(h) = 10*h**2 - 8*h + 7. Let x = 29 + -31. Let w(a) = x*k(a) - 18*n(a). Let w(g) = 0. What is g?
-2, 1
Let u = -2/391 + 397/1173. Factor 0 - 2/3*z**2 - z**3 - u*z**4 + 0*z.
-z**2*(z + 1)*(z + 2)/3
Let t be 1/(-3 + 30/9). Factor -3*d**3 - d**4 + 2*d**5 + 0*d**5 - 2*d - t*d**3 + 5*d**2 + 2*d**2.
d*(d - 1)**2*(d + 2)*(2*d - 1)
Let i(b) = b**2 + 6*b + 10. Let h be i(-5). Suppose 2*s + s - 3 = -4*f, -5*s + 5 = h*f. Solve f - 6*o**2 + 4*o**2 + 1 - 3*o**2 - 4*o = 0 for o.
-1, 1/5
Let v be (-880)/(-280) - 2/14. Let q(b) be the first derivative of -3 + b**2 - 4/3*b - 2/9*b**v. Solve q(d) = 0.
1, 2
Let j be 1 - 4/10*(-49 - -44). Factor 2/13 + 2/13*u**5 - 6/13*u + 4/13*u**j - 6/13*u**4 + 4/13*u**2.
2*(u - 1)**4*(u + 1)/13
Let y = 2531 + -2529. Factor 0 - 8/3*i - 4/3*i**3 - 4*i**y.
-4*i*(i + 1)*(i + 2)/3
Let t be 86/10 + 21/(-35). Let v be (2 + 3)*27/15. Factor -1 + v - t + z**3.
z**3
Let k be (-1*2/3)/(17/(-102)). Factor -34*s + 26*s - k*s**3 + 2*s**4 + 18*s**2 - 8*s**3.
2*s*(s - 4)*(s - 1)**2
Let v(r) be the second derivative of r**5/40 - 7*r**4/24 + 5*r**3/6 - 2*r - 7. Let v(t) = 0. Calculate t.
0, 2, 5
Let l(i) be the second derivative of -i**5/450 - i**4/180 + 2*i**3/15 + 11*i**2/2 + 11*i. Let s(o) be the first derivative of l(o). Factor s(q).
-2*(q - 2)*(q + 3)/15
Factor 1/4*s + 1/2*s**2 + 0 + 1/4*s**3.
s*(s + 1)**2/4
Let n(y) = y**2 + 5*y - 15. Let r be n(-7). Let l be (-868)/(-588) - r/(-7). Factor l*s**2 + 4/3*s + 0.
4*s*(s + 1)/3
Let r(w) = w - 11. Let x be r(10). Let m(n) = -n. Let s(z) = 4*z**4 + 12*z. Let u(l) = x*s(l) - 12*m(l). Let u(v) = 0. What is v?
0
Let p(w) be the first derivative of 0*w + 7 + w**5 + 0*w**2 + 5/12*w**6 + 5/8*w**4 + 0*w**3. Factor p(k).
5*k**3*(k + 1)**2/2
Solve -1/7*r**5 + 0 - 36/7*r**3 + 15/7*r**4 + 0*r**2 + 0*r = 0.
0, 3, 12
Let m(s) be the first derivative of 56/15*s**5 + 2744/9*s**3 + 18 + 0*s - 1/9*s**6 - 49*s**4 - 2401/3*s**2. Suppose m(w) = 0. Calculate w.
0, 7
Let f(l) be the third derivative of -l**5/90 + 13*l**4/36 - 4*l**3 + 13*l**2 - 8*l. Suppose f(d) = 0. Calculate d.
4, 9
Suppose -2401/3 + 833*k + 1/3*k**3 - 33*k**2 = 0. Calculate k.
1, 49
Suppose 0 = 3*t - 3*d + 2 + 7, 0 = t - 4*d + 12. Let -6*m**4 + 10*m**4 - 32*m**2 + t + 64 = 0. What is m?
-2, 2
Let b be (-3 - -4) + 6 + -7. Let m(q) be the second derivative of -q**4 + 4*q + 2*q**3 + b + 0*q**2 + 3/20*q**5. Suppose m(r) = 0. What is r?
0, 2
Let s(l) be the second derivative of 0*l**4 - 1/147*l**7 + 0 + 0*l**5 - 4*l + 2/105*l**6 + 0*l**2 + 0*l**3. Factor s(n).
-2*n**4*(n - 2)/7
Factor -1922 - 1/2*r**2 - 62*r.
-(r + 62)**2/2
Suppose 5*b - 5*h - 109 = -h, -5*h + 37 = 2*b. Determine f, given that -10 - 54*f**2 + 25*f**2 + 45*f - b*f**2 = 0.
2/5, 1/2
Solve -54/7*o**2 + 56 - 48*o - 2/7*o**3 = 0 for o.
-14, 1
Suppose 54/7*m**2 - 33/7*m**3 + 0 + 3/7*m**5 + 0*m**4 - 24/7*m = 0. What is m?
-4, 0, 1, 2
Let w be (301 + -1)/3 + (-1 - -5). Solve 16 - 63*i + 34*i + w*i**2 - 2*i**5 + 24*i**4 - 108*i**3 - 37*i + 32*i**3 = 0.
1, 8
Let i(r) = 4*r**2 + 4*r + 3. Let d be i(-2). Let o be 0 + ((-15)/(-10) - d/10). Factor 2/5*n**2 - o - 2/5*n**3 + 2/5*n.
-2*(n - 1)**2*(n + 1)/5
Let v(d) be the second derivative of d**6/225 + d**5/150 - d**4/5 - 16*d**3/45 + 32*d**2/15 + 3*d + 49. Let v(x) = 0. Calculate x.
-4, -2, 1, 4
Let z = -24 - -27. Let f(d) be the third derivative of 0 + 9*d**2 + 1/24*d**z + 0*d - 1/48*d**4 + 1/240*d**5. Solve f(p) = 0.
1
Suppose 2*a - 6*g - 32 = -8*g, -44 = -2*a - 5*g. Suppose -5*z = -10, -6*b + z = -11*b + a. Solve -3/5 + 3/5*f + 6/5*f**b = 0.
-1, 1/2
Let x(f) = f**3 - 2*f**2 + f + 1. Let k(p) = -5*p**4 + 32*p**3 - 34*p**2 + 7*p + 7. Let v(t) = k(t) - 7*x(t). Suppose v(r) = 0. Calculate r.
0, 1, 4
Let q(v) = v**2 - 3*v - 9. Let d be q(5). Let n be d*((-12)/4 + 6). Factor -167*g + 167*g - 3*g**n - 3*g**2.
-3*g**2*(g + 1)
Let u(r) be the third derivative of r**5/210 + r**4/42 - 2*r**2 - 24. Find h, given that u(h) = 0.
-2, 0
Let q(f) be the first derivative of -3*f**4/20 + 11*f**3/5 - 27*f**2/5 + 120. Find j, given that q(j) = 0.
0, 2, 9
Let x(y) = y**2 - 98*y + 89. Let f(m) = m**2 - 65*m + 59. Let c(o) = -8*f(o) + 5*x(o). Solve c(t) = 0 for t.
1, 9
Let h(f) be the third derivative of 7*f**6/80 - 89*f**5/30 + 27*f**4/4 - 16*f**3/3 - 68*f**2. Determine q so that h(q) = 0.
2/7, 2/3, 16
Let p be 1/(1/(-2)*(-4)/8). Let -52*g**3 + 38*g - 5*g + 19*g - 24 - 20*g**p + 44*g**2 = 0. Calculate g.
-3, -1, 2/5, 1
Suppose 0 - 27*s**3 + 186/7*s**2 + 0*s + 3/7*s**4 = 0. What is s?
0, 1, 62
Suppose 4*s - 3*r + 5 = -1, -3*r + 6 = -2*s. Suppose -15/4*a**3 + 33/4*a**2 - 3/2*a + s = 0. What is a?
0, 1/5, 2
Let y(f) be the second derivative of f**6/135 - 4*f**5/45 + 4*f**4/9 - 32*f**3/27 + 16*f**2/9 - 25*f - 3. Factor y(p).
2*(p - 2)**4/9
Let h be 0/(-3 + 2) - -2. Let i be (h/(-6))/((-3)/36). Factor 64 - 32*b**3 - 5*b**i - 13*b**4 + 96*b**2 + 22*b**4 - 128*b.
4*(b - 2)**4
Suppose 4 = -p - 3*f, 7*p = 5*p + 3*f + 19. Factor -4/3*h**3 + 2/9*h**2 + 0 + 8/3*h**4 - 16/9*h**p + 0*h.
-2*h**2*(2*h - 1)**3/9
Determine q so that 1/4*q**3 - 3/4*q**2 + 1/4*q**4 - 1/2 - 5/4*q = 0.
-1, 2
Factor 4/5*i**2 - 44/5*i + 112/5.
4*(i - 7)*(i - 4)/5
Let r(z) be the first derivative of -10/3*z**3 + 7 - 5/2*z**2 + 5/4*z**4 + 10*z. Suppose r(u) = 0. What is u?
-1, 1, 2
Let g(w) be the third derivative of -w**8/336 - w**7/70 + w**6/120 + w**5/20 - 10*w**2. Factor g(a).
-a**2*(a - 1)*(a + 1)*(a + 3)
Let i = 37 + 26. Factor -515*c**2 - i*c + 15*c**2 - 5 + 11*c - 48*c.
-5*(10*c + 1)**2
Let u(b) = 53*b + 2597. Let w be u(-49). Let n = -1 + 1. Solve w + 0*v**3 + 0*v**2 + 2/7*v**4 + n*v + 6/7*v**5 = 0 for v.
-1/3, 0
Let r(n) be the third derivative of -3*n**8/112 - 5*n**7/42 + n**6/20 - 8*n**2 + n. Suppose r(m) = 0. Calculate m.
-3, 0, 2/9
Factor 0 + 2*k + 1/2*k**2.
k*(k + 4)/2
Let v(h) be the second derivative of -h**7/42 - 2*h**6/15 + h**5/10 + h**4 - 3*h**3/2 + h + 9. Let v(r) = 0. What is r?
-3, 0, 1
Let k(c) = -4*c**3 - 103*c**2 - 572*c + 673. Let h(v) = 4*v**3 + 104*v**2 + 572*v - 672. Let f(q) = 3*h(q) + 4*k(q). Factor f(o).
-4*(o - 1)*(o + 13)**2
Let u(l) = 2*l**2 + 17*l - 5. Let i be ((-584)/36 - -7) + 2/9. Let p be u(i). Let 0*n + 0 - 14/9*n**5 - 22/9*n**3 + 32/9*n**p + 4/9*n**2 = 0. Calculate n.
0, 2/7, 1
Let j be (-132)/(-55) + 13/(-13). Find u, given that 1/5*u**3 - j*u + 2/5*u**2 + 4/5 = 0.
-4, 1
Let n(w) be the second derivative of w**8/840 - w**7/245 - w**6/315 - 16*w**3/3 - 13*w + 2. Let x(l) be the second derivative of n(l). Factor x(s).
2*s**2*(s - 2)*(7*s + 2)/7
Determine u so that 2*u**3 + 4*u**2 - u**3 - 2*u + u**3 - 2*u - 2*u = 0.
-3, 0, 1
Factor 2/3*v**4 + 0 - 8/3*v + 2*v**3 + 0*v**2.
2*v*(v - 1)*(v + 2)**2/3
Let o be (0/2 + -1)*-6. Let -6 - 4*w + o*w**2 + 2*w**2 - 10*w + 2 = 0. Calculate w.
-1/4, 2
Let 2/7*l**2 + 120/7*l + 118/7 = 0. Calculate l.
-59, -1
Let j be (1813/147 - (1 + 9)) + (-6)/(-1). Factor 10/3 - 5/3*g**3 - j*g + 20/3*g**2.
-5*(g - 2)*(g - 1)**2/3
Let s(a) be the third derivative of -a**9/45360 - a**8/5040 - a**7/1890 - 5*a**4/6 + a**2 + 12*a. Let d(z) be the second derivative of s(z). Factor d(p).
-p**2*(p + 2)**2/3
Suppose -72 - 128 = 5*v. Let i be (18/v)/((-3)/5). Suppose 3/2*s**2 + 3/4*s - 3/4*s**4 + 3/4*s**5 - i - 3/2*s**3 = 0. What is s?
-1, 1
Factor 1/6*z**4 - 2/3*z - 6*z**2 - 3/2*z**3 + 8.
(z - 12)*(z - 1)*(z + 2)**2/6
Factor 37*x**2 - 27*x**2 + 271*x + 203 + 111 + 654*x + 146.
5*(x + 92)*(2*x + 1)
Let o = -598 + 604. Let m(g) be the first derivative of 4/3*g**3 - 5*g**4 - 8 + o*g**6 + 0*g + 12/5*g**5 + 0*g**2. Factor m(n).
4*n**2*(n + 1)*(3*n - 1)**2
Let u(w) be the first derivative of w**4/66 + w**3/11 - 4*w**2/11 - 8*w - 1. Let q(y) be the first derivative of u(y). Factor q(n).
2*(n - 1)*(n + 4)/11
Let k(p) be the second derivative of -p**7/105 + 2*p**6/15 - 6*p**5/25 - 17*p**4/15 + 13*p**3/15 + 24*p**2/5 + 3*p - 42. Determine v, given that k(v) = 0.
-1, 1, 3, 8
Let m(p) be the second derivative of p**5/10 - 41*p**4/6 + 133*p**3 + 441*p**2 - 108*p. Factor m(w).
2*(w - 21)**2*(w + 1)
Let f(s) be the first derivative of -s**7/1260 + s**6/180 - s**5/90 - 4*s**3 - 11. Let h(r) be the third derivative of f(r). What is o in h(o) = 0?
0, 1, 2
What is w in -1/2*w**5 + 4*w**2 - 13/3*w**3 - 11/6*w + 1/3 + 7/3*w**4 = 0?
2/3, 1
Let k(a) be the first derivative of -