6*p**4 + 4*p**5 = 0.
-1, 1
Suppose 4*o = 3*o + 5. Let l = o + -3. Suppose -a**l - 2*a**3 + 0*a**3 - 2 - 6*a - 5*a**2 = 0. What is a?
-1
Let v(r) be the first derivative of r**6/96 - r**5/80 - 4*r**3/3 + 4. Let p(o) be the third derivative of v(o). Suppose p(g) = 0. What is g?
0, 2/5
Suppose 5*p - 15 = -5*v, p + 2 = 3*v + 1. Let z = p - -2. Determine o so that 0*o**5 + o**3 - o**2 + 2*o**z - o**5 - o**4 = 0.
-1, 0, 1
Let w(s) be the first derivative of s**3/15 + 4*s**2/5 + 16*s/5 - 12. Let w(i) = 0. Calculate i.
-4
Let n = 112 - 334/3. Factor -n + 0*q + 2/3*q**2.
2*(q - 1)*(q + 1)/3
Let b(k) = -k**3 - 3*k**2 - 4*k - 2. Let t = 17 + -19. Let g be b(t). Factor -3/5*w - 1/5*w**g - 2/5.
-(w + 1)*(w + 2)/5
Let w(f) be the first derivative of f**6/420 - f**5/105 - f**4/84 + 2*f**3/21 - 5*f**2/2 - 5. Let x(o) be the second derivative of w(o). Solve x(b) = 0 for b.
-1, 1, 2
Let l(n) = -16*n**4 + 140*n**3 - 308*n**2 + 340*n - 92. Let v(o) = o**3 + o**2 + o + 1. Let y(a) = -l(a) + 16*v(a). Let y(b) = 0. Calculate b.
3/4, 1, 3
Let a(m) be the second derivative of 0*m**4 + 0 + 2*m**2 - 4/3*m**3 + 8*m - 2/15*m**6 + 2/5*m**5. Factor a(j).
-4*(j - 1)**3*(j + 1)
Let t(r) be the first derivative of -r**3/6 + r**2/4 - 12. Let t(g) = 0. What is g?
0, 1
Let f(d) be the first derivative of d**5/90 - d**4/18 + 2*d**2 + 1. Let r(p) be the second derivative of f(p). What is g in r(g) = 0?
0, 2
Let l(h) = 4*h**3 - 104*h**2 + 100*h - 16. Let k(j) = -j**3 + 21*j**2 - 20*j + 3. Let t(v) = 16*k(v) + 3*l(v). Determine a so that t(a) = 0.
0, 1, 5
Let n(z) = -z**2 + 14*z + 3. Let v be n(14). Let w(r) be the second derivative of 1/5*r**v - r + 0 + 2/5*r**2 - 1/15*r**4. Determine l so that w(l) = 0.
-1/2, 2
Suppose 2*w + w = c - 9, 0 = -2*c - 5*w - 4. Let i(q) be the second derivative of -3*q + 1/24*q**c + 0 + 0*q**2 + 1/48*q**4. Suppose i(a) = 0. What is a?
-1, 0
Let k(b) be the first derivative of -2*b**5/45 + b**4/18 + 4*b**3/27 + 13. Factor k(g).
-2*g**2*(g - 2)*(g + 1)/9
Factor 2/5*g + 0*g**2 + 1/5*g**4 - 2/5*g**3 - 1/5.
(g - 1)**3*(g + 1)/5
Let z be 6/18*(-1 - (1 - 8)). Let i(y) be the second derivative of -1/42*y**4 + 2/21*y**3 + y + 0 - 1/7*y**z. Find p, given that i(p) = 0.
1
Let j(v) = -11*v**2 - 5*v - 6. Let b(o) = o**2 + 1. Let m(a) = -6*b(a) - j(a). Factor m(p).
5*p*(p + 1)
Let z(x) be the second derivative of -x**4/16 + 3*x**3/8 - 3*x**2/4 + 2*x. Factor z(m).
-3*(m - 2)*(m - 1)/4
Let j(y) be the third derivative of y**8/1176 - y**7/245 + y**6/420 + y**5/70 - y**4/42 - 16*y**2. Let j(z) = 0. What is z?
-1, 0, 1, 2
Let q be -3 + (8 + -3 - 3). Let m(p) = -3*p**3 + 3*p**2 + 6*p + 3. Let t(f) = -1. Let h(l) = q*m(l) - 3*t(l). Suppose h(w) = 0. What is w?
-1, 0, 2
Suppose 0 = 3*z + z - 60. Let u(h) = -3*h**3 - 18*h**2 - 15*h + 15. Let r(v) = v**2 + v - 1. Let n(g) = z*r(g) + u(g). Determine j so that n(j) = 0.
-1, 0
Suppose -2*p = -2*p - 2*p. Factor p + 2/11*q**2 + 2/11*q.
2*q*(q + 1)/11
Let s be ((-6)/2)/(36/(-24)). Factor -2/5*b + 0 - 2/5*b**s.
-2*b*(b + 1)/5
Let y = -4 + 6. Let c = y - 2. Let -v**2 - v**4 + v - v**3 + c*v + 2*v**2 = 0. Calculate v.
-1, 0, 1
Let c(a) be the third derivative of a**8/448 + a**7/280 - a**6/160 - a**5/80 - 3*a**2. Factor c(t).
3*t**2*(t - 1)*(t + 1)**2/4
Let j(n) = n**4 + n**3 - n - 1. Let v(m) = m**4 + 26*m**3 - 25*m**2 + 4*m - 6. Let q(c) = 6*j(c) - v(c). Factor q(x).
5*x*(x - 2)*(x - 1)**2
Let m(a) be the second derivative of a**7/42 + a**6/20 + a**5/40 - 20*a. Factor m(r).
r**3*(r + 1)*(2*r + 1)/2
Suppose 5*u = 2*u - 3*i - 12, 4*u - 16 = 4*i. Let 2/9*a**2 + 0*a + u = 0. What is a?
0
Let v(f) be the second derivative of -3/2*f**3 + 0*f**2 - f + 0 + 1/4*f**4. Factor v(g).
3*g*(g - 3)
Let h(a) = -a**4 + a**3 - a**2 + a + 1. Let r(s) = s**5 - 5*s**4 + 19*s**3 - 21*s**2 + 6*s - 3. Let m(u) = 3*h(u) + r(u). Let m(g) = 0. Calculate g.
0, 1, 3
Factor -1/2*m - 1/4 - 1/4*m**2.
-(m + 1)**2/4
Let q = -13 - -18. Suppose -27 + 7 = -q*t. Factor -2 + 2*y**2 + t*y**2 - 2*y + 0*y - 2*y.
2*(y - 1)*(3*y + 1)
Let z(u) = -14*u**5 + 14*u**4 - 2*u**3 - 4*u**2 - 5*u - 11. Let w(o) = -5*o**5 + 5*o**4 - o**3 - o**2 - 2*o - 4. Let d(t) = 11*w(t) - 4*z(t). Factor d(b).
b*(b - 1)**3*(b + 2)
Suppose q + 173 = 3*c, 3*c + 2*q = 113 + 45. Let k(l) = 3*l + 1. Let n be k(1). Factor 26*u**4 + 28*u**n - 15*u**2 - 16 - 54*u**3 + c*u - 21*u**2.
2*(u + 1)*(3*u - 2)**3
Let v(w) = -w**2 + 2*w - 6*w + 2*w**3 + 0*w**3 - 3. Let m(l) = 2*l**3 - 2*l**2 - 4*l - 4. Let g(h) = -3*m(h) + 4*v(h). Let g(x) = 0. What is x?
-2, 0, 1
Let v = 21 - 21. Factor -2/7*h**3 + 2/7*h**2 + 0 + v*h.
-2*h**2*(h - 1)/7
Let k(u) = 4*u**5 - 12*u**4 + 8. Let y(h) = -h**4 + h**3 + 1. Let m(i) = k(i) - 8*y(i). What is v in m(v) = 0?
-1, 0, 2
Let j(w) be the first derivative of 11*w**3/6 - 6*w**2 + 2*w - 17. Find s, given that j(s) = 0.
2/11, 2
Find s, given that -5 - 10*s**2 - 25/2*s - 5/2*s**3 = 0.
-2, -1
Let z be -6*2*(-1)/8. Let m(q) be the first derivative of -z*q**2 + 1/2*q**3 + 2*q + 3 - 1/16*q**4. Solve m(j) = 0.
2
Let c be -1 + -1 + (-7)/(-84)*25. Let i(y) be the first derivative of 0*y**4 + 0*y**3 - 1/10*y**5 + 4 + 0*y**2 - c*y**6 + 0*y. Suppose i(z) = 0. Calculate z.
-1, 0
Let z be (2/16)/(3/18). Factor 1/4 - 1/4*f**3 - z*f + 3/4*f**2.
-(f - 1)**3/4
Let g(u) = 3*u**2 - 9*u + 6. Let t(w) = -w**2 - w + 1. Let b(q) = 3*q**2 + 2*q - 1. Let l(n) = b(n) + 2*t(n). Let j(x) = -g(x) + 6*l(x). Factor j(k).
3*k*(k + 3)
Let y = -152 + 382. Let m = y - 1606/7. Factor -2/7*z + m*z**2 + 0 - 4/7*z**4 + 0*z**3 + 2/7*z**5.
2*z*(z - 1)**3*(z + 1)/7
Let b(r) be the first derivative of -2*r**3/9 + 7*r**2/3 - 4*r - 53. Factor b(o).
-2*(o - 6)*(o - 1)/3
Let l(j) be the third derivative of -1/72*j**4 + 3*j**2 + 1/90*j**5 + 0*j + 0 - 1/18*j**3. Factor l(m).
(m - 1)*(2*m + 1)/3
Let k(y) be the third derivative of -y**6/360 + y**4/24 - y**3/3 + y**2. Let l(j) be the first derivative of k(j). Solve l(g) = 0 for g.
-1, 1
Let u be (2 + 9/(-12))*4/10. Factor u*q**2 - 1/2 + 1/2*q - 1/2*q**3.
-(q - 1)**2*(q + 1)/2
Suppose -5*v + 6 = -4. Factor 0*r**2 + 6*r - 3*r**2 + 2*r**v + 1 - 10.
-(r - 3)**2
Suppose -5*r = -3*r - 4. Let o(p) be the second derivative of -1/30*p**4 + 0 + 1/5*p**2 + r*p + 0*p**3. Factor o(v).
-2*(v - 1)*(v + 1)/5
Suppose -6*d = -5*d - 3*s + 9, 3*d + 4*s = 12. Let m(n) be the second derivative of 0*n**3 - 1/45*n**6 + 4*n - 1/30*n**5 + d*n**4 + 0*n**2 + 0. Factor m(v).
-2*v**3*(v + 1)/3
What is y in 3/4*y + 9/4*y**3 + 0 + 9/4*y**2 + 3/4*y**4 = 0?
-1, 0
Let g(i) be the third derivative of i**6/280 + i**5/70 - 3*i**4/56 + i**2 - 53*i. Suppose g(d) = 0. What is d?
-3, 0, 1
Suppose -4*q = 106 + 66. Let c = q + 217/5. Factor 0 + 2/5*y - c*y**3 + 2/5*y**4 - 2/5*y**2.
2*y*(y - 1)**2*(y + 1)/5
Let k(q) = 2*q**3. Let n(r) be the first derivative of -r**5/5 + 2. Let h(v) = -k(v) - 6*n(v). Suppose h(w) = 0. What is w?
0, 1/3
Let r = 7 + -5. Let a be 1 + (1 - 4/r). Solve u**5 + 0*u**5 - 3*u**5 + a*u**3 + 2*u**3 = 0 for u.
-1, 0, 1
Factor 4/5*t**2 - 24/5*t + 4.
4*(t - 5)*(t - 1)/5
Determine p so that 44/9 - 2/3*p**2 + 62/9*p = 0.
-2/3, 11
Let w be 3/1*3/27. Let -1/6*y**3 + 0 - 1/6*y - w*y**2 = 0. What is y?
-1, 0
Suppose w + 3*v + 0 = 16, 0 = w + 4*v - 20. Let x(p) be the third derivative of 3*p**2 + 0 + 0*p - 1/12*p**w + 1/30*p**5 + 0*p**3. What is z in x(z) = 0?
0, 1
Let o(c) = -7*c**3 - 7*c**2 + c + 7. Suppose -b = -2*g - 2, -3*b - 2 = 5*g - 3*g. Let w(r) = r**3 + r**2 - 1. Let k(v) = g*o(v) - 6*w(v). What is y in k(y) = 0?
-1, 1
Let j = -2 + 1. Let i be (j + (0 - -3))/8. Solve -1/2*t**3 + 0*t**4 + 1/4*t + 0*t**2 + i*t**5 + 0 = 0.
-1, 0, 1
Let c = 6 + -3. Let v(i) = i**2 - 5*i - 2. Let g(q) = q**2 - 4*q - 1. Let k(l) = c*g(l) - 2*v(l). Suppose k(z) = 0. Calculate z.
1
Let x be (-5)/70 - 2/(-4). Factor x*w**2 + 0*w - 3/7*w**4 + 0 + 0*w**3.
-3*w**2*(w - 1)*(w + 1)/7
Let i = 20126/105 - 575/3. Let d(g) be the third derivative of 1/30*g**6 + 0 - 1/30*g**5 + 0*g - i*g**7 + 0*g**4 + 0*g**3 + 4*g**2. Solve d(u) = 0 for u.
0, 1
Let x(l) = l**3 + 20*l**2 + 37*l + 16. Let k(y) = y**3 + 40*y**2 + 73*y + 31. Let b(f) = 2*k(f) - 5*x(f). Determine p so that b(p) = 0.
-3, -2/3
Let y(a) be the second derivative of -1/5*a**6 + 0*a**2 + 1/2*a**4 + 0 - 2*a + 1/14*a**7 + 0*a**5 - 1/2*a**3. Solve y(l) = 0.
-1, 0, 1
Let x be -6 - (-2)/((-2)/