6. Determine m so that a(m) = 0.
-1, -2/3, 1
Let m(k) = -k**2 + 9*k - 8. Let b(q) = -8*q + 8. Let p(x) = 3*b(x) + 4*m(x). Factor p(j).
-4*(j - 2)*(j - 1)
Suppose 2*v - 217 = g, 0*g + 3*g + 5*v + 695 = 0. Let p = g + 2483/11. Solve -p*k**3 - 4/11 + 14/11*k + 10/11*k**2 = 0.
-1, 1/4, 2
Let k(r) be the third derivative of 2*r**7/105 + 2*r**6/15 + r**5/3 + r**4/3 - 7*r**2. Suppose k(b) = 0. What is b?
-2, -1, 0
Let z(x) = -x**5 + x**4 + x**3 - x**2 - x - 1. Let a(d) = -21*d**5 + 24*d**4 + 27*d**3 - 18*d**2 - 18*d - 18. Let q(y) = -a(y) + 18*z(y). Factor q(k).
3*k**3*(k - 3)*(k + 1)
Factor -15*k**2 - 33*k**4 - 9*k**3 - 37*k**4 - 6*k - 36*k**4 + 3*k**5 + 109*k**4.
3*k*(k - 2)*(k + 1)**3
Factor 1/5*i**2 + 0*i**3 + 0 - 1/5*i**4 + 0*i.
-i**2*(i - 1)*(i + 1)/5
Let m = -74/9 + 397/45. Suppose -3/5*k - 1/5 - 1/5*k**3 - m*k**2 = 0. What is k?
-1
Let j(p) = p**3 + 15*p**2 + p + 17. Let r be j(-15). Let x be (-3 + r)*3/(-3). Let -7/2*l - 9/2*l**2 + x = 0. What is l?
-1, 2/9
Let 1/4*d + 1/4*d**5 - 1/2*d**3 - 1/4*d**4 - 1/4 + 1/2*d**2 = 0. Calculate d.
-1, 1
Suppose v = -3*v. Let p(u) = -u**2 + 2*u + 8. Let i be p(3). Factor z**3 + v*z**2 + 0 + 0*z**4 - 1/2*z**i - 1/2*z.
-z*(z - 1)**2*(z + 1)**2/2
Let d be 1/(-4) + 21/20. Suppose 5*m = 10, 19*c - 18*c + 5*m = 12. Factor 6/5*k**3 + 2/5*k**c - d*k + 0.
2*k*(k + 1)*(3*k - 2)/5
Suppose d - 7 = -2*a + 4, -4*a + d = -13. Determine m so that 0 - 6*m + 1 + 1 - 5 + 3*m**a + 6*m**3 = 0.
-1, 1
Let o(z) be the first derivative of 2*z**3/33 - 2*z/11 + 19. Factor o(u).
2*(u - 1)*(u + 1)/11
Let u be (4/6)/(18/(-459)). Let q = -61/4 - u. Factor 1/4 + w**3 + 1/2*w - q*w**2.
(w - 1)**2*(4*w + 1)/4
Let d(c) be the first derivative of -c**3 + 4*c**2 - 4*c + 37. Determine v, given that d(v) = 0.
2/3, 2
Suppose 2*p = -2*p. Let f(g) be the second derivative of 2/3*g**3 + 2*g**2 + 4*g + 1/12*g**4 + p. Solve f(u) = 0.
-2
Let x be -2 + 2 - (-8 + -1). Let s = x - 7. Factor 0 - 1/4*z**s - 1/4*z**3 + 0*z.
-z**2*(z + 1)/4
Let b(c) be the third derivative of -13/132*c**4 - 6*c**2 + 0*c - 2/11*c**3 + 1/66*c**5 + 0. Suppose b(i) = 0. What is i?
-2/5, 3
Let a(b) = 2*b**2 - 3 - 7*b**2 - b**2 + 1. Let o(i) = i**3 - 13*i**2 - 5. Let w(p) = 5*a(p) - 2*o(p). Find g, given that w(g) = 0.
-2, 0
Let j(h) = 10*h**2 - 24*h + 42. Let w(r) = -9*r**2 + 24*r - 41. Let i(g) = -5*j(g) - 6*w(g). Factor i(b).
4*(b - 3)**2
Let y = -5 + 10. Determine m so that 6*m - y*m - 9*m + 8*m**3 + 28*m**2 - 28*m**4 = 0.
-1, 0, 2/7, 1
Let -1/6 + 1/12*t - 1/12*t**4 - 1/12*t**3 + 1/4*t**2 = 0. Calculate t.
-2, -1, 1
Find j, given that 8/5 + 2/5*j**2 + 2*j = 0.
-4, -1
Let t(l) = -162*l**4 + 357*l**3 - 239*l**2 + 37*l - 5. Let w(n) = -1134*n**4 + 2498*n**3 - 1674*n**2 + 258*n - 36. Let r(o) = 44*t(o) - 6*w(o). Factor r(h).
-4*(h - 1)**2*(9*h - 1)**2
What is b in 0 - 1/3*b**3 + 1/3*b - 1/3*b**4 + 1/3*b**2 = 0?
-1, 0, 1
Let w = 7 + -4. Let b(i) = 15*i**3 - 17*i**2 + 25*i - 4. Let y(a) = -7*a**3 + 9*a**2 - 12*a + 2. Let u = -1 - -8. Let f(m) = u*y(m) + w*b(m). Factor f(t).
-(t - 2)*(2*t - 1)**2
Suppose 4*k = 0, -5*k = -4*x - x + 10. Solve 4/3 - 2/3*z + 26/3*z**3 - 6*z**x - 10/3*z**4 = 0 for z.
-2/5, 1
Let h be ((-8)/(-10))/((-6)/(-45)). Let v(a) be the second derivative of 2*a + 0 - 1/50*a**5 + 0*a**2 - 1/75*a**h + 1/30*a**4 + 1/15*a**3. Factor v(d).
-2*d*(d - 1)*(d + 1)**2/5
Let y = -22 - -17. Let q = 11/2 + y. Determine v, given that q*v**3 + 1/2 - 1/2*v - 1/2*v**2 = 0.
-1, 1
Suppose 0 = 2*h + 3*o, 11 = h - 0*h - 4*o. Suppose 4*u + 3*f + f - 8 = 0, -1 = -u - 2*f. Factor 2*b**2 + 6*b**h - 12*b - 7*b**u + 4*b**2 + 8.
-(b - 2)**3
Let u(h) be the first derivative of -3 + 0*h**2 + 1/5*h - 1/15*h**3. Suppose u(y) = 0. Calculate y.
-1, 1
Let t = 27 - 11. Solve -1 + 6*v**2 - 7*v + t*v + 4 = 0 for v.
-1, -1/2
Let z = -5/6 - -13/12. Factor -z*c**3 + 0*c - 1/4*c**5 + 0 + 0*c**2 - 1/2*c**4.
-c**3*(c + 1)**2/4
Suppose 0 = -5*v + 2 + 3. Let k be v/(-1) - (-3 - -2). Suppose -4/5*t + 18/5*t**2 + k - 14/5*t**3 = 0. Calculate t.
0, 2/7, 1
Factor -1/2*g**4 + 7/4*g**3 - 2*g**2 + 0 + 3/4*g.
-g*(g - 1)**2*(2*g - 3)/4
Suppose -5*x - 12 = -2. Let c be 3 - (-5 - -3)/x. Factor 0*h**c + 5 + 2*h - 1 - 5 - h**2.
-(h - 1)**2
Suppose 5*v = 20 - 5. Let f = 1 + v. Factor 2*i**2 + 3 - 3*i**2 - f + 2*i**2.
(i - 1)*(i + 1)
Let u = 27 + -18. Factor 3*k**2 - 3*k + 0*k - 3*k**3 + u*k.
-3*k*(k - 2)*(k + 1)
Let r(u) be the first derivative of 16*u**5 - 110*u**4 - 275*u**3/3 + 215*u**2/2 - 30*u + 33. Factor r(p).
5*(p - 6)*(p + 1)*(4*p - 1)**2
Let w(u) be the third derivative of -u**8/168 + u**6/60 + 10*u**2. Solve w(v) = 0.
-1, 0, 1
Let q = -11 + 8. Let u(y) = -4*y**2 - 2*y - 1. Let o(b) = -3*b**2 - 2*b - 1. Let m(l) = q*o(l) + 2*u(l). Let m(r) = 0. Calculate r.
-1
Let p(b) be the second derivative of b**6/90 - b**5/60 - b**4/36 + b**3/18 + 10*b. Factor p(a).
a*(a - 1)**2*(a + 1)/3
Let h(s) be the first derivative of 0*s**2 + 2/27*s**3 + 3 - 2/9*s. Solve h(c) = 0 for c.
-1, 1
Let f = 6 + -4. Factor t**2 + f - 2 - t.
t*(t - 1)
Solve -2/5*w + 1/5*w**2 + 0 = 0 for w.
0, 2
Let b(v) be the second derivative of -v**6/1080 - 7*v**3/6 - 3*v. Let w(r) be the second derivative of b(r). Suppose w(a) = 0. What is a?
0
Suppose 0*m = m. Suppose 0*o - 4*o + 8 = m. Factor -3/4*g**4 + 3/4*g**3 - 1/4*g**o + 1/4*g**5 + 0 + 0*g.
g**2*(g - 1)**3/4
Factor -1/7*q**2 + 0*q + 0 + 1/7*q**3.
q**2*(q - 1)/7
Let p = 970/3 + -341. Let s = p - -18. Factor -2/3*i**3 + s*i**5 + 0*i**2 + 0 + 0*i**4 + 1/3*i.
i*(i - 1)**2*(i + 1)**2/3
Suppose -4*j = -0*j + 12. Let k be 1/(j/(-3)) - 1. Determine i, given that 0*i**4 + k*i - 2/7*i**5 + 0*i**2 + 0*i**3 + 0 = 0.
0
Let a = -8 - -8. Let b(z) be the third derivative of -1/180*z**6 - 1/630*z**7 + 0*z**5 - z**2 + 1/36*z**4 + 0 + a*z + 1/18*z**3. Solve b(y) = 0 for y.
-1, 1
Let t(k) be the second derivative of -k**7/315 - k**6/180 + k**5/90 + k**4/36 - k**2 - 3*k. Let u(i) be the first derivative of t(i). Solve u(a) = 0.
-1, 0, 1
Let g be 6 + 5 + (-760)/72. Determine r, given that 10/9*r**3 + g - 2*r**2 - 10/9*r + 14/9*r**4 = 0.
-1, 2/7, 1
Let y = 889 + -887. Factor -1/2*q + 1/6*q**y + 0.
q*(q - 3)/6
Let z(r) be the second derivative of -r**5/80 + r**4/12 + r**3/24 - r**2/2 - 5*r. Find b, given that z(b) = 0.
-1, 1, 4
Let j = 4 - -4. Let t = 11 - j. What is c in -33*c**2 + 28*c - 13*c**4 - 2*c**4 - 4 - c**4 - 56*c**t = 0?
-2, 1/4
Find m, given that -1/3*m**2 + 0*m + 0 = 0.
0
Suppose 0*p = -3*p + 6. Let j(g) = -g**4 - g**3 + g**2 - g. Let q(a) = 2*a**4 + 6*a**3 - 4*a**2 + 2. Let s(f) = p*q(f) + 6*j(f). Factor s(k).
-2*(k - 2)*(k - 1)**2*(k + 1)
Let v(l) = l**2 - 8*l + 9. Let z be v(6). Let m = 7 + z. Let 0 + 2/9*s**m + 0*s - 2/9*s**3 + 0*s**2 = 0. What is s?
0, 1
Solve -375*w**2 + 35*w**3 + 13*w**3 + 13*w**3 + 60 + 14*w**3 - 12*w = 0.
-2/5, 2/5, 5
Let u(v) be the third derivative of v**7/420 + v**6/80 + v**5/40 + v**4/48 - 26*v**2. Determine j, given that u(j) = 0.
-1, 0
Let h(b) be the first derivative of b**5/30 + b**4/24 - b**3/18 - b**2/12 + 3. Factor h(y).
y*(y - 1)*(y + 1)**2/6
Let l(v) = -v**5 - v**4 + v**3 + v**2 + 1. Let a(d) = 7*d**5 + d**4 - 3*d**3 - 5*d**2 - 5. Let y(b) = a(b) + 5*l(b). Factor y(c).
2*c**3*(c - 1)**2
Let o(z) be the first derivative of -z**6/1080 + z**5/180 - z**4/72 + 8*z**3/3 + 8. Let v(w) be the third derivative of o(w). Let v(r) = 0. Calculate r.
1
Suppose 2/11*b**4 + 0 + 0*b**2 + 2/11*b**3 + 0*b = 0. What is b?
-1, 0
Let m be (-4)/(-30) + (-7)/(-60). What is n in -m*n**2 + 0 + 1/4*n = 0?
0, 1
Let g(k) = -k**2 + 3*k + 2. Let f be g(5). Let j = f + 10. Determine y so that -2/3*y**j - 2/3*y + 0 = 0.
-1, 0
Let n(g) be the second derivative of 0*g**5 - 1/12*g**4 - 2/9*g**3 + 0 + 1/180*g**6 - g + 1/2*g**2. Let k(f) be the first derivative of n(f). Factor k(a).
2*(a - 2)*(a + 1)**2/3
Let k = -5 + 21. Determine q, given that 9*q**2 - 7*q**3 + q**4 + k*q**3 + 3*q + 2*q**4 + 0*q**2 = 0.
-1, 0
Suppose -4*o + 2 = -6. Let -l**5 + 2*l**5 - o*l**5 + 2*l**2 - 4*l**2 + 3*l**3 = 0. Calculate l.
-2, 0, 1
Let h = 11 - 2. Let v be 1*(h - 3)*1. Find b, given that -4 + 21*b - 5*b + 32*b**2 + v = 0.
-1/4
Factor 5*w**2 - 8 - 7 - 9*w - w.
5*(w - 3)*(w + 1)
Solve -2/9*m**2 + 0 + 0*m + 1/9*m**3 = 0 for m.
0, 2
Let n(m) be the first derivative of m**6/360 + m**5/40 + m**4/12 - 4*m**3/3 + 3. Let i(t) be the