*6/72 + r**5/12 - 5*r**4/72 - 5*r**3/18 + 69*r**2. Solve i(n) = 0.
-1, 1/2
Factor 0*z**3 + 2*z**3 - 6*z - 3*z**3 + 3*z**3 + 4.
2*(z - 1)**2*(z + 2)
Let r be 6/(-4) - (-2)/4. Let l be (r/(-2))/(-1)*-6. Solve -2 + 4*p**2 - 2*p - 2*p**2 + 2*p**l + 0*p = 0 for p.
-1, 1
Let i be 2 - 1/3*0. Suppose 6*l**2 - l**3 - 4*l**2 + 0*l**3 - 3*l + i*l = 0. Calculate l.
0, 1
Let a(w) be the third derivative of -w**8/1092 - w**7/273 - w**6/195 - w**5/390 + 33*w**2. Determine p, given that a(p) = 0.
-1, -1/2, 0
Suppose 0 - 2 = 2*g, 5*g + 5 = -3*m. Factor 2/9*b**2 - 2/3*b + m.
2*b*(b - 3)/9
Let i = -41 - -41. Factor i*t**2 + 0 + 2/5*t**3 - 1/5*t + 0*t**4 - 1/5*t**5.
-t*(t - 1)**2*(t + 1)**2/5
Let l be 2*(-10)/(-4) - 2. Factor -k**l - 3*k**3 - 8*k**4 - 2*k**4.
-2*k**3*(5*k + 2)
Let f be 1*27/15*(-18)/(-81). Factor 0 + 0*d + 0*d**4 - f*d**5 - 4/5*d**2 + 6/5*d**3.
-2*d**2*(d - 1)**2*(d + 2)/5
Let o(s) be the first derivative of -2 + 0*s + 3/16*s**4 - 1/2*s**3 + 3/8*s**2. Determine h, given that o(h) = 0.
0, 1
Let 10/3*k + 4/3 + 2*k**2 = 0. What is k?
-1, -2/3
Let z(c) be the first derivative of -c**6/18 + c**5/3 - c**4/4 - c**3 + 16. Factor z(u).
-u**2*(u - 3)**2*(u + 1)/3
Let l(z) be the third derivative of -1/112*z**8 - 3/70*z**7 + 2*z**2 + 0*z + 0*z**3 + 0 - 1/20*z**5 + 0*z**4 - 3/40*z**6. Factor l(n).
-3*n**2*(n + 1)**3
Let o(t) be the third derivative of t**8/224 - 3*t**7/140 + t**6/40 + 17*t**2. Let o(u) = 0. What is u?
0, 1, 2
Let f = 15 - 10. Determine d so that -d - 2*d**3 + d**3 + 7*d**2 - f*d**2 = 0.
0, 1
Suppose 3 = j - 3. Let c = j + -4. Factor -8/9*q + 2/9*q**c + 8/9.
2*(q - 2)**2/9
Factor 1/2*k**3 - 3/2*k + 0*k**2 - 1.
(k - 2)*(k + 1)**2/2
Let v = -30/11 - -101/33. Factor -1/3*t**2 + v*t + 0.
-t*(t - 1)/3
Let w(b) be the first derivative of -b**4 + 8*b**3 - 24*b**2 + 32*b - 6. Factor w(a).
-4*(a - 2)**3
Let g(v) be the third derivative of -v**6/320 - v**5/160 + 4*v**2. Solve g(d) = 0.
-1, 0
Let k(r) = r - 8. Let i = 6 - -5. Let p be k(i). What is f in -2/7 - 4/7*f**2 - 8/7*f + 6/7*f**4 + 8/7*f**p = 0?
-1, -1/3, 1
Let s(i) be the first derivative of 0*i**4 - 2/5*i**2 + 2/25*i**5 - 2/5*i**3 + 0*i + 3. Let s(o) = 0. Calculate o.
-1, 0, 2
Let d = -9 + 11. Let y be (-12)/(-3)*d/8. Factor -3/2*l - 1/2*l**2 - y.
-(l + 1)*(l + 2)/2
Let v(t) be the second derivative of -t**7/630 + t**5/180 - 3*t**2/2 - t. Let l(y) be the first derivative of v(y). What is b in l(b) = 0?
-1, 0, 1
Suppose 5*g**2 - 8*g**2 - 5 + 2*g**2 + 6*g = 0. What is g?
1, 5
Suppose 65*n - 71*n = 0. Find w such that 2/11*w + n + 2/11*w**3 + 4/11*w**2 = 0.
-1, 0
Suppose 4*r + r = -3*i - 17, 4*r + 18 = 2*i. Let u be (-16)/r + 13/(-4). Factor 3/4*o**2 - u + 3/4*o**3 - 3/4*o.
3*(o - 1)*(o + 1)**2/4
Let s(j) be the third derivative of -1/120*j**5 + 0*j**4 + 0*j + 1/240*j**6 + 0*j**3 - 5*j**2 - 1/672*j**8 + 1/420*j**7 + 0. What is v in s(v) = 0?
-1, 0, 1
Let b be (-1)/(-3) + 592/(-48). Let h be (-2 - 2)*9/b. Factor 8/5*u**2 - 8/5*u + 0 - 2/5*u**h.
-2*u*(u - 2)**2/5
Let o = 12726/267509 + 2/3223. Let u = o + 138/581. Let -2/7*f**2 + 0 + 0*f**3 + 0*f + u*f**4 = 0. What is f?
-1, 0, 1
Let k(p) = p + 1. Let d(y) = -18*y**3 + 6*y**2 + 18*y - 6. Let l = 1 - 3. Let b(v) = l*k(v) + d(v). Factor b(g).
-2*(g + 1)*(3*g - 2)**2
Let c(f) be the second derivative of f**5/90 - f**3/27 + 11*f. Factor c(j).
2*j*(j - 1)*(j + 1)/9
Let r(h) be the third derivative of -h**8/56 - h**7/21 + h**6/15 + 2*h**5/15 + 6*h**2. Solve r(m) = 0 for m.
-2, -2/3, 0, 1
Let d = 22/7 + -23/14. Let 3/2*v - 1/2*v**5 - d*v**4 + v**2 + 1/2 - v**3 = 0. Calculate v.
-1, 1
Let j(a) be the third derivative of a**7/2520 - a**6/120 + 3*a**5/40 - a**4/12 + 6*a**2. Let b(g) be the second derivative of j(g). Find d such that b(d) = 0.
3
Find o such that 0 + 1/7*o - 4/7*o**2 = 0.
0, 1/4
Let m(t) = 2*t**2 + 6*t + 4. Let x(l) = -l**2 - 5*l - 3. Suppose 2*k - 1 + 7 = 0. Let b(o) = k*m(o) - 4*x(o). Factor b(d).
-2*d*(d - 1)
Let g = -286 - -286. Factor -1/3*p - 1/3*p**2 + g.
-p*(p + 1)/3
Let r = 118 + -235/2. Let n**2 + 3/2*n + r = 0. What is n?
-1, -1/2
Suppose 0 = -5*k - 25, z + 10 = 6*z - 2*k. Factor 1/2*i**5 + 0*i**4 + 0*i - 1/2*i**3 + z + 0*i**2.
i**3*(i - 1)*(i + 1)/2
Let o(b) be the second derivative of 1/30*b**6 + 1/20*b**5 - 1/6*b**4 + 0 - b + 0*b**2 + 0*b**3. Factor o(t).
t**2*(t - 1)*(t + 2)
What is k in 12 - 2*k**2 - 4*k**2 + 4*k**2 - 2*k**2 + 8*k = 0?
-1, 3
Let l(w) be the first derivative of -w**4/26 - 8*w**3/39 - 5*w**2/13 - 4*w/13 - 7. Let l(c) = 0. Calculate c.
-2, -1
Let i(c) be the first derivative of 2*c**5/5 + c**4/2 - 2*c**3/3 - c**2 - 2. Let i(b) = 0. Calculate b.
-1, 0, 1
Let k(o) = -9*o**4 - 5*o**3 + 8*o**2. Let l(w) = 26*w**4 + 0*w**3 - 2*w**3 + 5*w**3 - 23*w**2 + 11*w**3. Let i(t) = -17*k(t) - 6*l(t). Factor i(y).
-y**2*(y - 1)*(3*y + 2)
Determine g so that -2/9*g**2 + 10/9 + 8/9*g = 0.
-1, 5
Let r(m) = -m**3 + 5*m**2 - 2. Let v = 0 + 2. Let a be r(v). Factor 3*j - 6*j**4 + a*j**3 + 0*j**2 + 2*j**2 - 7*j - 2*j**3.
-2*j*(j - 1)**2*(3*j + 2)
Suppose -2*l + 1 - 12 = 3*x, -4*x - 12 = 4*l. Let q(b) be the second derivative of 0 - 1/7*b**l + 2*b - 1/42*b**4 - 2/21*b**3. Solve q(d) = 0 for d.
-1
Let -3*p + 2*p**3 - p**2 - 3*p**2 + 4 + p + 0*p**3 = 0. What is p?
-1, 1, 2
Let b = 22 - 15. Let u be (-12)/(-42)*b/3. Factor -4/3 + 2*i - u*i**3 + 0*i**2.
-2*(i - 1)**2*(i + 2)/3
Let l(q) be the second derivative of 0 - 1/30*q**3 - 4*q + 0*q**2 - 1/60*q**4. Factor l(p).
-p*(p + 1)/5
Determine f, given that -14*f**2 + 17*f**2 - 5*f**3 + 2*f**3 = 0.
0, 1
Let c(q) be the first derivative of -q**8/2520 - q**7/252 - 7*q**6/540 - q**5/60 - 4*q**3/3 + 7. Let n(s) be the third derivative of c(s). Factor n(u).
-2*u*(u + 1)**2*(u + 3)/3
Solve 25*o**2 + 24 + 35*o - 9 - 33*o**3 + 38*o**3 = 0 for o.
-3, -1
Let i be 0/(-1 - (-4)/(-16)*0). Let u(l) be the third derivative of 3*l**2 + 1/30*l**4 + 0*l**3 + 0 + i*l - 1/30*l**5. Let u(y) = 0. Calculate y.
0, 2/5
Let l(j) be the first derivative of -j**4/16 + j**3/4 - j**2/4 - 15. Factor l(r).
-r*(r - 2)*(r - 1)/4
Let t(a) be the second derivative of a**7/2100 - a**6/900 + a**3/6 + a. Let w(q) be the second derivative of t(q). What is y in w(y) = 0?
0, 1
Let a = -79 + 159/2. Let s(c) be the first derivative of 0*c**3 + 0*c - a*c**4 + 2 - 2/5*c**5 + 0*c**2. Factor s(x).
-2*x**3*(x + 1)
Let k(c) = -c - c**3 + 1 - 3*c**3 + 3*c**3. Let n(g) = 6*g**3 - 6*g**2 + 17*g - 13. Suppose i - 1 + 0 = 0. Let r(m) = i*n(m) + 5*k(m). Factor r(q).
(q - 2)**3
Let t(p) = -p**3 - 2*p**2 + 5*p. Let n be t(-4). Factor 4*m - 5 + 12*m**3 + 5 + 4*m**4 + n*m**2.
4*m*(m + 1)**3
Suppose 5*s - 13 - 7 = 0. Factor 2 - w**2 - s + 3*w**2.
2*(w - 1)*(w + 1)
Let r(g) be the second derivative of -g**5/70 - g**4/42 + 5*g**3/21 - 3*g**2/7 + 4*g. What is p in r(p) = 0?
-3, 1
Let c(u) be the first derivative of -u**3/5 - 3*u**2/10 + 4. Solve c(s) = 0.
-1, 0
Suppose -8*n + 6 = -5*n. Let z(c) be the first derivative of -1/9*c**3 - 1/3*c - 1 - 1/3*c**n. Factor z(a).
-(a + 1)**2/3
Let z = 26/33 - -6/11. Find t, given that 2/3*t**2 + z - 2*t = 0.
1, 2
Suppose 2*s + c - 7 = 0, 4*s + 4*c + c = 11. Let m be 2/s - (9 + -9). Find l such that 0 + 1/2*l + m*l**2 = 0.
-1, 0
Let w(t) be the second derivative of 1/35*t**5 + 0*t**6 + 0*t**2 - 1/21*t**3 + 0*t**4 + 0 - 1/147*t**7 + 7*t. What is g in w(g) = 0?
-1, 0, 1
Let s = 14 - 10. Suppose 0 = -s*i + 12, 3*j - 2*i + 12 = 3*i. Factor -3/2*c - 1/2*c**2 - j.
-(c + 1)*(c + 2)/2
Let w(p) = p**2 - 7*p - 5. Let h be w(8). Let d(v) = 2*v**3 - v**2 + 4*v. Let q be d(h). Factor 2 + q*m**2 + 5 + 67*m**3 + 30*m**4 - 3 + 9*m**5 + 9*m**4 + 24*m.
(m + 1)**3*(3*m + 2)**2
Factor 1/3*d**2 + 0 + 0*d**3 - 1/3*d**4 + 0*d.
-d**2*(d - 1)*(d + 1)/3
Let c(h) = -5*h**2 - 16*h - 32. Let z(l) = -4*l**2 - 16*l - 32. Let s(f) = -4*c(f) + 6*z(f). Factor s(a).
-4*(a + 4)**2
Suppose -6*z - 12*z**2 - 3/4 = 0. Calculate z.
-1/4
Let u be (-2)/2*35/(-10). Let 1 - u*x + 3*x**2 = 0. What is x?
1/2, 2/3
Let c(y) be the third derivative of 4*y**5/75 - 3*y**4/20 + y**3/15 - 28*y**2. Factor c(h).
2*(h - 1)*(8*h - 1)/5
Let r(u) = -2*u**2 + 14*u - 5. Let q be r(8). Let h = -18 - q. Factor -4/3*o**h - 2/3*o**2 + 0*o + 0 - 2/3*o**4.
-2*o**2*(o + 1)**2/3
Factor 0 - 7/5*w**4 + 0*w - 2/5*w**2 - 9/5*w**3.
-w**2*(w + 1)*(7*w + 2)/5
Let n be (-2)/4*(-1 - -1). Suppos