= v**2 - v. Let w(j) = 2*j**3 + 24*j**2 + 156*j + 250. Let g(o) = 6*r(o) + w(o). Factor g(y).
2*(y + 5)**3
Find f, given that -4/9*f**2 - 2/9*f**5 + 2/9*f**4 + 2/9 - 2/9*f + 4/9*f**3 = 0.
-1, 1
Let b be (-85)/(-10)*(2 - 0). Let k be 2*(3 + b/(-6)). Determine w, given that -2/3 - w - k*w**2 = 0.
-2, -1
Let g(s) = s + 26. Let a be g(-12). Let j be (a/21)/((-3)/(-9)). Suppose 1 - 1/2*c**j + 1/2*c = 0. What is c?
-1, 2
Let t(c) = -c**2 - 10*c - 8. Let a be t(-9). Let l be (a/(-2))/(4/(-16)). Factor -3*y - 3*y**3 + 6*y**3 + 2 - y**2 - y**l.
(y - 1)*(y + 1)*(3*y - 2)
Factor -3/5*f**3 + 3/5*f + 6/5*f**2 - 6/5.
-3*(f - 2)*(f - 1)*(f + 1)/5
Let g = 209/35 - 39/7. Let i(b) be the first derivative of 2/5*b - 1/15*b**6 + 4/3*b**3 + g*b**5 - b**4 - b**2 + 1. Factor i(m).
-2*(m - 1)**5/5
Let d(z) = -z**2 - 6*z - 3. Let s be d(-5). Let j(c) be the second derivative of 1/4*c**3 + 0 + 1/4*c**2 - s*c - 1/24*c**4 - 3/40*c**5. Factor j(i).
-(i - 1)*(i + 1)*(3*i + 1)/2
Let -2*p**2 - 4*p**2 - p**2 + 5*p**2 = 0. Calculate p.
0
Let v(f) be the second derivative of f**4/3 + 4*f**3/3 + 2*f**2 - 7*f. Suppose v(t) = 0. What is t?
-1
Factor 1/3*z**2 - 2/3 - 1/3*z.
(z - 2)*(z + 1)/3
Let d(l) = 42*l**3 + 2*l**2 + 2*l - 6. Let r(o) = -126*o**3 - 6*o**2 - 5*o + 17. Let i(x) = -17*d(x) - 6*r(x). Suppose i(v) = 0. Calculate v.
-1/3, 0, 2/7
Let n(z) be the third derivative of 0 + 1/315*z**7 - 1/2016*z**8 + 0*z - 1/180*z**5 - 1/180*z**6 - 8*z**2 + 5/144*z**4 - 1/18*z**3. Find o, given that n(o) = 0.
-1, 1, 2
Let w(c) be the third derivative of 0*c**3 + 0*c - 4*c**2 + 1/12*c**4 - 1/60*c**5 + 0. Suppose w(a) = 0. What is a?
0, 2
Let t(q) = -2*q**2 - 9*q - 11. Let y(n) = n**2 + 4*n + 5. Let j(f) = -4*t(f) - 7*y(f). Let b be j(-7). Factor -2 + b*w**4 + 2*w + w + w - 4*w**3.
2*(w - 1)**3*(w + 1)
Suppose 28*n**4 + 0*n**3 - 29*n**4 - n + 2*n**3 - 1 + 2*n**2 - n**5 = 0. What is n?
-1, 1
Let u(b) = -3 + 0*b - 3 - 3*b + 2*b. Let w be u(-6). Let -2/7*d - 2/7*d**2 + w = 0. What is d?
-1, 0
Let t(f) be the third derivative of f**5/270 + f**4/108 - 2*f**3/27 + f**2. Solve t(v) = 0 for v.
-2, 1
Suppose -4*d = 23 - 299. Find k such that -15*k**3 - 48*k + 16*k**3 - d*k**2 - 9*k**4 - 19*k**3 - 12 - 24*k**3 = 0.
-2, -1, -2/3
Determine f so that f**4 - 2/3*f - f**2 + 0 + 2/3*f**3 = 0.
-1, -2/3, 0, 1
Let y(d) = 12*d**4 - 50*d**3 + 10*d**2 - 14. Let t(j) = -4*j**4 + 17*j**3 - 3*j**2 + 5. Let h(u) = -14*t(u) - 5*y(u). Factor h(a).
-4*a**2*(a - 2)*(a - 1)
Let a(s) be the first derivative of -s**5/10 + 5*s**4/8 - s**3/3 - 2*s**2 + 67. Let a(j) = 0. What is j?
-1, 0, 2, 4
Let t be 0 - 0 - -1 - 1/3. Factor 5/3*x + t + x**2.
(x + 1)*(3*x + 2)/3
Let p(j) be the third derivative of -1/2352*j**8 + 0*j**3 + 5*j**2 + 0*j**5 + 1/420*j**6 - 1/168*j**4 + 0 + 0*j + 0*j**7. Suppose p(d) = 0. Calculate d.
-1, 0, 1
Suppose k + 88 - 90 = 0. Factor 1/3*f + 0 - 1/3*f**k.
-f*(f - 1)/3
Let p(q) = 9*q**3 - 9*q**2 - 2*q + 2. Let g = 4 + -7. Let k(c) = -2*c - 3*c**2 + 4*c**3 + 1 + c - c**2. Let i(l) = g*p(l) + 7*k(l). Find b such that i(b) = 0.
-1, 1
Let y be (6*(-2)/(-48))/(3/36). Let q = -2 + 2. Let 1/2*u**2 + q + u - 1/2*u**y = 0. What is u?
-1, 0, 2
Let w(g) = g**2 + 23*g. Let a be w(-23). Let s(o) be the second derivative of 0*o**3 - 2*o + a + 0*o**2 - 1/8*o**4. Solve s(c) = 0.
0
Let a(k) be the first derivative of -k**4/10 + k**2/5 + 3. Solve a(o) = 0.
-1, 0, 1
Let d(s) be the first derivative of -s**6/50 - 3*s**5/50 + s**3/5 + 3*s**2/10 - 3*s - 3. Let p(i) be the first derivative of d(i). Factor p(b).
-3*(b - 1)*(b + 1)**3/5
Let y be 6 + -8 + (-14)/(-4). What is t in -3/2*t**2 - y*t - 1/2 - 1/2*t**3 = 0?
-1
What is g in 0*g**4 + 5/4*g**3 + 0 + 0*g - 5/4*g**5 + 0*g**2 = 0?
-1, 0, 1
Let j(s) be the second derivative of 2662*s**6/15 + 121*s**5 - 198*s**4 + 248*s**3/3 - 16*s**2 + 8*s. Determine w so that j(w) = 0.
-1, 2/11
Let s = 1/269 + 3223/1345. Let 0*z + 0*z**2 + 0 - 12*z**4 - s*z**3 - 15*z**5 = 0. What is z?
-2/5, 0
Determine d so that 3*d**2 + 6/5*d**3 + 6/5*d + 0 = 0.
-2, -1/2, 0
Let r(f) be the first derivative of f**4/18 - 2*f**3/9 + 2*f**2/9 - 23. Factor r(n).
2*n*(n - 2)*(n - 1)/9
Let q(m) be the first derivative of 0*m**3 - 1/5*m**5 - 1/15*m**6 - m + 0*m**2 - 1 - 1/6*m**4. Let b(x) be the first derivative of q(x). Factor b(i).
-2*i**2*(i + 1)**2
Let y be 1 + -3*1/5. Factor -y*p**5 + 2/5*p**3 + 0 + 2/5*p**2 + 0*p - 2/5*p**4.
-2*p**2*(p - 1)*(p + 1)**2/5
Let d(x) = 2*x + 8. Let o be d(-6). Let p = o - -7. What is m in -m**p - 2*m**2 + 2*m**2 = 0?
0
Let v(o) be the third derivative of -3*o**8/28 + 13*o**7/70 - o**5/20 + 8*o**2. Suppose v(h) = 0. What is h?
-1/4, 0, 1/3, 1
Let k be 30/7 + (-4)/14. Let u(f) be the second derivative of 0*f**2 + f + 1/33*f**3 - 1/22*f**k + 0 + 3/110*f**5 - 1/165*f**6. Let u(q) = 0. What is q?
0, 1
Let q = 6 + -1. Suppose 3 - 18 = -q*n. Factor -2/9*j**n + 0 - 2/9*j - 4/9*j**2.
-2*j*(j + 1)**2/9
Let b(x) be the first derivative of -4*x**3/27 + 4*x**2/9 - 4*x/9 - 9. Factor b(u).
-4*(u - 1)**2/9
Let v(l) be the first derivative of l**3/9 - 5*l**2/6 + 4*l/3 + 32. Find w such that v(w) = 0.
1, 4
Let l = 25 - 21. Factor -2 + 3 + 7 + 12*y - l*y**2 + 8.
-4*(y - 4)*(y + 1)
Let -4*u**2 + 5/2*u**4 + 2*u + 0 - 3/2*u**3 + u**5 = 0. Calculate u.
-2, 0, 1/2, 1
Suppose -3 = -v + 3*c + 3, v + 5*c = -10. Factor v*x - 1/7*x**2 + 4/7.
-(x - 2)*(x + 2)/7
Suppose -7*r - 2*d = -6*r - 13, -3*r + 4*d - 11 = 0. Factor 0 - 2/7*a**r - 2/7*a - 4/7*a**2.
-2*a*(a + 1)**2/7
Let 0*d + 0*d**2 + 0*d**3 + 3/5*d**4 + 0 + 3/5*d**5 = 0. What is d?
-1, 0
Let u(v) = -v**5 + v**4 + v**3 - 7*v**2 - 6. Let m(g) = g**2 + 1. Let k(w) = 6*m(w) + u(w). Factor k(s).
-s**2*(s - 1)**2*(s + 1)
Determine v so that -9*v**3 + 8*v**3 - 3*v**3 - 4*v + 8*v**2 + 0*v = 0.
0, 1
Let c(q) = q**2 + 5*q - 11. Let g be c(-6). Let r(y) = -4*y**2 + 3*y - 4. Let x(t) = t. Let l(u) = g*x(u) - r(u). Find n such that l(n) = 0.
1
Let s(b) = -b**3 + 15*b**2 - 13*b - 12. Let w be s(14). Factor -10*j**3 + 12*j**3 + w*j**2 - 4 + 2*j**2 - 2*j.
2*(j - 1)*(j + 1)*(j + 2)
Let k(a) be the third derivative of a**5/60 + a**4/6 + a**3/2 - 5*a**2. Factor k(l).
(l + 1)*(l + 3)
Let g be (21/(-189))/((-2)/3). Let n(v) be the second derivative of 23/60*v**6 + 0*v**2 + g*v**4 + 0*v**3 + v + 1/2*v**5 + 0 + 1/12*v**7. What is t in n(t) = 0?
-2, -1, -2/7, 0
Let j = 0 - 3. Let o = j - -3. Suppose 0 + 0*g - 1/4*g**3 + o*g**2 = 0. What is g?
0
Let u(k) = 2*k**2 + 6*k + 6. Let p be u(-3). Suppose 0 = -2*b - 0*b - 2*s + p, -6 = -2*b - 5*s. Factor -35/2*n**b - 3/2*n**2 + 0 + n.
-n*(5*n - 1)*(7*n + 2)/2
Let o(m) be the first derivative of -m**4/12 - m**3/3 - 23. Factor o(h).
-h**2*(h + 3)/3
Let q(p) be the second derivative of p**5/40 + p**4/24 + 4*p. Factor q(c).
c**2*(c + 1)/2
Let k = 91 + -86. Let c(i) be the first derivative of -2/11*i**2 - 2/11*i + 0*i**3 + 1/11*i**4 + 2/55*i**k + 3. Suppose c(b) = 0. What is b?
-1, 1
Find u, given that 0 - 2/7*u - 1/7*u**2 = 0.
-2, 0
Let d(s) be the first derivative of -3*s**5/10 - 3*s**4/4 + 3*s**2/2 + 3*s/2 - 15. Determine k so that d(k) = 0.
-1, 1
Let f = 39 - 39. Factor 0 + f*o - 48/5*o**4 + 0*o**2 + 14*o**5 + 8/5*o**3.
2*o**3*(5*o - 2)*(7*o - 2)/5
Let x(b) be the second derivative of 0 + 0*b**3 - 2*b - 1/42*b**4 + 1/7*b**2. Factor x(j).
-2*(j - 1)*(j + 1)/7
Let g(p) be the second derivative of p**7/210 + p**6/120 + 3*p**2/2 + 3*p. Let f(x) be the first derivative of g(x). Factor f(r).
r**3*(r + 1)
Let k = -81 + 81. Determine y so that -2/3*y**4 + k + 4/3*y + 2*y**2 + 0*y**3 = 0.
-1, 0, 2
Suppose 1/3 + 1/3*o**2 - 2/3*o = 0. What is o?
1
Let d be (-1)/(-3)*-1*-6. Suppose -4*i + d*h = -h - 14, 5*h + 12 = i. Factor 39*u**3 + 2*u - 11*u**3 - 22*u**i + 2*u.
2*u*(2*u - 1)*(7*u - 2)
Factor 9*v**3 - v**4 - 8*v**4 - 4*v**2 + v**2 + 3*v**5.
3*v**2*(v - 1)**3
Let z(j) = j**3 + 3*j**2 + 2*j + 2. Let l be z(-2). Factor 3*m**3 - 3 - 4*m**l - 1 + 6 - m.
(m - 1)**2*(3*m + 2)
Let p(v) = -v + 4. Suppose -s + 7 - 3 = 0. Let u be p(s). Determine k, given that 1/2*k**5 + 0*k + 1/4*k**2 + k**3 + u + 5/4*k**4 = 0.
-1, -1/2, 0
Let v(p) be the second derivative of -p**4/114 - 10*p**3/57 - 25*p**2/19 - 11*p. Factor v(s).
-2*(s + 5)**2/19
Let j(w) be the second derivative of 0*w**2 + 0 + 0*w**3 - 1/48*w**4 + 2*w. Factor j(l).
-l**2/4
Let t(a) be the third derivat