 Suppose -1/3 + 0*a + x*a**2 - 1/3*a**4 + 0*a**3 = 0. Calculate a.
-1, 1
Let u be (-288)/80 - 4*-1. Solve u*g**2 + 0*g + 6/5*g**3 + 2/5*g**5 + 6/5*g**4 + 0 = 0 for g.
-1, 0
Suppose 0 = 2*t - 1 - 7. Let d(k) be the second derivative of -8*k**2 - 68/3*k**3 - 67/3*k**t + 4*k + 161/10*k**5 + 0 - 49/3*k**7 + 392/15*k**6. Factor d(f).
-2*(f - 1)**2*(7*f + 2)**3
Let v = -147 - -149. Let -7/4*z**3 + 5/4*z**4 + 0 + 0*z + 1/2*z**v = 0. Calculate z.
0, 2/5, 1
Let m(y) be the second derivative of y**7/84 + y**6/15 + 3*y**5/20 + y**4/6 + y**3/12 - 7*y. Determine d so that m(d) = 0.
-1, 0
Let r be 2/3 + (-6)/36. Suppose r*h + 1/4*h**2 + 1/4 = 0. Calculate h.
-1
Let w(z) = 5*z**2 - 13*z - 3. Let k(j) = -11*j**2 + 27*j + 7. Let x(m) = 6*k(m) + 13*w(m). Let q be x(-7). Factor -d**4 - 2*d**q + 4*d + 8*d**3 + 4*d - 12*d**2.
-d*(d - 2)**3
Factor 13/6*y + 2/3*y**2 + 1/2.
(y + 3)*(4*y + 1)/6
Suppose -2*i + 24 = -4*t, 0 = -4*i + i - 6. Let b be (-26)/t + 4/14. Factor -3/2*m**2 + 1/2*m - 1/2*m**b + 0 + 3/2*m**3.
-m*(m - 1)**3/2
Let r(h) be the first derivative of h**8/112 + h**7/70 - h**6/40 - h**5/20 - h**2 + 1. Let p(t) be the second derivative of r(t). Solve p(j) = 0 for j.
-1, 0, 1
Factor -4*g**3 - 5*g**5 + 8*g**3 + g**3.
-5*g**3*(g - 1)*(g + 1)
Factor -24*f**3 - 128*f + 43*f**2 - 505*f**4 - 139*f**2 + 503*f**4.
-2*f*(f + 4)**3
Factor -3/5*u + 0 - 1/5*u**2.
-u*(u + 3)/5
Suppose 0 = -5*w + 4*j + 6, -5*j - 16 = -5*w - 11. Find y, given that 6/5*y**w + 0*y + 0 + 2/5*y**4 + 8/5*y**3 = 0.
-3, -1, 0
Let r(z) = 2*z**3 - 2*z**2 + 4*z + 2. Let l(t) = -2*t**3 + t**2 - 5*t - 3. Let v(s) = 4*l(s) + 6*r(s). Factor v(j).
4*j*(j - 1)**2
Solve 3*z**2 + 3*z**3 + 5*z**3 + 6*z - z**3 - 10*z**3 = 0 for z.
-1, 0, 2
Let f(j) be the first derivative of -2*j**2 + 4 + 2/3*j**3 - 6*j. What is x in f(x) = 0?
-1, 3
Factor -17*o**3 + 9*o**3 + 4 + 12*o + 8*o**2 - 10*o**5 - 12*o**4 + 6*o**5.
-4*(o - 1)*(o + 1)**4
Let h be ((-90)/75)/((-2)/5). Factor -1/3*p - h*p**5 + 2/3*p**3 + 0 - 4*p**4 + 4/3*p**2.
-p*(p + 1)**2*(3*p - 1)**2/3
Suppose -55 = -23*v - 9. Determine b so that 3/4*b + 1/2 - 3/4*b**v - 1/2*b**3 = 0.
-2, -1/2, 1
Let t(g) be the third derivative of 9*g**5/50 + g**4/10 - 14*g**2. Factor t(x).
6*x*(9*x + 2)/5
Let k = -64 + 69. Let s(z) be the second derivative of -1/8*z**3 - 2*z - 5/48*z**4 + 3/80*z**k + 0 + 1/8*z**2 + 1/30*z**6. Determine m, given that s(m) = 0.
-1, 1/4, 1
Let d(x) be the third derivative of -x**7/7560 + x**4/24 + x**2. Let y(i) be the second derivative of d(i). Let y(j) = 0. Calculate j.
0
Let f(q) = 18*q + 38. Let r be f(-2). Suppose 0 - 2/7*w**r + 2/7*w = 0. What is w?
0, 1
Let y = 17 + -21. Let s be 1/5 + y/(-80). Factor 0 + 1/4*j**4 + 0*j**2 + s*j**3 + 0*j.
j**3*(j + 1)/4
Let q(g) = g. Let h be q(-1). Let o = 3 + h. Let 0 - 1/2*d**3 - 1/2*d**4 + 1/2*d + 1/2*d**o = 0. Calculate d.
-1, 0, 1
Let p(y) = 11*y**2 + 31*y + 29. Let w(q) = -5*q**2 - 15*q - 15. Let u(h) = -3*p(h) - 7*w(h). Factor u(j).
2*(j + 3)**2
Factor -2 + 9*q + 8 + 22*q**3 - 6*q**3 - 36*q**2 + 5*q**3.
3*(q - 1)**2*(7*q + 2)
Let w(i) be the third derivative of -i**6/60 + i**5/5 - 3*i**4/4 - 14*i**2. Find f such that w(f) = 0.
0, 3
Let q(l) be the third derivative of -l**5/270 + l**4/36 + 8*l**2. Factor q(f).
-2*f*(f - 3)/9
Let -4/13 - 2/13*k + 2/13*k**2 = 0. What is k?
-1, 2
Suppose -5*y + 2*y - r + 5 = 0, -y = 2*r. Suppose 3*a + 4*j - 20 = a, 0 = -5*a + 2*j + y. Factor -w**3 + w**a + 2*w**3 - 2*w**2.
w**2*(w - 1)
Let d(o) = -o**2 - 28*o - 187. Let b be d(-12). Factor 6*y - 9/5 - b*y**2.
-(5*y - 3)**2/5
Let u(c) = 2*c**3 - 2*c**2 + 5*c - 10. Let x(j) = -2*j**3 + 2*j**2 - 6*j + 12. Let z(o) = 6*u(o) + 5*x(o). What is h in z(h) = 0?
0, 1
Let f be 216/(-162) + (-8)/(-6). Factor -1/2*g**5 + 0*g**2 + f*g**4 - 1/2*g + g**3 + 0.
-g*(g - 1)**2*(g + 1)**2/2
Factor -8*o**5 + o**4 + 5*o**3 - 7*o**5 + 14*o**5 + 3*o**2.
-o**2*(o - 3)*(o + 1)**2
Let w(v) be the second derivative of -2/3*v**3 + 1/8*v**5 - v**2 - 1/84*v**7 - 1/24*v**4 + 0 - v + 1/60*v**6. Factor w(q).
-(q - 2)**2*(q + 1)**3/2
Let o(l) be the first derivative of l**3/3 + l**2/3 - l/3 + 2. Factor o(y).
(y + 1)*(3*y - 1)/3
Factor -12/5 + 12/5*c**2 - 3/5*c**3 + 3/5*c.
-3*(c - 4)*(c - 1)*(c + 1)/5
Let f(m) = -15*m**2 + 15*m - 5. Let l(d) = d**3 - 15*d**2 + 15*d - 5. Let u(c) = -4*f(c) + 5*l(c). Factor u(a).
5*(a - 1)**3
Find u, given that -2/13*u**2 - 2/13*u**4 + 4/13*u**3 + 0 + 0*u = 0.
0, 1
Let h(t) be the first derivative of t**6/3 + 2*t**5/5 - 5*t**4/2 - 2*t**3/3 + 8*t**2 - 8*t - 8. Factor h(w).
2*(w - 1)**3*(w + 2)**2
Let f(k) be the third derivative of k**9/181440 + k**8/30240 + k**7/15120 - k**5/30 + 2*k**2. Let m(a) be the third derivative of f(a). Solve m(v) = 0 for v.
-1, 0
Let s(i) be the second derivative of 1/6*i**4 + 1/60*i**5 + 2/3*i**3 + 1/2*i**2 + 0 - i. Let j(x) be the first derivative of s(x). Find w such that j(w) = 0.
-2
Suppose f + 38 - 9 = 5*n, -3*n = 2*f + 45. Let q be 1 - 1 - 8/f. Solve 0*i + 1/3*i**4 - q*i**3 + 0 + 0*i**2 = 0 for i.
0, 1
Suppose -9*k = -k. Let o(a) be the second derivative of 0*a**2 + 1/147*a**7 + 0*a**4 + k*a**3 + 0*a**5 + 2*a - 2/105*a**6 + 0. Determine z, given that o(z) = 0.
0, 2
Let a = -5 - -7. Find t such that -3 + 3*t**2 - a*t**2 + 2 + t**3 - t = 0.
-1, 1
Let q(c) be the second derivative of -2/15*c**3 + 4*c - 1/30*c**4 + 1/75*c**6 + 0 + 1/25*c**5 + 0*c**2. Solve q(f) = 0 for f.
-2, -1, 0, 1
Let x(i) be the second derivative of i**4/15 - 14*i**3/15 + 24*i**2/5 - 59*i. Factor x(c).
4*(c - 4)*(c - 3)/5
Let y(m) be the third derivative of m**7/1050 + m**6/300 - m**5/100 - m**4/15 - 2*m**3/15 + 6*m**2 + 1. Factor y(c).
(c - 2)*(c + 1)**2*(c + 2)/5
Let g(d) = d**2 + 1. Let r(b) = -3*b**2 + b - 6. Let i be 4/(-18) - 25/9. Let u be -2 - (3 + -1) - i. Let q(f) = u*r(f) - 4*g(f). Factor q(a).
-(a - 1)*(a + 2)
Suppose -19 = -5*b + 6. Let o(p) = -4*p**4 - 4*p**3 + 4*p**2 - p - 5. Let v(s) = s**4 + s**3 - s**2 + 1. Let i(x) = b*v(x) + o(x). Factor i(g).
g*(g - 1)*(g + 1)**2
Let o(q) = -1. Let l(p) = -2*p**2 + 2*p + 1. Let s(u) = 3*u**2 - 2*u - 2. Let x(w) = -4*l(w) - 3*s(w). Let r(y) = -3*o(y) - x(y). Determine k so that r(k) = 0.
-1
Let u be 20/5 - (0 + -1). Suppose -l + 2 = -4*s, u*s = -4*l + 7*l - 6. Factor 2/3*h**3 + 2/3*h**2 + s + 0*h.
2*h**2*(h + 1)/3
Let v(y) be the first derivative of 5 + 0*y - 3*y**3 - 3/2*y**2 + 3*y**4. Solve v(z) = 0.
-1/4, 0, 1
Let x be (9 - 385/45)*1. Solve -x + 8/9*f**2 - 14/9*f = 0 for f.
-1/4, 2
Factor -1/2*o**2 - 1/4 - 1/4*o**5 + 3/4*o - 1/2*o**3 + 3/4*o**4.
-(o - 1)**4*(o + 1)/4
Let y(v) = 64*v**2 - 64. Let i(k) = 7*k**2 - 7. Let l(j) = 28*i(j) - 3*y(j). Factor l(a).
4*(a - 1)*(a + 1)
Let u(j) be the third derivative of 5*j**8/336 - j**7/6 + 7*j**6/24 + 23*j**5/12 - 5*j**4/3 - 40*j**3/3 + 9*j**2. Determine d, given that u(d) = 0.
-1, 1, 4
Factor 14/9*y - 4/3 - 2/9*y**2.
-2*(y - 6)*(y - 1)/9
Let m = -3749/3759 + -9/179. Let p = 236/105 + m. Determine w so that -2/5*w**4 + 0 + p*w**3 + 2/5*w - 6/5*w**2 = 0.
0, 1
Suppose -13 + 9 = -2*n. Find h, given that -2/3*h**n - 2*h - 4/3 = 0.
-2, -1
Let a(x) be the first derivative of -2*x**3/27 + 4*x**2/9 - 58. Suppose a(f) = 0. Calculate f.
0, 4
Let t(w) be the first derivative of 7*w**4 + 8*w**3/3 + 3. Factor t(n).
4*n**2*(7*n + 2)
Let z(m) be the second derivative of m**6/40 - m**5/10 + m**4/8 + m**2 + 2*m. Let l(g) be the first derivative of z(g). Factor l(s).
3*s*(s - 1)**2
Suppose y - 2 + 13 = 0. Let q = y + 14. Determine d, given that 0*d**2 + 0 - 2/5*d**q + 0*d = 0.
0
Let j(s) be the third derivative of s**8/10080 - s**7/1680 + s**6/720 - s**5/720 - s**3/2 + 3*s**2. Let h(o) be the first derivative of j(o). Factor h(f).
f*(f - 1)**3/6
Let t(k) be the first derivative of 6*k**2 - 4*k - 3*k**4 - 6 + 4/3*k**3. Suppose t(j) = 0. Calculate j.
-1, 1/3, 1
Suppose 45 = -5*t + 3*o, -3*t - 32 = -2*t + 4*o. Let c = 1 - t. Factor 2*y - 6*y**3 - c*y**4 - 13*y**2 - 3 - 1 + 12*y**4 - 14*y.
-(y + 1)**2*(y + 2)**2
Factor 52 - 71 + 43 + 18*q + 3*q**2.
3*(q + 2)*(q + 4)
Let r(f) = 10*f**3 + f**2 - 2*f + 1. Let q be r(1). Let -18*x**2 + 36*x - 1 - 13 - q + 3*x**3 = 0. What is x?
2
Let i(y) = 7*y**2 + 13*y + 11. Let g(p) = 11*p**2 + 20*p + 17. Let d(r) = -5*g(r) + 8*i(r). Let d(q) = 0. Calculate q.
-3, -1
Let n(y) be the first derivative of y**6/24 + y**