**5 - 1/4 - 5/2*z**f - 5/2*z**2 - 5/4*z**4 - 5/4*z.
-(z + 1)**5/4
Let d(i) be the second derivative of -i**4/36 - 2*i**3/3 + 49*i. Factor d(t).
-t*(t + 12)/3
Let l = -2 - -5. Factor -8 + 6*o**2 + 8*o + o**4 + o**4 + 3*o**l - 11*o**3.
2*(o - 2)**2*(o - 1)*(o + 1)
Find n, given that -4/7*n**5 - 6/7*n**4 + 8/7*n**2 + 0*n + 4/7*n**3 - 2/7 = 0.
-1, 1/2, 1
Let q(h) be the first derivative of h**6/2 - 3*h**4 + 2*h**3 + 9*h**2/2 - 6*h + 16. Determine r so that q(r) = 0.
-2, -1, 1
Let j(a) be the first derivative of -1/48*a**4 + a - 1 + 0*a**2 + 1/24*a**3. Let p(l) be the first derivative of j(l). Find v such that p(v) = 0.
0, 1
Let i(z) = 2*z**2 - 10*z + 6. Let m be i(7). Suppose -4*l + 33 = -w, 4*w + 14 = 4*l - m. Let 6*x**3 - l + 3*x**4 + 1 + 3 - 6*x = 0. What is x?
-1, 1
Let m(a) = -2*a - 7. Let w be m(-9). Let h be (-4)/6 - w/(-12). Find f, given that h*f**4 - 1/2*f**2 + 1/4 + 0*f + 0*f**3 = 0.
-1, 1
Let u(w) be the third derivative of w**7/420 + w**6/240 - w**5/120 - w**4/48 - 3*w**2. Solve u(s) = 0.
-1, 0, 1
Let g(k) be the second derivative of -k**4/6 - k**3/3 + 10*k. Suppose g(p) = 0. What is p?
-1, 0
Solve 320/3 - 80/3*a + 5/3*a**2 = 0 for a.
8
Let f(j) = -74*j**4 + 166*j**3 - 120*j**2 + 26*j - 4. Let r(c) = c**4 + c**3 - c**2 + c + 1. Let l(h) = f(h) + 2*r(h). Factor l(p).
-2*(p - 1)**2*(6*p - 1)**2
Let a = 7 - 5. Factor a*d**2 - 27*d - 2*d**3 + d**3 + 26*d.
-d*(d - 1)**2
Let v(m) be the third derivative of -m**10/151200 + m**9/37800 - m**7/6300 + m**6/3600 + m**4/12 + m**2. Let i(b) be the second derivative of v(b). Factor i(h).
-h*(h - 1)**3*(h + 1)/5
Let w(d) be the third derivative of -d**6/132 + 7*d**5/330 + 7*d**4/33 - 4*d**3/11 + 27*d**2. Suppose w(z) = 0. What is z?
-2, 2/5, 3
Let h = 34 + -34. Suppose h*d + 1/4*d**3 + 0 - 1/4*d**2 = 0. What is d?
0, 1
Let t(j) be the third derivative of 0*j**3 - 3/7*j**7 + 0*j**4 - 2/15*j**5 + 0*j - 3*j**2 + 0 + 25/168*j**8 + 2/5*j**6. Factor t(y).
2*y**2*(y - 1)*(5*y - 2)**2
Let l(q) be the third derivative of 0*q**3 + 0 - q**2 - 1/240*q**5 + 0*q - 1/96*q**4. Factor l(p).
-p*(p + 1)/4
Let v(o) be the second derivative of -o**6/180 - o**5/30 - 5*o**4/72 - o**3/18 - 34*o. Suppose v(g) = 0. Calculate g.
-2, -1, 0
Let w(m) be the first derivative of -25*m**6/6 - 7*m**5 - 5*m**4/2 - 5. What is f in w(f) = 0?
-1, -2/5, 0
Let d(o) = o**2 - 1. Let l(f) = -10*f**2 - 2*f + 11. Let n(x) = 22*d(x) + 2*l(x). Factor n(m).
2*m*(m - 2)
Let k be 3/(-96)*4*4/(-18). Let n(d) be the third derivative of 1/90*d**5 + 0 + k*d**4 + 0*d + 0*d**3 + d**2. Solve n(b) = 0 for b.
-1, 0
Suppose 2*y - 6 = -u, -2*y - 2*u = 3*u - 14. Find q, given that -q**y + 2 - 7/3*q = 0.
-3, 2/3
Let j(w) = w**2 - 1 + w + 3 - 3. Let p(t) = 3*t**3 - 8*t**2 + t + 2. Let o(f) = -2*j(f) - p(f). Factor o(l).
-3*l*(l - 1)**2
Let g(p) = 4*p**2 - 2. Let r be 8/(-36) - (-22)/18. Suppose 0*y = y + 2. Let d(b) = b**2 - 1. Let j(t) = r*g(t) + y*d(t). Let j(s) = 0. What is s?
0
Let x(o) be the second derivative of o**6/36 - o**5/40 - o**4/36 + 6*o. What is p in x(p) = 0?
-2/5, 0, 1
Factor -3*k + k**2 + 8*k - 6*k.
k*(k - 1)
Let p(k) be the first derivative of -2*k**6/21 + 4*k**5/35 + k**4/7 - 4*k**3/21 - 18. Suppose p(x) = 0. Calculate x.
-1, 0, 1
Let u(a) be the second derivative of -a**7/84 + a**6/60 + a**5/40 - a**4/24 + 9*a. Factor u(k).
-k**2*(k - 1)**2*(k + 1)/2
Let a(j) be the first derivative of 0*j + 0*j**3 - j**4 - 2*j**5 + 0*j**2 + 7/3*j**6 + 4. Factor a(t).
2*t**3*(t - 1)*(7*t + 2)
Let l = 43/3 + -14. Let t(h) be the third derivative of 0*h + l*h**3 - 1/4*h**4 + 0 + 0*h**5 - h**2 + 1/15*h**6. Factor t(x).
2*(x + 1)*(2*x - 1)**2
Solve -40 + 7*s**2 + 37 - 6*s + 2*s**2 = 0 for s.
-1/3, 1
Let y(i) be the first derivative of -i**6/60 - i**5/30 - i**2/2 + 1. Let b(h) be the second derivative of y(h). Suppose b(o) = 0. What is o?
-1, 0
Let b(a) be the second derivative of -a**6/10 + 3*a**5/10 - a**3 + 3*a**2/2 + 2*a. Factor b(o).
-3*(o - 1)**3*(o + 1)
Let c(s) = -s**3 + s**2 - 1. Let v(p) = -7*p**3 + 25*p**2 - 38*p + 11. Let f(b) = 18*c(b) - 2*v(b). Factor f(r).
-4*(r - 1)**2*(r + 10)
Suppose 0*h = b + 5*h, -b + 5*h = 0. Let b*m + 0 - 3/7*m**2 = 0. What is m?
0
Factor 2/7*x + 4/7 - 2/7*x**2.
-2*(x - 2)*(x + 1)/7
Let t(x) = -2*x**3 + 11*x**2 + 5*x + 8. Let u be t(6). Let p(j) be the first derivative of 0*j + 1/7*j**u - 2/21*j**3 - 2. Factor p(b).
-2*b*(b - 1)/7
Let t(n) be the second derivative of n**4/90 - 2*n**3/45 + n**2/15 - 5*n. Factor t(b).
2*(b - 1)**2/15
Factor -2/7*h**3 - 3/7*h**2 + 1/7*h**4 + 8/7*h - 4/7.
(h - 2)*(h - 1)**2*(h + 2)/7
Suppose 5*y - 20 = -10. Factor 2 - 2*l**y + 16/3*l.
-2*(l - 3)*(3*l + 1)/3
Factor 5 + 35/4*r**2 - 20*r.
5*(r - 2)*(7*r - 2)/4
Suppose 4*i + 4*y - 24 = 2*i, y = -5*i + 15. Suppose -6*d**i - d - 2*d**3 + 8*d**2 + d = 0. What is d?
0, 1
Let s(b) be the third derivative of 3/50*b**5 + 1/525*b**7 + 2/15*b**3 + 7/60*b**4 - 2*b**2 + 0 + 0*b + 1/60*b**6. Factor s(p).
2*(p + 1)**3*(p + 2)/5
Let y(d) be the first derivative of d**8/1680 - d**6/300 + d**4/120 + 3*d**2/2 + 3. Let c(x) be the second derivative of y(x). Factor c(w).
w*(w - 1)**2*(w + 1)**2/5
Let o be (-56)/(-26) - (64/(-26))/(-16). Find n such that -4/11*n**3 + 0 + 0*n**2 + 26/11*n**4 + 0*n - o*n**5 = 0.
0, 2/11, 1
Let u(r) = 6*r**3 - 6*r**2 + 8*r. Let n(d) = -2*d**3 + 2*d**2 - 3*d. Let z(v) = 8*n(v) + 3*u(v). Factor z(y).
2*y**2*(y - 1)
Suppose 2*k + 80 = 90. Factor -2/3*v**4 - 2/3 - 2/3*v + 4/3*v**3 + 4/3*v**2 - 2/3*v**k.
-2*(v - 1)**2*(v + 1)**3/3
Let z(g) = g**5 + g**3 - g**2 + 1. Let s(w) = -13*w**5 - 12*w**4 - 9*w**3 + 8*w**2 - 6. Let b = 8 - 9. Let n(h) = b*s(h) - 6*z(h). Factor n(y).
y**2*(y + 1)**2*(7*y - 2)
Let i(z) be the third derivative of -1/336*z**8 + 0 + 0*z**6 + 0*z**3 + 0*z + 1/30*z**5 + 1/24*z**4 - z**2 - 1/105*z**7. Determine g so that i(g) = 0.
-1, 0, 1
Let x(p) = p**2 - p - 1. Let i be x(-2). Let g be 2/4*2*i. Factor -2/7*n**g + 0*n + 2/7*n**3 + 0 + 0*n**4 + 0*n**2.
-2*n**3*(n - 1)*(n + 1)/7
Factor 2644 + 65*r**2 + 15*r - 2644 + 20*r**3.
5*r*(r + 3)*(4*r + 1)
Let j(m) be the second derivative of -1/30*m**4 + 0*m**2 - 1/15*m**3 + 2*m + 0. Factor j(y).
-2*y*(y + 1)/5
Let a(w) = -w**2 - 2*w + 6. Let g(z) = 5*z**2 + 11*z - 31. Let x(u) = -11*a(u) - 2*g(u). Factor x(y).
(y - 2)*(y + 2)
Let i(p) be the second derivative of -2*p**7/21 - 4*p**6/15 + 2*p**4/3 + 2*p**3/3 - 6*p. Factor i(j).
-4*j*(j - 1)*(j + 1)**3
Let u(i) be the second derivative of 1/12*i**4 + 0 + 0*i**3 + 3*i + 0*i**2. Let u(x) = 0. Calculate x.
0
Suppose 3*a - 4 = 5. Let s be 1*a/(-9)*-1. Factor -s*d**5 + 0*d**2 + 0 - 1/3*d**3 + 2/3*d**4 + 0*d.
-d**3*(d - 1)**2/3
Let x(f) be the first derivative of f**4/2 - 4*f**3/3 + f**2 + 11. Solve x(p) = 0 for p.
0, 1
Suppose v + v - q = -83, -2*q - 10 = 0. Let a be v/(-10) + (-2)/5. Factor 2*z**3 - 4*z**2 - 2*z**4 + 2*z**5 - a*z**5 + 6*z**2.
-2*z**2*(z - 1)*(z + 1)**2
Let a(h) = 8*h**5 + 45*h**4 + 51*h**3 + 24*h**2. Let z(q) = -4*q**5 - 22*q**4 - 26*q**3 - 12*q**2. Let w(r) = 2*a(r) + 5*z(r). Solve w(m) = 0 for m.
-3, -1, 0
Let n(g) be the second derivative of 5*g**4/12 - 5*g**3 - 35*g**2/2 + g. What is a in n(a) = 0?
-1, 7
Let o(q) = q**2 + q. Let a(g) = 12*g**2 + 6*g. Let x(s) = -a(s) + 10*o(s). Factor x(u).
-2*u*(u - 2)
Let v(l) = 5*l - 1. Let f(a) = a - 3. Let t be f(4). Let k be v(t). Factor -4*d**3 - 2*d**3 + d**k + 6*d**3.
d**4
Let d(h) be the first derivative of h**5/15 + h**4/6 - h**3/9 - h**2/3 - 1. Factor d(u).
u*(u - 1)*(u + 1)*(u + 2)/3
Let m(b) = 5*b**3 + 27*b**2 + 33*b + 17. Let t(n) = -60*n**3 - 325*n**2 - 395*n - 205. Let j(g) = 25*m(g) + 2*t(g). Factor j(a).
5*(a + 1)**2*(a + 3)
What is n in 0*n**5 + n**5 - 4*n**4 + n**3 + 2*n**4 = 0?
0, 1
Let p(r) be the third derivative of -r**8/84 + 2*r**7/35 - r**6/15 - 2*r**5/15 + r**4/2 - 2*r**3/3 + 21*r**2 + r. Determine t so that p(t) = 0.
-1, 1
Let p(u) be the third derivative of -u**8/16800 - u**7/6300 + u**4/12 + 5*u**2. Let l(n) be the second derivative of p(n). Factor l(h).
-2*h**2*(h + 1)/5
Factor -6*t**4 - 42*t**3 + 11*t**2 - 3*t + 36*t**4 - 9*t**5 + 7*t**2 + 6*t**3.
-3*t*(t - 1)**3*(3*t - 1)
Let n(b) = 10*b - 48. Let v be n(5). Factor -1/3*i**v + 1/3*i + 0.
-i*(i - 1)/3
Factor 2/9*m**2 + 0 - 2/9*m**4 - 2/9*m + 2/9*m**3.
-2*m*(m - 1)**2*(m + 1)/9
Suppose -8*q - 16 = -12*q.