
Let i be 9/12 - 36/(-16). Factor -2/7 + 2/7*w**i - 2/7*w + 2/7*w**2.
2*(w - 1)*(w + 1)**2/7
Suppose 5*h - 4*i = i + 5, 2*h = -5*i + 30. Suppose -26/7*c**3 - 12/7*c**2 - 2/7*c - 24/7*c**4 + 0 - 8/7*c**h = 0. What is c?
-1, -1/2, 0
Let l(u) be the third derivative of u**6/960 - u**5/96 + u**4/48 + 10*u**2. Factor l(s).
s*(s - 4)*(s - 1)/8
Let i(d) be the first derivative of d**6/14 - 24*d**5/35 + 9*d**4/4 - 2*d**3 - 30*d**2/7 + 72*d/7 + 50. Factor i(t).
3*(t - 3)*(t - 2)**3*(t + 1)/7
Let c = -542/3 + 183. Let m be (-3)/(-1 - (2 + -2)). Factor -m*z - 2/3 - c*z**2.
-(z + 1)*(7*z + 2)/3
Let h(d) be the first derivative of -2/3*d**3 + 0*d + 2 + 0*d**2. Suppose h(j) = 0. What is j?
0
Let i(c) = 5*c**4 + 3*c**3 - c**2 - 3*c + 4. Let a(o) = 6*o**4 + 3*o**3 - 2*o**2 - 4*o + 5. Let q(l) = 4*a(l) - 5*i(l). Factor q(g).
-g*(g + 1)**3
Let p(k) = -k**2 + 5*k - 4. Let h be p(3). Suppose -2*u**3 - 2*u**2 + 3*u**3 - h*u**5 + u**3 + 2*u**4 = 0. Calculate u.
-1, 0, 1
Let c(g) be the third derivative of g**5/180 - 2*g**3/9 + 5*g**2. Determine t so that c(t) = 0.
-2, 2
Factor 625*k**3 + 125/2*k**4 + 15625/2 + 5/2*k**5 + 15625/2*k + 3125*k**2.
5*(k + 5)**5/2
Factor 8*q + 70*q**3 - 5*q**2 + 9*q**2 - 74*q**3.
-4*q*(q - 2)*(q + 1)
Let j(r) = r + 6. Let s be j(-4). Let w(d) be the first derivative of -2/9*d**3 - 1 + 0*d**s + 1/6*d**4 + 0*d. Determine t so that w(t) = 0.
0, 1
Solve 2/3*y + 0*y**2 - 2/9*y**3 - 4/9 = 0 for y.
-2, 1
Factor 13*u**3 - 2 - 2*u**4 + 11*u**3 - 2*u**2 - 2*u**5 - 20*u**3 - 2*u + 6*u**2.
-2*(u - 1)**2*(u + 1)**3
Let v be (11 - -3) + 2*-1. Suppose p = -2*x + v, 5*p - 3*x + 4*x - 15 = 0. Factor -p*f - f**3 - f**2 + 2*f.
-f**2*(f + 1)
Let 5/4*a**2 + 1/2*a - 1/4*a**5 - 1/4*a**4 + 0 + 3/4*a**3 = 0. Calculate a.
-1, 0, 2
Let t(x) = x**2 + 3*x. Let q be t(-6). Solve 5*d**3 + q*d - 4*d**2 - 2 - 3*d**3 - 20*d + 6*d**2 = 0 for d.
-1, 1
Suppose 3*f = -20 - 37. Let t = -37/2 - f. Determine r so that t*r**2 + 1/2*r**3 + 0 + 0*r = 0.
-1, 0
Let l be 1 + 5 + (3 - 6). Find a, given that -2*a + 4*a - 4*a**2 + 12*a**l - 10*a**3 = 0.
0, 1
Suppose 0*t - 4*t + 8 = 0. Suppose -t*l - 2*l - 16 = 2*b, -2*b + 16 = -4*l. Suppose 1/4*j**5 + b*j + 0*j**2 - 1/4*j**3 + 0 + 0*j**4 = 0. Calculate j.
-1, 0, 1
Let t(s) = -5*s**3 + s**2 - 8 + 12*s + s**2 - s. Let f(w) = -w**3 + w**2 + w - 1. Let r(l) = -6*f(l) + t(l). Factor r(q).
(q - 2)*(q - 1)**2
Let -9/5*r - 3/5*r**2 - 6/5 = 0. Calculate r.
-2, -1
Let f(a) = a**5 + 20*a**3 + 10*a**2 + 3*a + 8. Let r(q) = -3*q**5 - q**4 - 59*q**3 - 31*q**2 - 10*q - 23. Let p(j) = 17*f(j) + 6*r(j). Factor p(z).
-(z + 1)**4*(z + 2)
Let s(b) be the first derivative of b**4/6 + 10*b**3/9 + 8*b**2/3 + 8*b/3 + 27. Factor s(r).
2*(r + 1)*(r + 2)**2/3
Let f(b) be the first derivative of -7*b**4/8 - 9*b**3/4 - 3*b**2/2 + b - 1. Let h(a) be the first derivative of f(a). Factor h(n).
-3*(n + 1)*(7*n + 2)/2
Suppose 0 = -2*w - 5*x + 6, -3*w - w + 5*x + 12 = 0. Suppose 0 = w*y - 5 - 10. Factor 0*f + 0*f**4 - 1/4*f**y + 0 + 0*f**3 + 0*f**2.
-f**5/4
Find c such that 0*c + 1/3*c**4 + 0*c**2 + 0 - 1/3*c**3 = 0.
0, 1
Suppose -z - 832 = -4*n, n - 5*n + 844 = 2*z. Let k = n + -1879/9. Suppose 0 + 0*t - 2/9*t**2 - k*t**3 = 0. What is t?
-1, 0
Suppose 0 = 9*q - 13*q + 16. Let o(p) be the second derivative of 1/105*p**7 + 0*p**2 + 0 + 0*p**3 + 0*p**q + 0*p**6 - 1/50*p**5 + 2*p. Factor o(n).
2*n**3*(n - 1)*(n + 1)/5
Let p(f) = f**3 - f**2. Let m(q) = -21*q**3 + 31*q**2 - 11*q - 3. Let u(s) = -m(s) - 4*p(s). Let i(c) = -c**3 - c. Let h(x) = -2*i(x) - u(x). Factor h(z).
-3*(z - 1)**2*(5*z + 1)
Suppose l - t = 4*t - 12, 2*l + 2*t = 12. Factor m - 3*m**2 - 3*m - 4*m + 0*m - l.
-3*(m + 1)**2
Let z(d) be the third derivative of -d**7/420 - d**6/180 + d**5/60 + d**4/12 - d**3 + d**2. Let q(x) be the first derivative of z(x). Factor q(m).
-2*(m - 1)*(m + 1)**2
Let k(n) = n**3 - 5*n**2 + 4. Let m be k(5). Suppose -g + m*g - 6 = 0. Factor 1/2*x**2 + g + 2*x.
(x + 2)**2/2
Determine z, given that -1/5*z + 1/5*z**3 + 0 + 0*z**2 = 0.
-1, 0, 1
Let v(n) = 3*n**2 + 6*n - 3. Let m be -1*(-5)/(-1)*-1. Let y(t) = -t**3 + 6*t**2 + 11*t - 6. Let p(u) = m*v(u) - 3*y(u). Factor p(k).
3*(k - 1)**2*(k + 1)
Let p(v) be the second derivative of v**7/231 - 4*v**6/55 + 24*v**5/55 - 32*v**4/33 - 9*v. Let p(a) = 0. Calculate a.
0, 4
Let w(j) be the first derivative of -j**7/2940 - j**6/1260 + 2*j**3/3 + 1. Let f(p) be the third derivative of w(p). Find z, given that f(z) = 0.
-1, 0
Solve 2 + 3 - 5*k + 3 + 10*k**2 - 12*k - k**3 = 0.
1, 8
Let h(t) be the second derivative of 1/12*t**2 - 1/18*t**3 + 1/72*t**4 + 0 + 3*t. Factor h(q).
(q - 1)**2/6
Let m(t) be the first derivative of t**7/1680 - t**5/240 - t**3 - 4. Let d(u) be the third derivative of m(u). Factor d(k).
k*(k - 1)*(k + 1)/2
Let m(z) be the third derivative of -z**6/30 - 4*z**5/15 - 2*z**4/3 - 2*z**2. Determine h so that m(h) = 0.
-2, 0
Factor 0 - 4/5*l**4 - 4/5*l**3 + 8/5*l**2 + 0*l.
-4*l**2*(l - 1)*(l + 2)/5
Let z(c) be the third derivative of 0*c + 1/60*c**6 - 1/15*c**5 + 1/12*c**4 + 0 + 0*c**3 - 4*c**2. Factor z(a).
2*a*(a - 1)**2
Let g(u) = u + 9. Let o be g(-5). Let d(v) be the second derivative of 0*v**3 - 1/2*v**2 + 1/12*v**o - 2*v + 0. Determine r so that d(r) = 0.
-1, 1
Factor 0 - 4/5*c + 0*c**2 + 4/5*c**3.
4*c*(c - 1)*(c + 1)/5
Let a = -24 - -35. Let k be 30/44 - 2/a. Factor 1/4*x + 1/4*x**5 - 1/4*x**4 - 1/4 + k*x**2 - 1/2*x**3.
(x - 1)**3*(x + 1)**2/4
Factor 420 - 420 - 8*o**4 - 4*o**5 - 5*o**3 + o**3.
-4*o**3*(o + 1)**2
Let v be 2 + (-1)/(2/(-36)). Suppose 0 = -2*m + 6*m + 3*q + 1, -4*m + 4*q = -v. Solve -1/3*z**m + 0 + 1/3*z = 0 for z.
0, 1
Factor -8/3*p**4 - 4/3*p**2 - 10/3*p**3 + 0*p - 2/3*p**5 + 0.
-2*p**2*(p + 1)**2*(p + 2)/3
Let t = 5 + -3. Factor -6*b + 8*b**2 + 9 - 5*b**2 - 6*b**t.
-3*(b - 1)*(b + 3)
Let p(t) be the second derivative of -t**4/24 - t**3/6 - t**2/4 - 4*t. Factor p(b).
-(b + 1)**2/2
Let i(l) = 7*l**3 + 17*l**2 + 25*l + 15. Let w(u) = -64*u**3 - 152*u**2 - 224*u - 136. Let y(f) = 28*i(f) + 3*w(f). Solve y(o) = 0 for o.
-3, -1
Let y(a) be the second derivative of 0 + 1/2*a**4 + 2/3*a**3 + 0*a**2 - 1/15*a**6 + 0*a**5 + 3*a. Suppose y(r) = 0. What is r?
-1, 0, 2
Factor 57/5*x**3 + 12/5 + 3/5*x**5 + 21/5*x**4 + 48/5*x + 15*x**2.
3*(x + 1)**3*(x + 2)**2/5
Let h(j) be the third derivative of j**6/60 + j**5/10 + j**4/6 + 32*j**2. What is b in h(b) = 0?
-2, -1, 0
Let r(y) = -y + 1. Let h be r(5). Let a = 4 + h. Factor 1/2*b**2 + a*b - 1/2.
(b - 1)*(b + 1)/2
Let o(n) = n**2 - n. Let v be o(2). Suppose -v*l + l = -2. Factor 5/3*w - 5/3*w**3 - 2/3 + 2/3*w**l.
-(w - 1)*(w + 1)*(5*w - 2)/3
Suppose 16 = m - 4*c, -2*m + 0*m - 5*c - 7 = 0. Factor -7*k**3 + 3*k**3 - m*k**3 + k**2 + 2*k + 5*k**4.
k*(k - 1)**2*(5*k + 2)
Suppose 3*f - 6 + 0 = 0. Let m = f - 0. Suppose 0 + 1/4*j**m - 1/4*j = 0. What is j?
0, 1
Let s = 51/110 - -2/55. Factor -1/2 - 1/2*h + s*h**3 + 1/2*h**2.
(h - 1)*(h + 1)**2/2
Let w(l) be the first derivative of l**6/21 - 2*l**5/35 - l**4/7 + 4*l**3/21 + l**2/7 - 2*l/7 + 10. Find g, given that w(g) = 0.
-1, 1
Let t(w) = w**2 + 1. Let j(p) = 15*p**2 - 10*p + 9. Let z(v) = -v. Let o(d) = j(d) + 4*z(d). Let b(s) = -o(s) + 5*t(s). Solve b(l) = 0.
2/5, 1
Let x(k) be the second derivative of 2*k**6/15 + 7*k**5/10 + 7*k**4/6 + 2*k**3/3 - 9*k. Factor x(j).
2*j*(j + 1)*(j + 2)*(2*j + 1)
Let z(d) = -3*d**3 - 4*d**2 - 5*d - 4. Let p(y) = -3*y**3 - 5*y**2 - 6*y - 4. Let a(x) = 7*p(x) - 6*z(x). Factor a(s).
-(s + 1)*(s + 2)*(3*s + 2)
Let m(t) be the first derivative of 2*t**5/15 - t**4/2 + 2*t**3/9 + t**2 - 4*t/3 + 6. Factor m(h).
2*(h - 2)*(h - 1)**2*(h + 1)/3
Suppose 3*w - 30 = -0*w. Let f be w/(-35) + (-32)/(-14). Suppose m**4 - 7*m**3 + 3*m**3 + m + 6*m**f + 0*m**4 - 5*m + 1 = 0. What is m?
1
Let l = 2482/5 - 496. Factor -l*d**3 + 0*d + 0*d**2 - 1/5*d**5 + 3/5*d**4 + 0.
-d**3*(d - 2)*(d - 1)/5
Let w(q) be the first derivative of 2*q**3/45 - 2*q**2/15 - 2*q/5 + 21. Factor w(x).
2*(x - 3)*(x + 1)/15
Factor -5*r - 2*r**3 + 2*r - r + 6*r**2.
-2*r*(r - 2)*(r - 1)
Let t(q) = -2*q**2 + 3*q + 12. Let u(c) = c**2 + c - 1. Let y(i) = -t(i) - 3*u(i). Factor y(j).
-(j + 3)**2
Let u = 785/3 - 5491/21. Let s(l) be the first derivative of -2 + 3/7*l**2 - 2/7*l - u*l**3. Let s(i) = 0. What is i?
1/2, 1
Suppose -6*b + 26 = -b + 3*y, 4