Solve -5/4*h**4 + 25/4*h**5 + 0 - 4*h**3 + s*h - h**2 = 0 for h.
-2/5, 0, 1
Let y(h) be the first derivative of -1/3*h**2 - h + 2 + 2/3*h**3 - 1/2*h**4. Let s(l) be the first derivative of y(l). Factor s(z).
-2*(3*z - 1)**2/3
Suppose 3*k = c + c - 4, -5*k + 60 = 5*c. Determine j, given that -j**3 - j + 3*j + 8*j**2 - j**3 - c*j**4 = 0.
-1, -1/4, 0, 1
Let i(y) be the second derivative of y**4/6 - y**3/3 - 2*y**2 - 19*y. Factor i(k).
2*(k - 2)*(k + 1)
Let w(f) = -8*f - 30. Let b(z) = 3*z + 10. Let n(j) = 11*b(j) + 4*w(j). Let s be n(10). Factor s*c**2 + 0 + 0*c - 2/5*c**3.
-2*c**3/5
Let t(i) = i**2 - 8*i + 7. Let x be t(6). Let z be 10/5 + x - -3. Determine a so that 1/4*a**2 + 0 + z*a - 1/4*a**4 + 0*a**3 = 0.
-1, 0, 1
Let v(l) = 3*l**4 + 22*l**3 + 66*l**2 + 72*l + 29. Let j(b) = -9*b**4 - 65*b**3 - 198*b**2 - 216*b - 88. Let o(c) = 2*j(c) + 7*v(c). Factor o(w).
3*(w + 1)**2*(w + 3)**2
Let f(q) = q**3 - 6*q**2 - 7*q - 5. Let i be f(7). Let x(s) = -s**2 - 4*s + 7. Let r be x(i). Let -1/2*m - 3/2*m**r - m**3 + 0 = 0. Calculate m.
-1, -1/2, 0
Suppose 0 = -5*d - 3*b + 2*b, 2*b = 0. Let g be ((-3)/(-6) - 0)*d. Factor 0 + 0*z**2 - 2/3*z**3 + g*z + 1/3*z**4.
z**3*(z - 2)/3
Let u(k) be the second derivative of -k**5/30 + k**4/6 + 4*k**3/9 - 13*k. Factor u(g).
-2*g*(g - 4)*(g + 1)/3
Let a = 19 + -16. Determine o so that -16/3*o**2 - a*o - 1/3*o**5 - 2/3 - 2*o**4 - 14/3*o**3 = 0.
-2, -1
Let d(j) = 9*j**4 + 10*j**3 + 9*j**2 + 8*j + 7. Let m(y) = -5*y**4 - 5*y**3 - 4*y**2 - 4*y - 4. Let q(r) = 4*d(r) + 7*m(r). Factor q(p).
p*(p + 1)*(p + 2)**2
Let p(r) be the first derivative of 2*r**7/245 - 9*r**6/280 + 3*r**5/70 - r**4/56 - 4*r**2 + 3. Let i(u) be the second derivative of p(u). Solve i(h) = 0 for h.
0, 1/4, 1
Factor -59 + 0*t**2 + t**2 + 58.
(t - 1)*(t + 1)
Factor -4/5*m**4 + 2/5 - 2/5*m - 6/5*m**2 + 2*m**3.
-2*(m - 1)**3*(2*m + 1)/5
Factor -54*p**2 + 30*p**3 + 45*p - 11*p**2 - p - 20 + 16*p - 5*p**4.
-5*(p - 2)**2*(p - 1)**2
Determine s, given that 14*s**3 - 4*s - 19*s**3 + 9*s**3 = 0.
-1, 0, 1
Let f = -91/20 - -23/4. Factor 3/5*x**3 - 3/5*x + 6/5*x**2 - f.
3*(x - 1)*(x + 1)*(x + 2)/5
Let n(z) be the first derivative of 2*z**3/3 + 2*z**2 - 6*z + 7. Factor n(i).
2*(i - 1)*(i + 3)
Let a(r) be the third derivative of -r**8/420 - 2*r**7/175 - r**6/50 - r**5/75 + 10*r**2. Factor a(j).
-4*j**2*(j + 1)**3/5
Suppose 1 = -2*k + 4*l - 5, -5*l + 24 = 3*k. Suppose k*v + q - 5*q = -20, -2*v + q - 5 = 0. Factor -2/5*t**2 - 2/5*t + v.
-2*t*(t + 1)/5
Let n = -8 - -11. Suppose 13 = 5*s + n. Factor 1 - 1 - 4*q + s + 2*q**2.
2*(q - 1)**2
Solve 2*l**3 + 7*l**2 + l**2 + 2*l**3 = 0.
-2, 0
Let b be (2 + (-1 - 1))/2. Find c such that 2*c**2 + 2 - 4 + b*c**2 = 0.
-1, 1
Factor -41*h**3 - 3*h**4 + 41*h**3 + 3*h**2.
-3*h**2*(h - 1)*(h + 1)
Let f be 0/(4/(-20)*-5). Let v(h) be the third derivative of 1/840*h**7 + 2*h**2 + f*h**4 + 0*h - 1/240*h**5 + 0*h**3 + 0*h**6 + 0. Factor v(g).
g**2*(g - 1)*(g + 1)/4
Suppose -4*l + 0 - 8 = 0. Let h be (-9)/l*(-2)/(-3). Let -2*a**2 + a**2 - 2*a**2 + 0*a**3 - 4*a**h + a = 0. What is a?
-1, 0, 1/4
Find f such that 2/9*f**5 + 0*f - 2/9*f**3 + 2/9*f**2 - 2/9*f**4 + 0 = 0.
-1, 0, 1
Let i(h) be the third derivative of -4*h**2 + 0*h - 1/660*h**6 + 0 + 1/132*h**4 + 0*h**3 + 0*h**5. Solve i(l) = 0.
-1, 0, 1
Let -1/4*i**3 + 1/2*i**2 + 1/4*i - 1/2 = 0. What is i?
-1, 1, 2
Let v(f) = f**4 + f**3 - 4*f**2 - f + 3. Let j(c) = -c**4 - c**3 + 3*c**2 + c - 2. Let s(d) = 3*j(d) + 2*v(d). Factor s(b).
-b*(b - 1)*(b + 1)**2
Let j be 2/(16/14) + (-15 - -14). Factor 3/4*l + j*l**4 - 3/4*l**3 - 3/4*l**2 + 0.
3*l*(l - 1)**2*(l + 1)/4
Let d(o) be the second derivative of o**6/120 + 3*o**5/80 - 4*o. Suppose d(a) = 0. What is a?
-3, 0
Let w(r) be the first derivative of r**7/2100 + r**6/900 - r**5/300 - r**4/60 - r**3/3 - 3. Let j(t) be the third derivative of w(t). Factor j(x).
2*(x - 1)*(x + 1)**2/5
Let l be 4*(3 + (-4 - -2)). Suppose -16*n - 88*n**2 - 56*n**4 - 34*n**l - 9*n**3 - 147*n**3 = 0. What is n?
-2/3, -2/5, 0
Factor -9*j**5 + 3*j**3 - j - 3*j**3 + 2*j**2 - 2*j**4 + 10*j**5.
j*(j - 1)**3*(j + 1)
Suppose 14 = -2*d + 6*g - 2*g, 5*d + 17 = 4*g. Let p be d/(-5)*(15 - 14). Find f, given that -1/5*f**4 + 0 - p*f**2 + 2/5*f**3 + 0*f = 0.
0, 1
Let a(g) be the second derivative of -1/6*g**3 + 0*g**2 + 1/12*g**4 - 3*g + 0. Factor a(y).
y*(y - 1)
Let v(x) be the first derivative of x**5/10 + x**4/3 + x**3/3 - x - 2. Let d(s) be the first derivative of v(s). Determine j so that d(j) = 0.
-1, 0
Let i(j) be the second derivative of -j**7/126 + j**5/60 + 8*j. Factor i(d).
-d**3*(d - 1)*(d + 1)/3
Let n = 134 + -130. Factor 0*k + 16/7*k**3 - 2/7 + 6/7*k**n + 12/7*k**2.
2*(k + 1)**3*(3*k - 1)/7
Let f(q) be the third derivative of q**7/3780 - q**6/810 + q**5/540 - q**3/3 - q**2. Let a(i) be the first derivative of f(i). Let a(r) = 0. What is r?
0, 1
Let i(q) be the third derivative of 13/15*q**5 - 7/60*q**6 - 8/3*q**3 - 5/3*q**4 + 0*q - q**2 + 0. Factor i(v).
-2*(v - 2)**2*(7*v + 2)
Suppose 2*u - 3 + 1 = 0. Let n(i) = 4*i**3 + 5*i**2 + 2*i + 3. Let b(v) = -v**3 + v - 1. Let z(q) = u*n(q) + 2*b(q). What is c in z(c) = 0?
-1, -1/2
Let h be 1 - -1 - (-14)/(-8). Let v(b) be the first derivative of 0*b - h*b**4 - b**5 - b**2 + 5/3*b**3 + 1/2*b**6 + 1. Solve v(w) = 0.
-1, 0, 2/3, 1
Factor -1/5*x**2 + 12/5 + 4/5*x.
-(x - 6)*(x + 2)/5
Suppose 7*z - z = 0. Let o(d) be the second derivative of 1/36*d**4 + 2*d + 0*d**2 + z - 1/18*d**3. Factor o(h).
h*(h - 1)/3
Let o(b) be the first derivative of 2/21*b**3 + 1 + 0*b - 2/7*b**2. Solve o(f) = 0.
0, 2
Let n(l) = 2*l**2 - l - 2. Let u be n(2). Factor 46*w**2 - 4*w - 4 + u - 40*w**2.
2*w*(3*w - 2)
Let c(w) = -w - 2. Let j be c(5). Let u be ((-6)/(-18))/(j/(-12)). Factor 6/7*z**2 + 0 + 2/7*z**3 + u*z.
2*z*(z + 1)*(z + 2)/7
Let k = 1253/5 + -250. Let -6/5*w**2 - 12/5*w + 9/5*w**4 + 12/5*w**3 - k = 0. Calculate w.
-1, -1/3, 1
Solve -8/7*j**2 - 4/7*j + 0 - 5/7*j**3 - 1/7*j**4 = 0.
-2, -1, 0
Suppose -x - 1 = -3. Suppose -x*w + 2 = -w. Factor 2 + 2*p**3 - 4*p**2 + 3*p**2 - p**2 - 4*p**3 + w*p.
-2*(p - 1)*(p + 1)**2
Let v(d) = -d**3 + 2*d**2 + 5*d - 6. Let o = 30 + -27. Let f be v(o). Factor 2/7*p**3 + 0*p**2 - 2/7*p + f.
2*p*(p - 1)*(p + 1)/7
Let o(w) = w**2 - 9*w - 8. Let j = -17 + 27. Let q be o(j). Factor 18/7*m + q*m**2 + 4/7.
2*(m + 1)*(7*m + 2)/7
Suppose 2*s = 7*s - 5. Let a be (0 - s)/((-39)/26). Factor 2/3*k**2 + 0*k + 0 + a*k**3.
2*k**2*(k + 1)/3
Let q(a) be the first derivative of 2*a**5/55 + 2*a**4/11 + 10*a**3/33 + 2*a**2/11 - 2. Determine z so that q(z) = 0.
-2, -1, 0
Solve 4*a**2 + 0 - 8*a + 1 - 4 + 7 = 0.
1
Let l(m) = 4*m**2 + 6*m - 42. Let f(s) = -8*s**2 - 13*s + 85. Let d(t) = 6*f(t) + 13*l(t). Solve d(o) = 0.
-3, 3
Suppose 3 = 2*n + 1. Let r be (0/((-1)/(-1)))/n. Let -2/7*y**4 - 2/7*y**3 + r + 2/7*y**2 + 0*y + 2/7*y**5 = 0. What is y?
-1, 0, 1
Let x(u) = -u**2 - 2*u - 6. Let v(c) = 5*c**2 + 9*c + 31. Let d(q) = 2*v(q) + 11*x(q). Suppose d(o) = 0. Calculate o.
-2
Let j(h) be the third derivative of h**7/147 + h**6/35 + 2*h**5/105 + 5*h**2. Factor j(v).
2*v**2*(v + 2)*(5*v + 2)/7
Factor 2*p**2 + 6*p**5 - 5*p**3 - 4*p**5 - 2*p**4 + 3*p**3.
2*p**2*(p - 1)**2*(p + 1)
Let b(y) = 14*y**4 - 14*y**3 - 6*y**2 - 2*y + 8. Let p(h) = -5*h**4 + 5*h**3 + 2*h**2 + h - 3. Let f(d) = -3*b(d) - 8*p(d). Let f(j) = 0. What is j?
-1, 0, 1
Let m(o) be the second derivative of 0*o**5 + 0*o**2 + 1/3*o**3 + o + 1/1260*o**6 - 1/84*o**4 + 0. Let v(u) be the second derivative of m(u). Factor v(j).
2*(j - 1)*(j + 1)/7
Let c(g) = g**2 + 24*g + 23. Let f be c(-23). Let s(u) be the first derivative of 0*u + f*u**2 + 1/12*u**3 - 2. Factor s(r).
r**2/4
Let m be ((-9)/(-3) - 1) + 2. Suppose -2*t = -5*r + m*r - 5, -5*r = 3*t - 40. Solve 0*u**3 + 1/4*u - 1/2*u**4 - 1/4*u**r + 0 + 1/2*u**2 = 0 for u.
-1, 0, 1
Let n(g) = -4*g**3 - 16*g**2 + 8*g + 6. Let z(a) = -3*a**3 - 15*a**2 + 8*a + 5. Let d(h) = 5*n(h) - 6*z(h). Solve d(c) = 0 for c.
0, 1, 4
Let i be 14/(-42) + 31/3. Find p such that 10*p**3 - i*p + 4*p**2 - 4*p**4 - 2*p**3 + 2*p = 0.
-1, 0, 1, 2
Let c(b) be the second derivative of b**4/48 + b**3/24 - b**2/4 + 13*b. Solve c(y) = 0 for y.
-2, 1
Factor -3*a - 3/2 - 9/8*a**2 + 3/8*a**4 + 3/4*a**3.
3*(a - 2)*(a + 1)**2*(a + 2)/8
Let o be 780/90 + (-14)/((-6)/(-3)). Fa