r = 55, -2*r - 8 = -3*f. Suppose 2*h + f = 4*h. Find o, given that 2*o**3 - 6*o**2 - 2 - 2*o**h + 2*o**3 + 6*o = 0.
1
Let d = 12 + -10. Let m(l) be the second derivative of -1/30*l**6 + 0*l**5 + 1/12*l**4 + 0 + 0*l**d + 0*l**3 + l. What is k in m(k) = 0?
-1, 0, 1
Let -2/19*c**5 + 0*c**2 + 0 + 0*c + 0*c**4 + 0*c**3 = 0. What is c?
0
Let 8/7*q**2 - 10/7*q + 2/7 = 0. Calculate q.
1/4, 1
Let m(a) = -4*a**3 + 12*a**2 - a - 7. Let x = 8 - 15. Let p(f) = -2*f**3 + 6*f**2 - f - 3. Let t(j) = x*p(j) + 3*m(j). Let t(k) = 0. Calculate k.
0, 1, 2
Factor 10/13*f**2 + 0 + 8/13*f**3 + 0*f - 2/13*f**4.
-2*f**2*(f - 5)*(f + 1)/13
Let s(o) be the second derivative of -o**7/84 - o**6/15 - 3*o**5/20 - o**4/6 - o**3/12 + 3*o. Find d such that s(d) = 0.
-1, 0
Let j(s) = -14*s**3 - 18*s**2 + 6*s. Let z be 166/(-6) - 4/12. Let l(t) = -t**2 - t. Let u(d) = z*l(d) - 2*j(d). Determine n so that u(n) = 0.
-2, -2/7, 0
Let d(m) = m + 1. Let t be d(4). Solve -x**2 - 2*x - 1 - 3 + x + t*x = 0 for x.
2
Let d(n) be the third derivative of -n**6/24 - n**5/12 - 15*n**2. Suppose d(y) = 0. Calculate y.
-1, 0
Let c(p) be the third derivative of -2*p**7/105 + p**5/15 - 5*p**2. Factor c(o).
-4*o**2*(o - 1)*(o + 1)
Let l(w) be the second derivative of -3*w**5/5 + w**4/4 + 2*w**3 - 3*w**2/2 - 11*w. Factor l(o).
-3*(o - 1)*(o + 1)*(4*o - 1)
Let f(p) = 103*p + 314. Let q be f(-3). What is r in 0 + 2/5*r**q + 6/5*r**4 + 0*r + 2/5*r**2 + 6/5*r**3 = 0?
-1, 0
Let m(l) be the first derivative of 0*l + 2/13*l**2 + 10/39*l**3 - 1. Suppose m(b) = 0. Calculate b.
-2/5, 0
Factor 5/2*f**2 + 40 + 20*f.
5*(f + 4)**2/2
Factor -4/3*f**2 + 0 + 0*f + 2/3*f**4 + 2/3*f**3.
2*f**2*(f - 1)*(f + 2)/3
Let m(i) = i**3 + 4*i**2. Let u be m(-4). Let o(s) be the first derivative of -1/20*s**5 + 1/8*s**2 + u*s - 1 + 1/12*s**3 - 1/16*s**4. Factor o(d).
-d*(d - 1)*(d + 1)**2/4
Let p(g) = 6*g**2 + g + 2. Let y be p(-1). What is h in -4*h**4 + y*h**3 + 3*h**3 - 8*h + 3*h**3 - 5*h**3 + 4 = 0?
-1, 1
Suppose 0 = -5*j + 36 - 11. Suppose 5*l + 2*k - 8 = j, -3*k = -5*l + 18. Determine p so that l*p**2 + 2*p**5 - p**4 + 3*p**3 + 0*p**4 - 2*p**4 - 5*p**5 = 0.
-1, 0, 1
Let y = 5 + -12. Let c(h) = 4*h**2 - 9*h - 7. Let m(b) = -b**2 + 3*b + 2. Let q(w) = y*m(w) - 2*c(w). Factor q(k).
-k*(k + 3)
What is m in -35*m - m**5 + m**3 + 3*m**2 + 35*m - 3*m**4 = 0?
-3, -1, 0, 1
Let q(y) = -5*y**2 - 3*y + 3. Let t(j) = -9*j**2 - 5*j + 5. Let h(n) = 5*q(n) - 3*t(n). Determine a, given that h(a) = 0.
0
Let z(p) be the first derivative of p**8/1512 + 2*p**7/945 - p**2/2 - 1. Let s(o) be the second derivative of z(o). Factor s(h).
2*h**4*(h + 2)/9
Suppose 0 = -2*f - 5 + 25. Let y(m) = m**3 - m**2 - m + 3. Let t be y(0). Factor 15*o**3 + 13*o**t - 9*o**2 + 8*o - f*o**3 - 15*o**2.
2*o*(3*o - 2)**2
Let g(o) be the second derivative of 25*o**7/28 - 11*o**6/12 + 13*o**5/40 - o**4/24 + 17*o. Let g(n) = 0. What is n?
0, 1/5, 1/3
Suppose 1/3*t - 1/3*t**2 + 2/3 = 0. Calculate t.
-1, 2
Let a(r) be the second derivative of -r**6/165 + r**5/55 + r**4/22 - 4*r**3/33 - 4*r**2/11 - 3*r. Factor a(o).
-2*(o - 2)**2*(o + 1)**2/11
Factor 5*b**2 + b**2 - 4*b**2 - 4*b.
2*b*(b - 2)
Let p be -11*-5*20/275. Factor -2/5*l**p + 2/5 + 0*l**2 + 4/5*l**3 - 4/5*l.
-2*(l - 1)**3*(l + 1)/5
Let q(v) be the second derivative of -v**5/270 - v**4/54 + v**2 + v. Let m(b) be the first derivative of q(b). Factor m(c).
-2*c*(c + 2)/9
Let o(s) = -3*s**3 + 5*s**2 - 16*s + 10. Let k(b) = 4*b**3 - 4*b**2 + 16*b - 9. Let z(r) = -4*k(r) - 6*o(r). Suppose z(h) = 0. Calculate h.
2, 3
Let b(v) be the first derivative of 14/3*v**3 + 3 - 4*v + 5*v**2. Factor b(h).
2*(h + 1)*(7*h - 2)
Solve -18*v + 5*v**3 + 10 + 6*v**3 - 6*v**3 + 3*v = 0.
-2, 1
Suppose 4 = 2*y - 0. What is g in -y*g + 1 - 2*g**2 + g**2 - 1 - 1 = 0?
-1
Let k(b) be the third derivative of -2*b**6/15 - 3*b**5/5 - b**4/3 + 3*b**2. Solve k(l) = 0.
-2, -1/4, 0
Let x(l) be the second derivative of l**4/12 - l**3/2 + l**2 - 9*l. Solve x(t) = 0.
1, 2
Let w(a) be the first derivative of -2*a**5/45 + 16*a**3/27 - 32*a/9 - 35. Let w(o) = 0. What is o?
-2, 2
Let c(g) be the second derivative of 1/30*g**3 + 0*g**2 + 0 + 2/75*g**6 + 3*g + 0*g**5 - 1/20*g**4. Factor c(k).
k*(k + 1)*(2*k - 1)**2/5
Let g(f) be the third derivative of f**6/225 + 7*f**5/300 - f**4/30 + 7*f**3/6 + 4*f**2. Let n(b) be the first derivative of g(b). Factor n(r).
2*(r + 2)*(4*r - 1)/5
Suppose -4*c + 1 + 15 = 0. Let d(r) be the third derivative of -2*r**2 + 0*r**3 + 0 + 1/300*r**5 + 0*r - 1/600*r**6 + 0*r**c. Factor d(n).
-n**2*(n - 1)/5
Suppose 2*m - 8 = -0. Find x, given that 2*x + 2*x**4 - 2*x**3 - x**3 - 2 + 4*x**2 - 4*x**m + 2*x**5 - x**3 = 0.
-1, 1
Let o(g) = -g**3 - 6*g**2 - 5*g + 2. Let h be o(-5). Factor 7*b - 3*b**h - 27 - 14*b - 11*b.
-3*(b + 3)**2
Let j(t) be the first derivative of -t**4/18 - 2*t**3/27 + 4*t**2/9 + 8*t/9 - 15. Find c such that j(c) = 0.
-2, -1, 2
Let q(h) = h**4 - 8*h**3 - h**2 + 4*h - 4. Let b(a) = 3*a**4 - 23*a**3 - 2*a**2 + 11*a - 11. Let y(i) = -4*b(i) + 11*q(i). Factor y(w).
-w**2*(w - 3)*(w - 1)
Let y be 2/(-2) - (-9 + -2). Suppose y*i - 288 = 7*i. Find v such that -1 + 112*v**4 - 38*v - 30*v**3 + i*v**5 - 108*v**2 - 3 - 28*v**3 = 0.
-1, -2/3, -1/4, 1
Let j be ((-12)/(-2))/2 - 15. Let a be (-5)/j + (-3)/(-12). Find o, given that 0 + 2/3*o**4 - a*o + 2/3*o**3 - 2/3*o**2 = 0.
-1, 0, 1
Factor 3*z**2 + 90 + 3*z**3 - 3*z**5 - 3*z**4 - 90.
-3*z**2*(z - 1)*(z + 1)**2
Let r = -2/49 + 55/147. Let m = 2 + 1. Let r*v**m + 0 + 1/3*v - 2/3*v**2 = 0. Calculate v.
0, 1
Factor 0*g - 81*g**3 + 3*g + 13*g**2 + 23*g**2 + 0*g - 2.
-(3*g - 1)**2*(9*g + 2)
Factor -2*o + 32*o**3 - 33*o**3 + 3*o**2 - 6*o**2.
-o*(o + 1)*(o + 2)
Let z(k) be the third derivative of -k**9/3024 + k**7/420 - k**5/120 + 7*k**3/6 + 6*k**2. Let l(r) be the first derivative of z(r). Factor l(i).
-i*(i - 1)**2*(i + 1)**2
Let v(i) = 2*i**2 - 4*i - 4. Suppose 3*y + 77 = 2. Let t be y/(-15) - 4/6. Let z(u) = -u**2 + u + 1. Let r(w) = t*v(w) + 4*z(w). Factor r(g).
-2*g**2
Factor 42*h - 48*h + 3*h**2 - 2*h**2 - 3*h**2 - 4.
-2*(h + 1)*(h + 2)
Let y = 12 - 10. Suppose 4*n = y*n. Factor 0*q**3 + 3/5*q**5 + 0*q**2 + 0 + n*q - 3/5*q**4.
3*q**4*(q - 1)/5
Let q = -9 + 12. Determine w so that 0*w**3 + 10*w**4 - 11*w**4 + 0*w**q - w**5 = 0.
-1, 0
Let m be ((-3)/(-4) - 1)/(5/(-10)). Let j(l) be the second derivative of 1/6*l**3 - 1/40*l**5 + m*l**2 - 1/16*l**4 - 2*l + 0 + 1/120*l**6. Factor j(q).
(q - 2)**2*(q + 1)**2/4
Find o such that o**2 + 2*o**3 - 2*o - 3/2 + 1/2*o**4 = 0.
-3, -1, 1
Let t = -67/297 - -13/54. Let k = 47/198 - t. Factor 160/9*j + 80/9*j**3 - 20/9*j**4 + k*j**5 - 160/9*j**2 - 64/9.
2*(j - 2)**5/9
Let y(g) be the third derivative of -1/120*g**6 + 0*g + 0*g**4 - 3*g**2 + 0 + 0*g**3 + 1/336*g**8 + 0*g**7 + 0*g**5. Suppose y(z) = 0. Calculate z.
-1, 0, 1
Suppose -2*m - m = -0*m. Let q(y) be the third derivative of -1/120*y**5 - y**2 + 0*y**4 + 0 + m*y**3 + 0*y. Factor q(v).
-v**2/2
Let b(o) be the first derivative of 8*o + 8*o**2 - 10/3*o**3 + 10. Factor b(x).
-2*(x - 2)*(5*x + 2)
Let w be 1/((-2 + 5)/(-9)). Let n be (-2)/(-3*(-4)/w). Factor -n*c**2 - c - 1/2.
-(c + 1)**2/2
Let m(t) be the second derivative of 0 - 1/42*t**7 - 1/6*t**3 - 1/2*t**2 + 1/6*t**4 - 1/30*t**6 + 1/10*t**5 - 4*t. Solve m(l) = 0 for l.
-1, 1
Factor 0*w**3 + 0*w + 1/9*w**4 - 2/9*w**2 + 1/9.
(w - 1)**2*(w + 1)**2/9
Let p(u) be the second derivative of 0 + 1/50*u**5 - 1/15*u**4 + 0*u**2 - 2*u + 0*u**3. Suppose p(g) = 0. What is g?
0, 2
Let k(y) be the third derivative of y**7/231 - 7*y**6/330 + 2*y**5/55 - y**4/66 - y**3/33 + 22*y**2. What is a in k(a) = 0?
-1/5, 1
Let v(b) be the first derivative of -2*b**5/5 + b**4 - 2*b**2 + 2*b - 20. Factor v(g).
-2*(g - 1)**3*(g + 1)
Let f be 0 + -85*(0 + -1). Solve -3750*c**5 - 113 + f*c**2 - 4500*c**3 - 31 - 565*c**2 + 816*c + 8625*c**4 = 0 for c.
-2/5, 2/5, 3/2
Let d(c) be the second derivative of -5*c**5/14 - 10*c**4/21 + 17*c**3/7 - 18*c**2/7 - 13*c. Factor d(x).
-2*(x + 2)*(5*x - 3)**2/7
Let f be (-3)/(-2*3/24). Let t be 27/f + (-2)/8. Factor 0*i**2 + 3*i - i**2 - t*i.
-i*(i - 1)
Let w(f) be the third derivative of 0*f + 0*f**5 + 0*f**4 - 3*f**2 - 1/60*f**6 + 1/168*f**8 + 0*f**3 + 0 + 0*f**7. Factor w(b).
2*b**3*(b - 1)*(b + 1)
Let v(n) = 3*n**3 - 4*n + 4. Let y be v