
Factor -50/9*k**2 - 8/9 - 32/9*k - 2/9*k**5 - 38/9*k**3 - 14/9*k**4.
-2*(k + 1)**3*(k + 2)**2/9
Let w = -8/25 + 74/75. Let g be (-2)/(-12)*(74 + -70). Find y such that -1/3*y**3 + 1/3*y - g*y**2 + w = 0.
-2, -1, 1
Let u(a) be the third derivative of a**10/3150 + a**9/2520 + a**8/6720 + a**5/12 - a**2. Let c(z) be the third derivative of u(z). Find i, given that c(i) = 0.
-1/4, 0
Let d(c) be the first derivative of -c**6/30 + 2*c**5/25 - 2*c**3/15 + c**2/10 - 5. Determine b, given that d(b) = 0.
-1, 0, 1
Let y(k) be the second derivative of 0*k**4 + 0 + 0*k**2 - 5/63*k**7 + 0*k**3 + k - 1/15*k**5 - 7/45*k**6. Factor y(u).
-2*u**3*(u + 1)*(5*u + 2)/3
Suppose -5*n + 13 = 3*i, 0*n - 2*n + 1 = -3*i. What is d in 6*d - n*d - 2*d - 2*d**2 = 0?
0, 1
Let s(i) be the second derivative of 0 + 5/18*i**3 + i - 7/36*i**4 + 1/3*i**2. Factor s(f).
-(f - 1)*(7*f + 2)/3
Suppose 0 = -w + 2*w + 5, -15 = -2*s + 3*w. Let m(c) be the third derivative of -3*c**3 - 1/2*c**4 + 0 + s*c - 1/30*c**5 - 3*c**2. Factor m(k).
-2*(k + 3)**2
Let k = 22 + -16. Let z be ((-3)/k)/(5/(-20)). Determine b so that 0*b**z + 1/3*b**3 - 2/3*b**4 + 0 + 1/3*b**5 + 0*b = 0.
0, 1
Let g(p) be the third derivative of -p**5/660 + p**4/66 - 17*p**2. Factor g(o).
-o*(o - 4)/11
Let y(n) be the third derivative of -n**9/30240 - n**8/3360 - n**7/840 - n**6/360 - n**5/30 + 3*n**2. Let s(i) be the third derivative of y(i). Factor s(k).
-2*(k + 1)**3
What is r in r**2 - 4*r**2 + 5*r**3 + r**2 + 3*r**2 + 4*r**4 = 0?
-1, -1/4, 0
Let 12*g + 2*g**3 - 8 + 4*g**3 - 6*g**2 - 5*g**3 = 0. Calculate g.
2
Let w(c) be the first derivative of c**4/26 + 14*c**3/39 + 15*c**2/13 + 18*c/13 - 15. Let w(o) = 0. Calculate o.
-3, -1
Let f(k) be the second derivative of -k**9/30240 + k**8/13440 + k**4/3 - 2*k. Let w(l) be the third derivative of f(l). Find p such that w(p) = 0.
0, 1
Let r(s) be the first derivative of s**3/2 - 3*s**2/2 - 17. Factor r(g).
3*g*(g - 2)/2
Suppose 6/7*g**4 + 18/7*g + 4/7 + 22/7*g**3 + 30/7*g**2 = 0. Calculate g.
-1, -2/3
Suppose 5*g = -5*q - 0*q + 40, -3 = -g + 4*q. Suppose -9*c + g*c = 0. Factor -2/3*h**2 + 2/3*h**4 + 1/3*h + 0 - 1/3*h**5 + c*h**3.
-h*(h - 1)**3*(h + 1)/3
Let v(a) = -a**3 - a**2. Let k(o) = -o**4 - o - 6*o**2 - 5*o**3 + 4*o - 5*o. Let g(r) = k(r) - v(r). Factor g(f).
-f*(f + 1)**2*(f + 2)
Let i be 30/(-9)*(1 - 20/8). Let v(u) be the second derivative of 1/10*u**i + 0 + u + 0*u**2 - 1/6*u**4 + 0*u**3. Determine o so that v(o) = 0.
0, 1
Let r(i) be the second derivative of i**6/60 - i**5/20 - 7*i**4/24 - i**3/3 - 29*i. Factor r(o).
o*(o - 4)*(o + 1)**2/2
Let j be (1 - 6/(-10))*(-5)/(-6). Suppose -2/3*l**2 - j*l - 2/3 = 0. Calculate l.
-1
Let b be 2/12*(-15 - -27). Factor -18/5 + 12/5*v - 2/5*v**b.
-2*(v - 3)**2/5
Suppose -3*q + 4 = -2. Let t(d) be the third derivative of 0 + 1/105*d**7 - 1/12*d**4 - 1/30*d**5 + 0*d - q*d**2 + 0*d**3 + 1/60*d**6. Factor t(o).
2*o*(o - 1)*(o + 1)**2
Let k be 857/1305 - 6/27. Let n = k + -1/29. Factor -2/5*h**2 + 8/5*h**3 + n - 8/5*h.
2*(h - 1)*(h + 1)*(4*h - 1)/5
Let b(i) be the third derivative of i**7/105 + 10*i**2. Factor b(d).
2*d**4
Let l(q) be the third derivative of -q**7/21 - q**6/12 - q**4/3 - 5*q**2. Let k(c) = 0*c**3 - c**3 + c**4 - c - 2*c**4. Let f(u) = -8*k(u) + l(u). Factor f(x).
-2*x**3*(x + 1)
Suppose -y - 1 - 2 = -b, -2*y = 4*b - 12. Suppose p**2 - 4 + 6*p - 3*p**2 + y*p**2 = 0. Calculate p.
1, 2
Let s(p) = 6*p**4 - 15*p**3 + 18*p**2 - 15*p. Let n(l) = 17*l**4 - 44*l**3 + 54*l**2 - 44*l + 1. Let i(d) = -3*n(d) + 8*s(d). Determine b, given that i(b) = 0.
1
Let x(z) be the third derivative of -z**8/1680 + z**6/600 + 5*z**2. Factor x(o).
-o**3*(o - 1)*(o + 1)/5
Let t(j) = j**2 + 3*j + 2. Let v be t(-4). Let f be (-30)/72 + 4/v. Solve 1/2*n - f*n**2 - 1/4 = 0 for n.
1
Factor -32*g**3 - 5*g**4 - 3*g - 11*g**4 - 16*g**2 - 4*g**2 - g.
-4*g*(g + 1)*(2*g + 1)**2
Let m(l) be the first derivative of -3 - 1/2*l**2 + 0*l + 4/3*l**3. Factor m(s).
s*(4*s - 1)
Let m = 24 - 10. Let c = -11 + m. Find h such that 0*h + 0 + 2/3*h**2 - 4/3*h**c = 0.
0, 1/2
What is p in 0 + 12/5*p - 1/5*p**2 = 0?
0, 12
Let a(o) be the first derivative of -o**8/1176 - 2*o**7/735 + o**5/105 + o**4/84 - 3*o**2/2 - 4. Let w(q) be the second derivative of a(q). Factor w(z).
-2*z*(z - 1)*(z + 1)**3/7
Let x be 1/(-2) + (-45)/(-54). Let w = 43/21 - 5/7. Let -x*u**2 + w*u - 4/3 = 0. Calculate u.
2
Let c(b) be the first derivative of b**3/9 - b**2 + 3*b - 1. Suppose c(v) = 0. Calculate v.
3
Let l(z) be the third derivative of -z**7/420 - z**6/80 - z**5/120 + z**4/16 + z**3/6 + 10*z**2. Determine m, given that l(m) = 0.
-2, -1, 1
Let n = 5228/3 + -1742. Solve -2 - 4/3*q + n*q**2 = 0.
-1, 3
Let b be (-9)/(-6)*8/6. Factor -8 - 4 + 21*t**2 - 24*t**b + 12*t.
-3*(t - 2)**2
Let s be 0/((-1)/1 - 3). Factor s*z + 0 - 1/4*z**4 + 1/4*z**3 + 1/4*z**2 - 1/4*z**5.
-z**2*(z - 1)*(z + 1)**2/4
Factor -154*f**2 - 152*f**2 - 4*f**3 + 302*f**2 + 2*f**3.
-2*f**2*(f + 2)
Let x = 12 - 4. Suppose 4*a - x*a = -12. Let -w**2 + a*w**2 - w + 11*w**3 - 12*w**3 = 0. Calculate w.
0, 1
Let q(p) = -10*p**3 + 10*p + 5. Let z(o) = -o**3 + o + 1. Let d(m) = q(m) - 5*z(m). Find g, given that d(g) = 0.
-1, 0, 1
Let t = -656 - -946. Let h be t/75 + 6/45. Factor -2/5*d**3 + 0*d**2 + 0*d + 0 + 2/5*d**h.
2*d**3*(d - 1)/5
Suppose 4*p + 2 = -m - 4*m, 0 = 3*m + 3*p + 3. Factor -3*w**3 - 1 - 15*w**2 + 22*w**2 - 5*w + m.
-(w - 1)**2*(3*w - 1)
Let a = -1 - -6. Suppose 20 = -a*c, -6*m - 8 = -3*m + 2*c. Factor m - 1/2*k**2 - 1/2*k.
-k*(k + 1)/2
Determine j, given that 3*j**3 - 4*j - 7*j**3 + 5*j**3 = 0.
-2, 0, 2
Let r(h) be the first derivative of -3*h**4/8 + h**3 - 4. Factor r(f).
-3*f**2*(f - 2)/2
Let q = 443/1710 - 9/38. Let s(c) be the second derivative of 0*c**2 - q*c**6 + c + 0 + 0*c**5 + 0*c**3 + 0*c**4. Factor s(o).
-2*o**4/3
Let u(m) be the second derivative of -1/15*m**5 + 2*m + 0*m**3 - 1/6*m**4 + 1/3*m**2 + 0. Determine v, given that u(v) = 0.
-1, 1/2
Let o(s) = -26*s**3 + 36*s**2 - 10*s - 16. Let l(j) be the first derivative of -5*j**4/4 + 7*j**3/3 - j**2 - 3*j + 6. Let a(y) = 16*l(y) - 3*o(y). Factor a(x).
-2*x*(x - 1)**2
Suppose -4*i + 20 = -0*i. Let c(s) = -s - 3. Let a be c(-5). Factor -2*o + 3*o**a - o - o + i*o.
o*(3*o + 1)
Let q(g) be the second derivative of 1/12*g**2 + 0 + 1/18*g**3 + 1/72*g**4 - 4*g. Determine v so that q(v) = 0.
-1
Let f(q) be the third derivative of q**5/150 - q**4/30 - q**3/5 - 3*q**2. Factor f(y).
2*(y - 3)*(y + 1)/5
Let v(k) be the second derivative of 2*k**7/21 - 2*k**5/5 + 2*k**3/3 - 4*k. Find z, given that v(z) = 0.
-1, 0, 1
Let m(p) be the first derivative of -p**5/120 - p**4/72 + 5*p - 10. Let f(z) be the first derivative of m(z). Factor f(d).
-d**2*(d + 1)/6
Let d(k) = 8*k + 10. Let h(u) = 23*u + 29. Let t(s) = 17*d(s) - 6*h(s). Let b be t(-3). Determine g so that -g**2 - g**2 + 0*g**b = 0.
0
Let j = 62 - 59. Factor 1/2*z**j - 1/2*z**4 + 0*z + 0 - 1/2*z**5 + 1/2*z**2.
-z**2*(z - 1)*(z + 1)**2/2
Let z = -2/87 - -95/348. Determine b so that z*b + 0 + 1/4*b**3 + 1/2*b**2 = 0.
-1, 0
Let b(g) be the third derivative of 0*g + 9/2*g**4 + 27/40*g**6 + g**2 + 0 + 27/10*g**5 + 4*g**3. Factor b(a).
3*(3*a + 2)**3
Let w(m) = m**2 + 5*m - 8. Let z be w(-7). Suppose -z = -0*a - 3*a. Factor 0*t + 4/3*t**2 + 2/3*t**4 - a*t**3 + 0.
2*t**2*(t - 2)*(t - 1)/3
Let y = 4 - -1. Let n = y - 3. Factor -2*s**3 - 8*s**3 - 2*s**n - 2*s**2.
-2*s**2*(5*s + 2)
Let y = -8/369 + 10/41. Determine w, given that 0 + 2/3*w**3 - 2/3*w**4 + y*w**5 - 2/9*w**2 + 0*w = 0.
0, 1
Let w(o) be the third derivative of o**8/1344 - o**6/240 + o**4/96 - 15*o**2. Let w(x) = 0. What is x?
-1, 0, 1
Let b(y) = -4*y**3 - 8*y**2 - 4*y + 7. Let h(g) = 2*g**3 + 4*g**2 + 2*g - 3. Let z(k) = 3*b(k) + 7*h(k). Determine i so that z(i) = 0.
-1, 0
Let l(w) be the second derivative of w**4/54 + 2*w**3/27 + 13*w. Factor l(s).
2*s*(s + 2)/9
Determine t so that 4/11 + 6/11*t - 6/11*t**3 - 4/11*t**2 = 0.
-1, -2/3, 1
Let s(n) = -n**3 + 7*n**2 - 3*n. Let o be s(6). Suppose 0*h - 18*h**2 + 4*h**5 + o*h**4 + 10*h**3 + 4*h - 18*h**5 = 0. Calculate h.
-1, 0, 2/7, 1
Suppose 0*x + 2*j - 13 = -x, 3*j + 13 = 5*x. Suppose 2*h - 24 = -4*d, -h + 5*d - 1 = 15. Factor x + h*c - 4*c - 3 - 2*c**2.
-2*(c - 1)*(c + 1)
Let -3*b - 20/3*b**4 + 4/3*b**2 + 9*b**3 