6). Factor o - 2/5*x**3 + 4/5*x + 2/5*x**2.
-2*x*(x - 2)*(x + 1)/5
Let o = -9 - -14. Factor 4*k**o - 8*k**2 + 2*k**3 - 6*k**3 + k**4 + 7*k**4.
4*k**2*(k - 1)*(k + 1)*(k + 2)
Let o(m) be the second derivative of -m**8/2240 + m**7/420 + m**4/3 + 3*m. Let y(g) be the third derivative of o(g). Factor y(v).
-3*v**2*(v - 2)
Let o(m) be the second derivative of -m**8/672 + m**7/210 - m**5/60 + m**4/48 + m**2/2 + 2*m. Let d(j) be the first derivative of o(j). Factor d(b).
-b*(b - 1)**3*(b + 1)/2
Factor -21*b**2 - 30*b**2 + 46*b**2 + 20*b + 60.
-5*(b - 6)*(b + 2)
Let k(w) be the third derivative of -w**6/140 + w**5/105 - 30*w**2. Suppose k(n) = 0. What is n?
0, 2/3
Let o(s) = s**2 + 4*s + 5. Let v be o(-3). Let 0 + 0*i - 2/9*i**3 - 2/9*i**v = 0. Calculate i.
-1, 0
Let p = -122 + 126. Let v(y) be the third derivative of -1/18*y**3 + 0 + 1/18*y**p - 1/60*y**5 + 2*y**2 + 0*y. Determine h, given that v(h) = 0.
1/3, 1
Let y(q) be the second derivative of q**4/12 - q**3/6 - 3*q**2 - q. Let y(v) = 0. What is v?
-2, 3
What is g in -3 + 2*g - 9*g + 5 - 4*g**2 + 0*g**2 = 0?
-2, 1/4
Solve -28/9*m**4 + 0*m - 4/3*m**5 + 0 + 28/9*m**3 + 4/3*m**2 = 0.
-3, -1/3, 0, 1
Let h(o) be the third derivative of -7*o**7/15 - 91*o**6/60 - 9*o**5/5 - 23*o**4/21 - 8*o**3/21 - 17*o**2. Factor h(g).
-2*(g + 1)*(7*g + 2)**3/7
Let z(c) be the first derivative of -c**3 + 2*c**2 + 4*c - 5. Let j(v) = -2*v**2 + 4*v + 4. Let k(h) = 4*j(h) - 3*z(h). Factor k(l).
(l + 2)**2
Let z(q) be the first derivative of 3/2*q**2 + 3 + 0*q - 6*q**3. Factor z(g).
-3*g*(6*g - 1)
Factor 12*r - r**2 + 4*r**2 + 3*r**2 - 23*r**3 + 11*r**3 + 3*r**4 - 9.
3*(r - 3)*(r - 1)**2*(r + 1)
Let w(m) be the third derivative of m**7/630 + m**6/180 + m**5/180 - 3*m**2. Factor w(a).
a**2*(a + 1)**2/3
Let v(d) = -11*d**3 + 22*d**3 + 8*d + 32*d**2 + 13 + 26*d**3. Let x(k) = 9*k**3 + 8*k**2 + 2*k + 3. Let y(o) = 6*v(o) - 26*x(o). Determine h so that y(h) = 0.
-1, -1/3, 0
Suppose -6*g + 10 = -11*g. Let c be 11/5 - g/(-10). Factor -o**2 + 2*o**2 - 3*o**c.
-2*o**2
Let t(z) be the third derivative of -z**8/560 - z**7/70 - z**6/24 - z**5/20 + z**3/2 + 3*z**2. Let b(q) be the first derivative of t(q). Factor b(k).
-3*k*(k + 1)**2*(k + 2)
Suppose 1 + 29 = 6*t. Let 2/7*o**3 + 6/7*o**2 + 2/7*o**t - 6/7*o**4 + 0 - 4/7*o = 0. What is o?
-1, 0, 1, 2
Let v(c) be the first derivative of c**6/10 - c**5/10 - c**4/12 - c - 3. Let g(d) be the first derivative of v(d). Factor g(o).
o**2*(o - 1)*(3*o + 1)
Let -15*x**5 - 27*x**2 + 13*x**2 + 5*x**3 + 21*x**4 + 4*x**2 - x**4 = 0. What is x?
-2/3, 0, 1
Let l(w) be the first derivative of w**6/39 - 2*w**5/13 + 3*w**4/26 + 6*w**3/13 - 3. Suppose l(o) = 0. What is o?
-1, 0, 3
Let z(v) = 13*v**5 - 21*v**4 + 3*v**3 - 4*v**2 - 9. Let d(f) = 3*f**5 - 5*f**4 + f**3 - f**2 - 2. Let r(x) = -9*d(x) + 2*z(x). Determine y so that r(y) = 0.
0, 1
Let z(j) be the third derivative of j**8/20160 + j**7/5040 - j**5/20 - j**2. Let x(q) be the third derivative of z(q). Let x(d) = 0. What is d?
-1, 0
Let j(n) be the second derivative of n**10/226800 + n**4/12 + n. Let q(o) be the third derivative of j(o). What is x in q(x) = 0?
0
Let h(d) be the first derivative of -d**3/3 - d**2/2 - 1. Let q(v) = v**4 - 2*v**3 + 5*v**2 + 7*v - 1. Let m(j) = 10*h(j) + 2*q(j). What is o in m(o) = 0?
-1, 1
Let n(v) be the third derivative of v**5/180 - v**4/72 - v**3/9 + 8*v**2. Let n(w) = 0. Calculate w.
-1, 2
Let r = 80 - 479/6. Let o(f) be the first derivative of -1/24*f**6 + 1/8*f**4 + r*f**3 - 1 - 1/8*f**2 - 1/4*f - 1/20*f**5. Solve o(n) = 0.
-1, 1
Let v = 1 - 1. Suppose -90*i + 85*i + 30 = 0. Find g, given that -4 - 3*g**2 + 1 + v + i*g = 0.
1
Let a be ((-18)/189)/(1/(-7)). Determine j, given that 2/3*j + 4/3*j**2 - a*j**4 - 2/3 + 2/3*j**5 - 4/3*j**3 = 0.
-1, 1
Let r be (-5)/25 + 0/(-2). Let b = r + 7/10. Solve 0*y**2 + b*y**3 - 1/2*y + 0 = 0 for y.
-1, 0, 1
Determine o, given that -6*o**2 - 18/5*o**3 - 2/5 - 14/5*o = 0.
-1, -1/3
Let d = -29/44 - -10/11. Factor 1/4*r - 1/4*r**3 + 0 - 1/4*r**2 + d*r**4.
r*(r - 1)**2*(r + 1)/4
Let h be (-16)/(-6)*12*5/80. What is w in 10/7*w**4 + 12/7*w**3 + 0 + 2/7*w**h - 24/7*w**5 + 0*w = 0?
-1/3, -1/4, 0, 1
Let f be (-4)/18 + 26/(-18) + 3. Factor 2/3*i**2 + 0 + f*i.
2*i*(i + 2)/3
Let g(d) be the second derivative of d**7/2100 + d**6/450 - d**5/75 - d**4/12 + 7*d. Let f(x) be the third derivative of g(x). Find a such that f(a) = 0.
-2, 2/3
Suppose -5*v - 7 = t, v - 4*t - 4 = -3*v. Let u be (2/3)/(v/(-6)). Factor -3*m**3 - m - m**2 + 2 + m**3 - u*m**2.
-(m + 1)*(m + 2)*(2*m - 1)
Let m be (2 + 18/(-8))*-5*1. Factor -27/2 + m*v**5 + 50*v**3 - 171/2*v**2 - 13*v**4 + 243/4*v.
(v - 3)**3*(v - 1)*(5*v - 2)/4
Let i = 410/21 - 56/3. Find d such that 2/7 - 6/7*d - 2/7*d**3 + i*d**2 = 0.
1
Let y(n) be the second derivative of -7*n**5/20 + 19*n**4/12 - 4*n**3/3 - 2*n**2 - 13*n. Suppose y(g) = 0. What is g?
-2/7, 1, 2
Find v, given that -3/2*v + 3/4 + 3/4*v**2 = 0.
1
What is x in 10/11*x + 0 - 2/11*x**2 = 0?
0, 5
Suppose 0 = -m - 4 - 1. Let q be (-6)/m*(-5)/(-2). Solve 2 - 4*a**q - 4 + 3*a**4 + 10*a**3 - 1 - 6*a = 0.
-1, 1
Suppose 20*g**5 + 8*g**3 + 11*g**5 + 16*g**5 - 48*g**2 - 51*g**5 + 16*g**4 - 36*g = 0. What is g?
-1, 0, 3
Let m(a) = a**3 - 5*a**2 + 4. Let o be m(5). Let f(q) = q**2 - 2*q - 3. Let u be f(o). Factor -h**4 - 1/2*h**u + h**2 + 1/2*h + 0*h**3 + 0.
-h*(h - 1)*(h + 1)**3/2
Suppose -55 = -4*g - g. Let a = g - -10. Solve -3*h**3 - a*h - 9 + 5 - 15*h**2 - 5 = 0 for h.
-3, -1
Let c(u) be the second derivative of 0*u**4 + 0*u**3 + 0*u**2 - 1/60*u**6 + 3*u + 1/56*u**7 + 0 + 0*u**5. Factor c(i).
i**4*(3*i - 2)/4
Let o(p) be the second derivative of p + 0*p**3 - 1/60*p**5 + p**2 + 0 + 1/12*p**4. Let x(y) be the first derivative of o(y). Factor x(d).
-d*(d - 2)
Let k(g) be the third derivative of -g**6/720 + g**5/360 + g**4/144 - g**3/36 - 4*g**2. Factor k(c).
-(c - 1)**2*(c + 1)/6
Find s such that 2*s**3 + s**5 - 2*s**5 - s**5 = 0.
-1, 0, 1
Let n(p) be the second derivative of -40*p**7/21 - 20*p**6/3 - p**5/4 + 95*p**4/6 + 85*p**3/6 + 5*p**2 - 13*p. Suppose n(o) = 0. What is o?
-2, -1, -1/4, 1
Factor -21/5*z**2 - 6/5*z + 0 - 3*z**3.
-3*z*(z + 1)*(5*z + 2)/5
Let b(g) be the second derivative of g**5/5 + g**4 + 2*g**3 + 2*g**2 + 20*g. Solve b(f) = 0 for f.
-1
Let m(p) be the third derivative of -p**8/1848 + 4*p**7/1155 - p**6/110 + 2*p**5/165 - p**4/132 - 4*p**2. Factor m(l).
-2*l*(l - 1)**4/11
Let w = 5 - 3. Factor 1 + 4*z**3 - w*z**3 - 3*z - 4*z**3 + z**3 + 3*z**2.
-(z - 1)**3
Let g(o) = -32*o**3 - 8*o**2 + 20*o + 32. Let k(q) = -13*q**3 - 3*q**2 + 8*q + 13. Let t(n) = 5*g(n) - 12*k(n). Factor t(b).
-4*(b - 1)*(b + 1)**2
Let a(w) = 2*w**2 - 10*w + 4. Let p be a(5). Factor -3*i - i + 8 + 7*i**2 + p*i**3 - 19*i**2 + 4*i**4.
4*(i - 1)**2*(i + 1)*(i + 2)
Let h(n) be the first derivative of -3*n**5/35 + n**3/7 - 28. Factor h(y).
-3*y**2*(y - 1)*(y + 1)/7
Let c(b) be the second derivative of -1/110*b**5 - 2*b - 1/66*b**4 + 0 + 0*b**2 + 0*b**3. Factor c(r).
-2*r**2*(r + 1)/11
Let r(n) = -n**2 + 15*n - 17. Let x be r(13). Let k = x + -9. What is m in -2/3*m**2 + k + 0*m = 0?
0
Let k(i) = 6*i**4 - 23*i**3 + 48*i**2 - 17*i + 7. Let p(j) = 4*j**4 - 15*j**3 + 32*j**2 - 11*j + 5. Let z(t) = -5*k(t) + 7*p(t). Solve z(q) = 0 for q.
0, 1, 2
What is k in 5/3*k + 1/3*k**4 + 1/3*k**5 - 1 + 2/3*k**2 - 2*k**3 = 0?
-3, -1, 1
Let c(p) = -48*p**2 - 111*p - 57. Let r(k) = 7*k**2 + 16*k + 8. Let y be ((-7)/(-14))/(2/16). Let f(g) = y*c(g) + 27*r(g). Factor f(v).
-3*(v + 2)**2
Let h(d) be the third derivative of d**5/60 - d**4/12 + d**2. Let b be h(2). Factor 0*o + b - 2/7*o**3 - 2/7*o**2.
-2*o**2*(o + 1)/7
Factor 0 + 8/3*w - 4/3*w**2.
-4*w*(w - 2)/3
Let o = -164 + 167. What is m in -1 - 13/4*m**o + 4*m - 9/4*m**2 + 13/4*m**4 - 3/4*m**5 = 0?
-1, 1/3, 1, 2
Let q = -85 + -72. Let j = 1735/11 + q. Factor 2/11*i**2 + 0*i + 0 - j*i**3 + 6/11*i**4.
2*i**2*(i - 1)*(3*i - 1)/11
Factor o**3 + 17*o**3 + 14*o - 3*o**4 + 7*o - 36*o**2 + 3*o.
-3*o*(o - 2)**3
Let n(s) be the second derivative of 0*s**3 - 1/252*s**7 + 0 - 1/40*s**5 + 1/60*s**6 + 1/72*s**4 + 0*s**2 - 4*s. Find q such that n(q) = 0.
0, 1
Let u(n) be the third derivative of 32*n**7/105 + 4*n**6/3 + 17*n**5/15 + n**4/3 + 10*n**2. Factor u(b).
4*b*(b + 2)*(4*b + 1)**2
Suppose 27