**2 + s**4 + 4*s + 2*s**4 - 10*s**u + s**4.
2*s*(s - 2)*(s - 1)*(2*s + 1)
Suppose 3 = r - 0. Suppose -r - 3 = -3*k. Factor 1/3*d**3 + 0 - 1/3*d**k + 1/3*d**4 - 1/3*d.
d*(d - 1)*(d + 1)**2/3
Factor -8/9*j - 2/3 - 2/9*j**2.
-2*(j + 1)*(j + 3)/9
Let n(p) be the third derivative of -p**7/210 - 11*p**6/360 - p**5/15 - p**4/18 - 53*p**2. Find y, given that n(y) = 0.
-2, -1, -2/3, 0
Let u(m) be the first derivative of 16*m**3/3 + 8*m**2 + 4*m + 56. Suppose u(z) = 0. What is z?
-1/2
Let l(f) be the first derivative of -1/2*f**4 - 4/3*f**3 + 2 + 0*f - f**2. Factor l(n).
-2*n*(n + 1)**2
Let t(n) be the third derivative of n**8/168 + 11*n**7/420 + n**6/240 - 13*n**5/120 - 5*n**4/48 + n**3/6 - 16*n**2. Suppose t(g) = 0. What is g?
-2, -1, 1/4, 1
Suppose -3 + 11 = 2*k. Determine p, given that 40*p**4 + 3*p + 56*p**2 - 114*p**3 + 16*p**4 - k + 3*p = 0.
-1/4, 2/7, 1
Let m be (-212)/(-12) - (-4)/6. Let c = -18 + m. Let -1/3*t**3 + 1/3*t - 1/3 + c*t**2 = 0. What is t?
-1, 1
Let k(d) be the second derivative of 0*d**2 + 1/18*d**4 + 0 - 1/40*d**5 - 1/36*d**3 + d. Factor k(m).
-m*(m - 1)*(3*m - 1)/6
Suppose -1375 + 1375 - 6*a - 3*a**3 - 3*a**3 - 15*a**2 = 0. Calculate a.
-2, -1/2, 0
Let c be 2/8 + 1/(-4). Let y = c - -2. Factor -2/3*s**y + 0 + 2/3*s.
-2*s*(s - 1)/3
Let d(n) = -8*n**3 + 23*n**2 - 31*n + 19. Let f(t) = 33*t**3 - 93*t**2 + 123*t - 75. Let j(x) = 21*d(x) + 5*f(x). Find z, given that j(z) = 0.
2
Suppose y + 3 = 2*y. Let d(j) be the first derivative of -1 + y*j**2 + 2*j**3 + 1/2*j**4 + 2*j. Factor d(q).
2*(q + 1)**3
Suppose 2*g + 0*o + 4*o = -30, 3*g = -3*o - 54. Let y be (-14)/g - 14/(-6). Find u, given that u - 2*u**4 - 4*u**3 + 2*u**2 + 3*u + 0*u**y = 0.
-2, -1, 0, 1
Let w(f) be