 2*h**t + 4*h**2 = 0 for h.
-1, 0, 1
Let r = 287 - 573/2. Determine n so that -1/4*n**4 + 1/4 + 0*n**2 + 1/2*n**3 - r*n = 0.
-1, 1
Let y(m) = -3*m**3 - 13*m**2 + 31*m + 7. Let f(v) = -2*v**3 - 9*v**2 + 21*v + 5. Let p(r) = 7*f(r) - 5*y(r). Let p(o) = 0. What is o?
-4, 0, 2
Factor -2/23*s**2 + 0 + 0*s + 2/23*s**3.
2*s**2*(s - 1)/23
Suppose 0*x = -2*x + 20. Suppose -4*f = f - x. Factor 2/7 + 0*c - 2/7*c**f.
-2*(c - 1)*(c + 1)/7
Let a(t) = -7*t**5 + 3*t**4 - t**3 - 3*t**2 + 2*t. Let p(h) = -20*h**5 + 9*h**4 - 3*h**3 - 9*h**2 + 6*h. Let d(w) = -17*a(w) + 6*p(w). Factor d(j).
-j*(j - 2)*(j - 1)**2*(j + 1)
Suppose -4*p + y - 13 = -4*y, -5*p = -4*y + 5. Let s(c) be the first derivative of -1 + 0*c - c**2 - 2/3*c**p. Factor s(h).
-2*h*(h + 1)
Let m(w) = -3*w - 12. Let d be m(-5). Let i**4 + 2*i**d - 3*i**3 + 0*i**3 = 0. Calculate i.
0, 1
Let m(i) be the first derivative of -3/20*i**5 + 1 + 0*i - 1/16*i**4 + 2/3*i**3 - 1/2*i**2. Factor m(b).
-b*(b - 1)*(b + 2)*(3*b - 2)/4
What is p in -4 + 0*p**3 - 42*p**2 - 4*p**3 + 4*p + 54*p**2 - 8*p**4 + 0*p**3 = 0?
-1, 1/2, 1
Let s(q) be the third derivative of -q**6/240 - 7*q**5/120 - 11*q**4/48 - 5*q**3/12 - 13*q**2 + 2*q. Suppose s(w) = 0. What is w?
-5, -1
Let t(j) be the second derivative of -1/120*j**4 - 1/300*j**5 - 2*j**2 + 0*j**3 - 3*j + 0. Let n(o) be the first derivative of t(o). Factor n(y).
-y*(y + 1)/5
Let p(h) = -h**3 - 5*h**2 - 2*h - 6. Let n be p(-5). Factor -j**2 + 4*j**5 - 3*j**5 - 6*j**3 + j**n + 5*j**3.
j**2*(j - 1)*(j + 1)**2
Let a(t) = 3*t**3 - 1. Let w be a(1). Factor 2*m**3 - 2*m**5 - 5*m - w*m**4 + 0*m**5 + 2*m**2 + 5*m.
-2*m**2*(m - 1)*(m + 1)**2
Suppose 18 = -r + 20. Let p(t) be the first derivative of -12*t**3 + 21*t**4 + 2*t**2 - 343/8*t**6 + 49/5*t**5 + r + 0*t. Factor p(h).
-h*(3*h + 2)*(7*h - 2)**3/4
Suppose 0 = -85*s + 91*s. Factor 0 + 1/2*a**5 + 1/2*a**4 - 1/2*a**2 + s*a - 1/2*a**3.
a**2*(a - 1)*(a + 1)**2/2
Determine t so that -12*t + 2*t - 12*t**2 - 6*t - 11*t = 0.
-9/4, 0
Factor 0 + 4/5*a - 4/5*a**2.
-4*a*(a - 1)/5
Let k(v) be the first derivative of -v**4/24 + v**3/12 + v**2/2 - v + 3. Let f(g) be the first derivative of k(g). What is p in f(p) = 0?
-1, 2
Let l(g) be the first derivative of 2/5*g + 0*g**2 - 2/15*g**3 + 9. Factor l(p).
-2*(p - 1)*(p + 1)/5
Let x be (1/4)/((-40)/(-96)). Let 0*s + 0 + x*s**2 - 3/5*s**3 = 0. Calculate s.
0, 1
Factor 2 - 4 - 4*s**2 + 6*s - 5*s + 5*s.
-2*(s - 1)*(2*s - 1)
Let l(a) = 12*a**3 - 4*a**2 - 48*a. Let y(b) = b**3 + b**2 - b + 1. Let z(t) = -l(t) + 16*y(t). Factor z(o).
4*(o + 1)*(o + 2)**2
Let o be 1 + (11/4 - 1). Factor 0 - 17/4*x**4 - 21/4*x**3 - 1/2*x - 5/4*x**5 - o*x**2.
-x*(x + 1)**3*(5*x + 2)/4
Let h(t) = 6*t**3 - 30*t**2 + 31*t - 29. Let g(m) = -2*m**3 + 10*m**2 - 10*m + 10. Let b(n) = -11*g(n) - 4*h(n). Let b(s) = 0. Calculate s.
1, 3
Let l(y) be the first derivative of 5/3*y**3 + 0*y - 1/2*y**2 + 7 - 7/4*y**4 + 3/5*y**5. Determine b so that l(b) = 0.
0, 1/3, 1
Let m(d) = d**2 - 9*d + 18. Let q be m(7). Let s(i) be the first derivative of 1/2*i**q + 4/3*i**3 - 4 + i**2 + 0*i. Determine f so that s(f) = 0.
-1, 0
Let v be ((0/(-1))/3)/1. Suppose v*y + y = 2. Solve 2*d**3 + 0*d**4 + 0*d - 4/3*d**y - 2/3*d**5 + 0 = 0.
-2, 0, 1
Factor 3*f + 2*f + 645 - 5*f**3 - 630 - 15*f**2.
-5*(f - 1)*(f + 1)*(f + 3)
Suppose -34*g = -8*g. Factor -2/15*h**2 + g - 2/15*h.
-2*h*(h + 1)/15
Let m = -9 - -12. Factor -j - 2*j**2 + j**3 + 4*j**3 - 3*j - m*j**3.
2*j*(j - 2)*(j + 1)
Let g = -1/55 + 117/385. Factor g*a**2 - 2/7*a - 4/7.
2*(a - 2)*(a + 1)/7
Let j(u) be the second derivative of -5*u**4/12 + 5*u**2/2 - 3*u. Suppose j(z) = 0. What is z?
-1, 1
Let 5/4*v**3 + 0*v + 7/4*v**4 + 0 - 1/2*v**2 = 0. Calculate v.
-1, 0, 2/7
Suppose -3*z + 12 = 3*i, 0*i + 2*i = -4*z + 18. Suppose 20 = z*d - d. What is g in g**d - 2*g**5 - 5*g + 2 - 1 - 10*g**3 + 5*g**4 + 10*g**2 = 0?
1
Determine y so that -8/5 - 18/5*y**3 - 14/5*y**2 + 8*y = 0.
-2, 2/9, 1
Let s(r) be the second derivative of -r**7/14 + 3*r**5/10 - r**3/2 + 21*r. Solve s(v) = 0.
-1, 0, 1
Let q(m) be the third derivative of 0*m**5 + 1/6*m**3 + 0*m**4 - 3*m**2 + 0 + 0*m + 1/180*m**6. Let x(w) be the first derivative of q(w). Solve x(z) = 0.
0
Let a = -21 + 14. Let o(x) = 39*x**3 - 32*x**2 - 2*x + 9. Let u(b) = -38*b**3 + 32*b**2 + 2*b - 8. Let l(r) = a*u(r) - 6*o(r). Factor l(y).
2*(y - 1)*(4*y - 1)*(4*y + 1)
Let a(v) = -4*v**3 + 60*v**2 - 104*v + 56. Let g(r) = -r**3 + 20*r**2 - 35*r + 19. Let i(s) = 3*a(s) - 8*g(s). Factor i(p).
-4*(p - 2)**2*(p - 1)
Let h(m) be the second derivative of -m**6/10 - 11*m**5/20 - 5*m**4/4 - 3*m**3/2 - m**2 - 5*m. Determine c so that h(c) = 0.
-1, -2/3
Suppose 1/6*h**5 + 1/2*h**2 + 1/6*h**3 - 1/2*h**4 + 0 - 1/3*h = 0. What is h?
-1, 0, 1, 2
Suppose 0*m + 4*m = -4. Let x = 1 - m. Factor 6/7*h**x + 8/7*h + 2/7.
2*(h + 1)*(3*h + 1)/7
Let c be -2 - -1*(-2 - -7). Factor -3*q + q**3 - c*q**2 + 9 + 3*q**3 - q**3 - 6.
3*(q - 1)**2*(q + 1)
Let w = -4 + 7. Determine k so that -2*k**5 - 3*k + 3*k + 2*k**w + 0*k**5 = 0.
-1, 0, 1
Let y be 4/15*6/(-34). Let k = 38/85 + y. What is t in -t**2 - 7/5*t - k = 0?
-1, -2/5
Suppose 3*v - 8 = 4. Factor 10*x - 4*x**4 + 8*x**4 - 3*x**2 - v*x - 6*x**3 - x**4.
3*x*(x - 2)*(x - 1)*(x + 1)
Let d(c) be the second derivative of c**10/15120 - c**8/3360 - c**4/12 + c. Let j(l) be the third derivative of d(l). Suppose j(f) = 0. Calculate f.
-1, 0, 1
Suppose 9 = c - 10. Suppose -4 = 5*u - c. Factor 0*f - 2*f**u - 4/7*f**2 - 10/7*f**4 + 0.
-2*f**2*(f + 1)*(5*f + 2)/7
Let s = 43 - 43. Let x(i) be the second derivative of -1/15*i**3 + 0*i**2 + 1/35*i**7 - 2*i + 3/25*i**5 + 0*i**4 - 8/75*i**6 + s. Factor x(k).
2*k*(k - 1)**3*(3*k + 1)/5
Let j(v) be the third derivative of v**7/3780 + v**6/405 + v**5/135 + v**3/6 - 2*v**2. Let i(r) be the first derivative of j(r). Determine w so that i(w) = 0.
-2, 0
Let q be ((-2)/18)/((-34)/153)*8. Solve -8/7*d + 0 - 10/7*d**3 - 16/7*d**2 - 2/7*d**q = 0.
-2, -1, 0
Let z be (-1)/4 - 70/8. Let a be 24/z*15/(-50). Let -2*f + 2*f**3 + 4/5 - a*f**2 = 0. What is f?
-1, 2/5, 1
Suppose 53*w - 60*w + 21 = 0. Factor 4/3 + 1/3*s**w - s**2 + 0*s.
(s - 2)**2*(s + 1)/3
Let v(n) be the second derivative of 3/4*n**2 + 0 - 1/4*n**4 + 7/8*n**3 + n. Solve v(j) = 0 for j.
-1/4, 2
Factor -40*s**2 - 24*s**2 + 8*s + 76*s**2.
4*s*(3*s + 2)
Suppose -5*g + 47 = -3*a, g - 3*g - 5*a + 25 = 0. Factor -3*w**2 + g*w - 28*w - 14 - 13.
-3*(w + 3)**2
Let o be (6/(-10))/((-1)/5). Determine w, given that -10*w**3 + 22*w**o - 2*w**4 - w**5 - 13*w**3 = 0.
-1, 0
Let j = -3 - -5. Let x(v) be the first derivative of 0*v + 0*v**j + 1/10*v**4 + 1 + 0*v**3 - 2/25*v**5. Suppose x(p) = 0. Calculate p.
0, 1
Solve 102*q**5 - 552*q**2 - 13*q**5 - 48 - 240*q**3 + 336*q + 58*q**5 + 357*q**4 = 0 for q.
-2, 2/7, 1
Let l(k) be the third derivative of -1/20*k**5 + 0 + 0*k**3 - 3*k**2 - 1/4*k**4 + 0*k. Factor l(c).
-3*c*(c + 2)
Let t(y) be the first derivative of y**2 - 4 + 2/3*y**3 + 0*y. Factor t(n).
2*n*(n + 1)
Let b(k) = -2*k**2 - 10*k - 6. Let q be b(-4). Factor 1/6*t + 1/3 - 1/6*t**q.
-(t - 2)*(t + 1)/6
Let j be 7/21 + 28/90. Let z = 1/45 + j. Find k, given that 0*k + 2/3 - z*k**2 = 0.
-1, 1
Solve -15*n**4 + 5*n + 16*n**3 + 2*n**3 + 15*n**2 - 18*n**5 - 2*n - 3*n**3 = 0.
-1, -1/2, -1/3, 0, 1
Let f = 180 - 180. Let -1/5 + f*w + 1/5*w**2 = 0. Calculate w.
-1, 1
Let i(o) be the third derivative of o**8/1344 - o**7/280 + o**6/160 - o**5/240 - 12*o**2. Suppose i(z) = 0. What is z?
0, 1
Let d(l) be the third derivative of l**10/10080 - l**9/2520 + l**8/2240 + l**4/8 - 7*l**2. Let g(a) be the second derivative of d(a). Factor g(f).
3*f**3*(f - 1)**2
Let c(t) = -t**2 + 4*t - 11. Let f(x) = 5*x**2 - 19*x + 56. Suppose s = -6*y + 3*y - 5, 20 = 2*s - 4*y. Let a(k) = s*f(k) + 22*c(k). Factor a(h).
-2*(h - 3)**2
Let n(g) be the third derivative of -g**8/10080 - g**7/1260 - g**6/360 + g**5/60 - 4*g**2. Let w(z) be the third derivative of n(z). Factor w(u).
-2*(u + 1)**2
Let k = 52 + -34. Let l = k + -35/2. Factor -3/4*d**3 - 1/4*d**2 + l*d + 0.
-d*(d + 1)*(3*d - 2)/4
Let y(z) be the first derivative of z**6/6 - z**4/2 + z**2/2 + 3. Factor y(b).
b*(b - 1)**2*(b + 1)**2
Suppose a + 3*o = -3, 4*a + 2 = -4*o + 2*o. Let 2*p - 4/3 - 2/3*p**3 + a*p**2 = 0. What is p?
-2, 1
Factor -3/5*b**2 - 18/5 + 2