be (-1)/4 - 4/(-16). Suppose 4*g + 5*b = n, 2*g + b = -b. Factor -2/9*i**2 + g*i + 2/9.
-2*(i - 1)*(i + 1)/9
Suppose -8*t - 8 = -10*t. Let -8*o**4 - 10*o**3 - 12*o**2 - 2*o**3 - 2*o - 2*o**5 + 0*o**5 + t*o**2 = 0. What is o?
-1, 0
Let y(t) = 9*t**3 + 17*t**2 + 3*t. Let q(s) = -28*s**3 - 52*s**2 - 8*s. Let w(d) = 5*q(d) + 16*y(d). Suppose w(v) = 0. Calculate v.
-2, -1, 0
Find j such that -2/3*j**2 - 2/5 - 14/15*j - 2/15*j**3 = 0.
-3, -1
Factor -3*b**4 - 517*b**3 + 541*b**3 - 7*b**4 - 12*b + 22*b**2.
-2*b*(b - 3)*(b + 1)*(5*b - 2)
Let r(l) = 4*l - 15. Let n be r(5). What is q in 2/5 - 4/5*q**n + 2/5*q**4 - 4/5*q**2 + 8/5*q**3 - 4/5*q = 0?
-1, 1/2, 1
Let u(z) be the first derivative of -2*z**3/21 + 5*z**2/7 - 8*z/7 - 14. Factor u(r).
-2*(r - 4)*(r - 1)/7
Let s(z) = 26*z**2 + 69*z + 400. Let j(v) = -7*v**2 - 17*v - 100. Let u(f) = -22*j(f) - 6*s(f). Factor u(l).
-2*(l + 10)**2
Let s(r) = r**2 - r. Let a(h) = 7*h**2 - 6*h - 1. Let u(x) = 13*x**2 - 11*x - 2. Let b(z) = 11*a(z) - 6*u(z). Let i(f) = -3*b(f) - 6*s(f). Factor i(w).
-3*(w - 1)**2
Let z be 6 + 2*(-1 + 0). Suppose -z = -4*u + 12. Factor s**2 + 2*s**u - 6*s**3 + 3*s**2 - 2*s + 2*s**2.
2*s*(s - 1)**3
Determine i so that -4/5*i**2 + 4/5*i**4 - 3/5*i**3 + 0 - 1/5*i**5 + 4/5*i = 0.
-1, 0, 1, 2
Let r(i) = i**4 + i**3 - i**2 + i - 1. Let j(w) = -10*w**4 - 11*w**3 + 8*w**2 - 9*w + 9. Let b(s) = 2*j(s) + 18*r(s). Factor b(x).
-2*x**2*(x + 1)**2
Let r = 212 - 1480/7. Let p(w) be the second derivative of 0 + 1/42*w**4 + 3*w + 4/21*w**3 + r*w**2. Factor p(c).
2*(c + 2)**2/7
Let g(u) be the first derivative of -9/4*u**2 + 6 + 0*u**3 - 3*u + 3/8*u**4. Factor g(k).
3*(k - 2)*(k + 1)**2/2
Let n(y) be the second derivative of 5*y**7/42 + y**6/6 - y**5/2 - 13*y. Suppose n(u) = 0. Calculate u.
-2, 0, 1
Factor -5*n**2 - 4*n + 4*n**2 - 5*n**3 - 4*n**2 + 13*n**2 + n**4.
n*(n - 2)**2*(n - 1)
Let p = -17 + 19. Let z(x) be the second derivative of 2*x - 1/15*x**3 + 0*x**p + 1/60*x**4 + 0. Factor z(w).
w*(w - 2)/5
Let p(o) be the second derivative of -3*o**5/35 + 39*o**4/28 - 13*o**3/7 - 27*o**2/14 + 8*o + 3. Find f, given that p(f) = 0.
-1/4, 1, 9
Let f be (-1)/3 + (-24)/9. Let w(b) = 2*b**2 - 3*b - 3. Let i(t) = 3*t**2 - 4*t - 4. Let x(u) = f*i(u) + 4*w(u). Determine l, given that x(l) = 0.
0
Let z(w) be the third derivative of w**5/270 - w**4/6 + 3*w**3 - 61*w**2. Find u such that z(u) = 0.
9
Let t(z) = -z**3 + 6*z**2 - 6*z + 7. Let x be t(5). Let n be (-3 - -2 - -1) + x. Factor 5*h**3 + n*h**3 - 5*h**3.
2*h**3
Factor -6/7*o**3 - 2/7*o**2 + 0*o - 2/7*o**5 + 0 - 6/7*o**4.
-2*o**2*(o + 1)**3/7
Let j(r) be the third derivative of -r**6/15 - r**5/15 + r**4/3 + 2*r**3/3 - 7*r**2. Suppose j(z) = 0. Calculate z.
-1, -1/2, 1
Let s(j) be the second derivative of -81*j**7/70 - 63*j**6/25 + 51*j**5/25 - 2*j**4/5 - 5*j. Solve s(d) = 0 for d.
-2, 0, 2/9
Suppose h + 5*o + 4 = 5*h, -2*h = 3*o - 2. Let g = h - -1. Factor -2/3 - 2/3*b**g + 4/3*b.
-2*(b - 1)**2/3
Factor 4/3*b**5 - 1/3*b**2 + 0*b + 0 + 2/3*b**3 + 7/3*b**4.
b**2*(b + 1)**2*(4*b - 1)/3
Let w(v) be the first derivative of 27*v**5/40 - 5*v**4/8 - 8*v**3/9 - v**2/3 - 2*v - 4. Let l(x) be the first derivative of w(x). Factor l(n).
(n - 1)*(9*n + 2)**2/6
Determine g so that 0 - 3/7*g - 1/7*g**2 = 0.
-3, 0
Suppose -9 = -5*g + 11. Factor 2*s**4 - s**4 + 3*s**3 + s**5 - g*s**3 - s**2.
s**2*(s - 1)*(s + 1)**2
Let x(y) be the first derivative of -5 + 1/360*y**6 + 1/6*y**4 + 1/30*y**5 + 0*y**2 + 0*y - y**3. Let a(p) be the third derivative of x(p). Factor a(z).
(z + 2)**2
Let m = 881/333 - -17/222. Let s = 50/9 - m. Solve 1/3 - 2*b**3 - 1/2*b - s*b**2 = 0 for b.
-1, -2/3, 1/4
Let c(k) be the third derivative of k**8/1344 - k**6/480 + k**2. Find v, given that c(v) = 0.
-1, 0, 1
Let w(k) = -k + 7. Let s be w(4). Suppose -3*v = -19 - 2. Suppose 4*z - 18*z**5 + 10*z - 44*z**s + 10*z**4 - 16*z**2 + 50*z**4 + v - 3 = 0. What is z?
-1/3, 1, 2
Let m(o) = -o - 3. Let q be m(-3). Let y = q + 2. Factor 4*t + 2*t**2 - 4*t**3 + 6*t**2 - 2*t**2 + 0*t**y.
-2*t*(t - 2)*(2*t + 1)
Let f be ((-104)/9 - 2)/((-44)/33). Let w(l) be the first derivative of -21/16*l**4 - f*l**3 + 4 + 49/20*l**5 - 15/2*l**2 - 2*l. Suppose w(i) = 0. Calculate i.
-1, -2/7, 2
Suppose -8 = -2*p - 8. Let m(j) be the third derivative of 1/240*j**5 + p*j**4 + 0 + 2*j**2 - 1/24*j**3 + 0*j. Factor m(v).
(v - 1)*(v + 1)/4
Let 0 + 2/3*o**2 - 2/3*o - 2/3*o**4 + 2/3*o**3 = 0. Calculate o.
-1, 0, 1
Let f(s) be the second derivative of -1/16*s**4 + 0*s**2 + 5*s + 0 + 0*s**3. Factor f(r).
-3*r**2/4
Let h be (18/3)/(3/2). Let c(y) be the second derivative of 2/3*y**2 - 1/18*y**h - y + 0 + 1/9*y**3. Factor c(q).
-2*(q - 2)*(q + 1)/3
Let u be (-3)/(-14) + 8/28. Let y = -5/6 + 13/12. Find t such that y*t**2 + 1/4 - u*t = 0.
1
Let u(b) be the second derivative of 1/6*b**4 + b + 0*b**2 + 0*b**3 + 0. Factor u(a).
2*a**2
Let t(a) be the second derivative of a**5/150 - 2*a**4/45 + 4*a**3/45 + 20*a. Solve t(z) = 0.
0, 2
Let a(x) be the second derivative of -x**5/80 + x**4/16 + 2*x. Factor a(g).
-g**2*(g - 3)/4
Let s(y) = y. Let l(h) = 5*h**2 - 7*h - 30. Let z(c) = -l(c) - 2*s(c). Factor z(k).
-5*(k - 3)*(k + 2)
Let g(s) be the second derivative of s**9/128520 + s**8/28560 - s**6/3060 - s**5/1020 + s**4/12 - 5*s. Let z(n) be the third derivative of g(n). Factor z(f).
2*(f - 1)*(f + 1)**3/17
Suppose 0*b + 12/7*b**2 - 16/7 + 4/7*b**3 = 0. Calculate b.
-2, 1
Let 2/5*s + 2/5*s**4 + 4/5 - 6/5*s**2 - 2/5*s**3 = 0. Calculate s.
-1, 1, 2
Suppose -3*f + 16 - 3*f**2 + 3*f**3 + 0*f**3 - 13 = 0. What is f?
-1, 1
Let v(l) be the third derivative of 0*l + 1/195*l**6 + 1/39*l**3 + 5*l**2 + 1/65*l**5 + 1/1365*l**7 + 0 + 1/39*l**4. Factor v(z).
2*(z + 1)**4/13
Suppose -2 = d + d - 5*t, 5*t = -5*d + 30. Let k = -274 - -2474/9. Factor 0 + 2/9*z + k*z**2 + 4/3*z**3 + 8/9*z**d + 2/9*z**5.
2*z*(z + 1)**4/9
Let x be 1/(-4*(-4)/32). Let m = 375 + -1869/5. Factor -2/5*t + 0 - 6/5*t**x - 2/5*t**4 - m*t**3.
-2*t*(t + 1)**3/5
Let n(l) be the second derivative of l**7/63 + 7*l**6/90 + 3*l**5/20 + 5*l**4/36 + l**3/18 - 4*l. Factor n(h).
h*(h + 1)**3*(2*h + 1)/3
Suppose 0 = 4*p - 2*f + 4, -p + 4*f - 3*f - 3 = 0. Let c be p + -1 + 16/18. Factor 2/9*m**2 - 8/9*m + c.
2*(m - 2)**2/9
Let w(y) be the second derivative of -y**8/1344 + y**6/120 + y**5/120 - y**4/32 - y**3/12 - y**2/2 + 7*y. Let n(z) be the first derivative of w(z). Factor n(x).
-(x - 2)*(x - 1)*(x + 1)**3/4
Let a(d) = d + 10. Let v be a(-7). Let m = -3 - -8. Factor o**v + 1 + m*o - 6*o - 4*o**3 - 5*o**2.
-(o + 1)**2*(3*o - 1)
Suppose 0 = u + 2*r + 2 + 2, -u + 4*r = -2. Let l = 6 + u. Factor 5*j**l + 2*j**2 - 3*j**4 + 0*j**4 + 4*j**3.
2*j**2*(j + 1)**2
Let x(d) = -17*d**4 - 27*d**3 - 10*d**2 + 4*d + 4. Let f(y) = 18*y**4 + 27*y**3 + 9*y**2 - 3*y - 3. Let g(r) = -4*f(r) - 3*x(r). Let g(w) = 0. Calculate w.
-1, -2/7, 0
Let l be 2/(0 + 1 + 0). Let b(t) be the first derivative of 2*t + l + t**2 + 1/6*t**3. Let b(m) = 0. Calculate m.
-2
Let s(n) = 4*n**2 + 20*n - 24. Let c(b) = -4*b**2 - 20*b + 24. Let k(v) = -5*c(v) - 4*s(v). Factor k(x).
4*(x - 1)*(x + 6)
Suppose 4*s - 28 + 18 = 2*q, 4*s - 5*q = 13. Suppose -1/3*i**2 - 3 - s*i = 0. Calculate i.
-3
Let t(q) = 8*q**3 + 4*q**2 - 6*q + 2. Let f(a) = -a**5 - a**4 - 9*a**3 - 5*a**2 + 7*a - 3. Let y(s) = -2*f(s) - 3*t(s). Solve y(p) = 0 for p.
-2, -1, 0, 1
Factor -l**3 - 3/2*l**2 - 1/2*l + 0.
-l*(l + 1)*(2*l + 1)/2
Let l(a) be the first derivative of -a**3/2 - 3*a**2/2 + 9*a/2 - 1. Solve l(r) = 0 for r.
-3, 1
Factor -1/2*h**4 + 12*h + 4*h**3 - 11*h**2 - 9/2.
-(h - 3)**2*(h - 1)**2/2
Let u(a) = a**2 + 13*a - 35. Let j(l) = 12*l**2 + 142*l - 386. Let s(b) = 6*j(b) - 68*u(b). Factor s(y).
4*(y - 4)**2
Let u(k) = -k**2 + 2 + 5*k**2 - 5*k**2 - 2*k. Let t(v) = v**2 + 2*v - 1. Suppose 5 + 3 = 2*b. Let i(r) = b*u(r) + 6*t(r). Find w, given that i(w) = 0.
-1
Suppose 0 = -2*f - f. Suppose 3*t + 0*t = f. Determine q so that 0 - 1/4*q**2 + t*q = 0.
0
Let c(v) = 7*v**4 - 2*v**2 - 1. Let b(t) = 36*t**4 - 9*t**2 - 6. Let q(h) = -4*b(h) + 21*c(h). Let q(j) = 0. Calculate j.
-1, 1
Let l(x) = x**2 - 9*x + 2. Let v be l(9). Let u be (4/(-10))/(9/(-30)). Factor -u*i + 2*i**v - 2/3.
2*(i - 1)*(3*i + 1)/3
Let p(d) be the first derivative of -3*d**4/20 + d**3/5 + 3*d**2/10 - 3*d/5 - 10. Factor