8)). Factor 9*k**5 + 1 - 8*k**5 + 16*k - 5 + 19*k**3 - 25*k**d - 2*k**4 - 5*k**4.
(k - 2)**2*(k - 1)**3
Let u(l) be the first derivative of -3*l**4/20 - 1. Factor u(f).
-3*f**3/5
Let y(g) = -5*g**5 - 4*g**4 - 2*g**3 - 14*g**2 - 13*g + 4. Let p(m) = -m**5 - m**4 - m**2 - m + 1. Let k(v) = 6*p(v) - y(v). Factor k(a).
-(a - 2)*(a + 1)**4
Let v = -31/15 + 12/5. Factor v*g**2 + 1/3*g + 0.
g*(g + 1)/3
Find t, given that -3*t**4 - 16*t**3 - 25 + 23 - 21*t**2 - t**4 - 11*t = 0.
-2, -1, -1/2
Solve -4*d**2 - 5 + d**2 - 3*d + 5 = 0 for d.
-1, 0
Let x(s) = s. Let c(q) = q**2 + 3*q. Let p(o) = -o**3 + 4*o**2 + 2. Let g be p(4). Let v(a) = g*x(a) - c(a). Factor v(l).
-l*(l + 1)
Let f = 3/5 + 3/20. Suppose 1/4*s**3 + 0*s - 1 + f*s**2 = 0. Calculate s.
-2, 1
Let q(t) be the first derivative of 0*t - 1/420*t**6 + 1 - 1/7*t**4 + 8/21*t**3 + 1/35*t**5 - t**2. Let j(v) be the second derivative of q(v). Factor j(g).
-2*(g - 2)**3/7
Let i(u) be the second derivative of -u**8/5880 + u**6/1260 + u**3/6 - 2*u. Let h(b) be the second derivative of i(b). Factor h(z).
-2*z**2*(z - 1)*(z + 1)/7
Let 1/4 - w**3 - 1/4*w**2 + w = 0. Calculate w.
-1, -1/4, 1
Determine h, given that 0*h + 16/5*h**3 + 32/5*h**4 + 0 + 2/5*h**2 = 0.
-1/4, 0
Let h(p) be the first derivative of -3/2*p**4 + 3/5*p**5 + 0*p**2 + 3 + 0*p**3 + 0*p. Let h(a) = 0. Calculate a.
0, 2
Factor 0 - 1/5*k**2 + 2/5*k.
-k*(k - 2)/5
Let b(j) be the second derivative of 0*j**2 - 1/84*j**4 + 0*j**3 - 7*j + 0. Factor b(x).
-x**2/7
Let w(q) = 3*q**4 - 4*q**3 + 2*q**2 + 2*q + 1. Let d(c) = 9*c**3 - 5 - 1 - 4*c - 5*c**2 - 7*c**4 + 2 + 1. Let i(g) = -2*d(g) - 5*w(g). Factor i(k).
-(k - 1)**3*(k + 1)
Suppose 2*a - 4*b = -0*a + 4, 0 = a - 3*b. Suppose -a*r + r + 10 = 0. Solve o**r + 0*o**2 + 0*o**2 + 1 - 2*o = 0 for o.
1
Let y(w) = w**2 - 2*w + 5. Let b(n) = -2*n**2 + 4*n - 9. Let p(a) = -4*b(a) - 7*y(a). Find q, given that p(q) = 0.
1
Suppose 92*i = 84*i + 32. Suppose 0*a + 0 + 3*a**i - 3/4*a**2 + 9/4*a**3 = 0. What is a?
-1, 0, 1/4
Let p(s) be the first derivative of s**6/720 + s**5/60 + s**4/16 + 4*s**3/3 - 5. Let z(k) be the third derivative of p(k). Suppose z(m) = 0. What is m?
-3, -1
Let m(r) be the third derivative of r**5/12 - 5*r**4/12 + 5*r**3/6 - 8*r**2. Determine o, given that m(o) = 0.
1
Let v be (-3)/4*(-6 + 2). Factor -2*f**v + 24*f**2 - 48*f + 32 - 2*f**3 + f**3 - f**3.
-4*(f - 2)**3
Determine c so that 4*c**2 + 3*c**3 + 0 + 4/3*c + 2/3*c**4 = 0.
-2, -1/2, 0
Suppose 6 = g + 2*i, 5*i = -3*g + 4*g - 20. Let q be 4/g - 9/45. Let -1/5*t**3 + q*t**2 - 1/5*t**4 + 1/5*t + 0 = 0. What is t?
-1, 0, 1
Let g(r) be the second derivative of -38/5*r**5 + 157/12*r**4 - 22/3*r**3 + 14/3*r**7 + 2*r**2 - r + 0 - 161/30*r**6. Let g(j) = 0. What is j?
-1, 1/4, 2/7, 1
Let n = 15/2 - 7. Let u(o) be the first derivative of 0*o + n*o**2 + 1/6*o**6 + 4/3*o**3 + 2 + 4/5*o**5 + 3/2*o**4. Determine q, given that u(q) = 0.
-1, 0
Let a(y) be the second derivative of -y**6/480 - y**5/120 - y**4/96 - 3*y**2/2 - 3*y. Let u(q) be the first derivative of a(q). Let u(m) = 0. Calculate m.
-1, 0
Let b(d) be the first derivative of 2*d**3/9 - 1. Determine m so that b(m) = 0.
0
Let j = 247/7 - 35. Let i(y) = -2*y**2 + y + 2. Let m be i(0). Factor 0*d + j - 2/7*d**m.
-2*(d - 1)*(d + 1)/7
Let m(f) be the second derivative of -f**6/45 + 2*f**5/15 - f**4/6 + 2*f - 7. Suppose m(o) = 0. What is o?
0, 1, 3
Factor -105*g - 120*g - 8 + 20*g**3 - 4*g**4 + 253*g - 36*g**2.
-4*(g - 2)*(g - 1)**3
Let m(l) be the first derivative of 0*l**2 + 2 + 0*l + 1/420*l**5 + 1/1260*l**6 - 1/42*l**4 - l**3. Let w(n) be the third derivative of m(n). Factor w(j).
2*(j - 1)*(j + 2)/7
Let z(x) be the third derivative of 5*x**8/168 - x**7/14 + x**5/12 + 2*x**2. Factor z(o).
5*o**2*(o - 1)**2*(2*o + 1)
Let z = 13 + -11. Factor 1/5*d**3 + 0 + 0*d + 0*d**z.
d**3/5
Factor 21*l**2 - 23*l**2 + 4*l - 4 - 2*l + 4*l.
-2*(l - 2)*(l - 1)
Let d be 1/((-4)/(-6)*(-2)/(-4)). Solve 2/9*m**2 + 2/9*m**d - 2/9*m - 2/9 = 0.
-1, 1
Let l(u) = -16*u**3 + 74*u**2 - 29*u. Let y(b) = 5*b**3 - 25*b**2 + 10*b. Let a be (2/4)/(3/24). Let c(f) = a*l(f) + 11*y(f). Factor c(x).
-3*x*(x - 2)*(3*x - 1)
Let s be -6 - 52*(-8)/68. Factor 4/17*k**3 - 2/17*k - 2/17*k**5 - 2/17 + 4/17*k**2 - s*k**4.
-2*(k - 1)**2*(k + 1)**3/17
Let g(l) be the first derivative of -14*l**6/9 - 76*l**5/15 + 13*l**4/3 + 76*l**3/9 - 4*l**2 - 68. What is m in g(m) = 0?
-3, -1, 0, 2/7, 1
Suppose -21 = -4*y - 9. Let i(d) be the first derivative of y + 0*d**4 - 1/9*d**3 + 1/15*d**5 + 0*d + 0*d**2. Let i(h) = 0. What is h?
-1, 0, 1
Let z(i) be the first derivative of 175*i**6/12 + 109*i**5/2 + 5*i**4 - 380*i**3/3 - 20*i**2 + 40*i + 40. Find v, given that z(v) = 0.
-2, -2/5, 2/7, 1
Let l(o) be the third derivative of -5*o**8/42 + 9*o**7/35 + o**6/15 - 3*o**5/10 - o**4/6 + 2*o**2. Let l(v) = 0. What is v?
-2/5, -1/4, 0, 1
Let f(a) be the third derivative of 2/45*a**5 + 0*a + 1/36*a**4 + 1/60*a**6 + 0 + 0*a**3 - a**2. Factor f(h).
2*h*(h + 1)*(3*h + 1)/3
Suppose 0 + 0*a + 3/2*a**2 - 3/2*a**3 + 3/8*a**4 = 0. Calculate a.
0, 2
Suppose 4*k = -3*h + 27, 5*h = -5*k - 0*k + 40. Solve -s + 5*s + 3*s**2 - 4*s - k*s**3 = 0 for s.
0, 1
Let a be (-9)/6*(-20)/3. Let c = a + -7. Factor 0*f**2 + 0*f + 1/2*f**c - 3/2*f**4 - 2*f**5 + 0.
-f**3*(f + 1)*(4*f - 1)/2
Let l(o) be the first derivative of o**3 - 9*o**2/2 - 12. Find k such that l(k) = 0.
0, 3
Let b(a) be the second derivative of -3/10*a**2 + 0 + 4*a - 1/5*a**3 - 1/20*a**4. Solve b(m) = 0.
-1
Solve 5 - n**2 - n + 9 - 8 = 0 for n.
-3, 2
Let y(n) be the second derivative of n**7/252 - n**6/45 + n**5/20 - n**4/18 + n**3/36 + 18*n. Suppose y(m) = 0. Calculate m.
0, 1
Let d(o) = 4*o**5 - o**3 + 2*o**2 - 2. Let f(c) = -7*c**5 + 3*c**3 - 4*c**2 - c + 4. Let w(a) = 5*d(a) + 3*f(a). Find l such that w(l) = 0.
-2, -1, 1
Let y(a) be the second derivative of -a**7/231 + a**6/165 + 14*a. Determine m, given that y(m) = 0.
0, 1
Let m(g) be the third derivative of g**6/150 + 4*g**5/75 + g**4/6 + 4*g**3/15 - 16*g**2. Factor m(n).
4*(n + 1)**2*(n + 2)/5
Let d(h) be the second derivative of h**7/105 - h**5/25 + h**3/15 - 13*h. Factor d(b).
2*b*(b - 1)**2*(b + 1)**2/5
Factor 0 + 1/4*v**3 + 0*v**2 - 1/4*v.
v*(v - 1)*(v + 1)/4
Let n(y) = y**4 + 9*y**3 + 18*y**2 + 10*y - 3. Let c(b) = 4*b**4 + 28*b**3 + 54*b**2 + 30*b - 10. Let m(l) = -3*c(l) + 10*n(l). Factor m(s).
-2*s*(s - 5)*(s + 1)**2
Suppose -2 - 4 = -2*v. Determine d so that 6*d**3 - 6*d - v*d**5 - 2*d**3 + 2*d**3 + 3*d = 0.
-1, 0, 1
Suppose 2*d + 0*l + 19 = l, -3*l = d - 1. Let a = 14 + d. Find z, given that -3*z - 2*z**2 - 2*z + a*z**2 + 2 - z**3 = 0.
1, 2
Let b(i) = -117*i - 114. Let r be b(-1). Solve 0*y + 9/7*y**2 - 12/7 - 3/7*y**r = 0 for y.
-1, 2
Let f(v) be the first derivative of -2*v**5/5 - v**4/2 + 2*v**3 + v**2 - 4*v + 4. Factor f(d).
-2*(d - 1)**2*(d + 1)*(d + 2)
Let i(s) = s**2 + s + 1. Let u(c) = 3*c**2 + 33*c - 36. Let l(o) = 6*i(o) + u(o). Factor l(k).
3*(k + 5)*(3*k - 2)
Suppose -2*o + 6 = 2*t - 0*t, -5*t = -5. Factor -3*g**o - g - g**3 + 3*g**2 - 2*g**2.
-g*(g + 1)**2
Let h(o) be the second derivative of -o**6/105 + o**5/35 - o**4/42 - o - 1. Find s, given that h(s) = 0.
0, 1
Solve 101*r - 101*r + 2*r**3 - r**2 = 0 for r.
0, 1/2
Suppose 3*s - 4 = -n - 0, -n = 5*s - 10. Let x(o) be the first derivative of -3 - 2/5*o**5 + 2/3*o**s + 0*o + 1/6*o**6 - 1/2*o**2 + 0*o**4. Factor x(i).
i*(i - 1)**3*(i + 1)
Let h(i) be the third derivative of 0*i + 0*i**3 + 0 + 3*i**2 - 1/480*i**6 + 0*i**4 - 1/240*i**5. Find r such that h(r) = 0.
-1, 0
Suppose 0 = -3*w - 15, -3*s - w - 5 = -0*s. Let a(f) be the third derivative of 0*f + s*f**3 + 1/84*f**4 - 3*f**2 - 1/210*f**5 + 0. What is g in a(g) = 0?
0, 1
Let u be 9/(-21)*12/(-18). Let w be ((-2)/(-3))/((-14)/(-12)). Factor 0*p - w*p**3 + 0*p**2 - 6/7*p**4 + 0 - u*p**5.
-2*p**3*(p + 1)*(p + 2)/7
Let 0*p - 2/9*p**3 + 0 + 4/9*p**2 = 0. Calculate p.
0, 2
Let d = 10 + -8. Suppose 2*k + d*k = 0. Let 0*a**3 - 1/4*a**4 + k - 1/2*a + 3/4*a**2 = 0. Calculate a.
-2, 0, 1
Let t(m) be the second derivative of -m**5/60 - m**4/12 - m**3/9 - 3*m. Factor t(p).
-p*(p + 1)*(p + 2)/3
Solve -8/3 + 0*a + 2*a**3 + 14/3*a**2 = 0.
-2, -1, 2/3
Let x(m) = 6*m**5 + 6*m**4 - 6*m**3 - 2*m**2 - 4*m + 4. Let l(k) = -11*k**5 - 11*k**4 + 11*k**3 + 4*k