1*r**7. Factor g(k).
2*k*(k - 1)*(k + 1)**3
Suppose 0*r + r + 2*v = -3, -5*r + v = -29. Factor -1/3*k**3 + 1/3*k**4 - 1/3*k**2 + 0*k + 0 + 1/3*k**r.
k**2*(k - 1)*(k + 1)**2/3
Suppose -26 = -k - 3*u - 0*u, 2*k = 3*u + 52. Let c be 2/(-8) + k/40. Let 0*t - c + 2/5*t**2 = 0. Calculate t.
-1, 1
Factor -1/3*g + g**3 + 0 - 2/3*g**4 + 0*g**2.
-g*(g - 1)**2*(2*g + 1)/3
Let p be 4/(-3)*(-19)/((-95)/(-6)). Solve -2/5*x + 0 - 12/5*x**3 - 2/5*x**5 - 8/5*x**4 - p*x**2 = 0 for x.
-1, 0
Suppose 0 = 4*l + 3 - 11. Factor -u + 0*u - u + l*u**3.
2*u*(u - 1)*(u + 1)
Let h = -3 + 3. Suppose h = -l - 2*l. Determine r so that l*r + 2*r**2 + 0*r - 3*r**3 = 0.
0, 2/3
Let n(c) be the first derivative of c**3/3 + c - 4. Let p(a) = 2*a**3 + a**2 - 2*a + 9. Let z(y) = 5*n(y) - p(y). Factor z(j).
-2*(j - 2)*(j - 1)*(j + 1)
Let s(w) = -w**2 - 1. Let v(y) = -6*y + 15*y**2 - 21*y**2 + 1 - 4. Let q(g) = 3*s(g) - v(g). Factor q(u).
3*u*(u + 2)
Let n(d) = -4*d**2 + 6*d - 5. Let y(j) = -3*j**2 + 5*j - 4. Let c(x) = -4*n(x) + 6*y(x). Factor c(g).
-2*(g - 2)*(g - 1)
Let z(h) be the second derivative of -h**8/3360 + h**7/1890 + h**6/360 - h**5/90 + h**4/6 + h. Let m(a) be the third derivative of z(a). Factor m(s).
-2*(s - 1)*(s + 1)*(3*s - 2)/3
What is l in 13*l - 5*l**3 - 5*l**4 - 13*l = 0?
-1, 0
Let b be (2 - 2/2)*34. Let n = b - 168/5. Determine x, given that n + 2/5*x**2 - 4/5*x = 0.
1
Let w(x) = -2*x**4 - 2*x**3 + 2*x**2 + 2*x - 2. Let f(d) = -2*d**4 - 3*d**3 + 2*d**2 + 3*d - 3. Let k(u) = -2*f(u) + 3*w(u). Suppose k(o) = 0. Calculate o.
-1, 0, 1
Factor -44/5*o**4 + 76/5*o**3 - 4/5 + 2*o**5 + 26/5*o - 64/5*o**2.
2*(o - 1)**4*(5*o - 2)/5
Let n(t) be the first derivative of -t**6/120 - t**5/40 + t**3/12 + t**2/8 + t + 3. Let y(a) be the first derivative of n(a). Find j, given that y(j) = 0.
-1, 1
Let a(k) = -k**2 + 8*k + 3. Let w be a(8). Let l be w/(-2)*4/(-27). Factor 2/3*d**2 - 2/3*d**3 - l*d + 2/9*d**4 + 0.
2*d*(d - 1)**3/9
Let g(x) = -20*x**2 - 35*x - 26. Let j(v) = -7*v**2 - 12*v - 9. Let w(m) = 6*g(m) - 17*j(m). Let l be w(-5). Factor -i + l + 3*i + i**2 + i.
(i + 1)*(i + 2)
Let s(r) = -8*r**4 - 40*r**3 - 67*r**2 - 24*r - 11. Let v(q) = -2*q**4 - 10*q**3 - 17*q**2 - 6*q - 3. Let u(o) = 6*s(o) - 22*v(o). Factor u(z).
-4*z*(z + 1)**2*(z + 3)
Let i(m) be the first derivative of -4/5*m**2 + 2/15*m**3 + 8/5*m - 10. Determine c so that i(c) = 0.
2
Find y such that -9*y + 1/4*y**2 + 81 = 0.
18
Let q = 65/41 - 7/82. Factor q*z**3 - 1/3 - 10/3*z**2 + 13/6*z.
(z - 1)**2*(9*z - 2)/6
Let w(d) be the second derivative of -d**4/3 + 2*d**3/3 + 8*d. Suppose w(n) = 0. What is n?
0, 1
Let u(g) = -g**3 - g**2 + g + 3. Let x be u(0). Factor 6*j + 0*j**3 + x*j**2 - 9*j**3 + 6*j**5 - 3*j**4 - 3*j**5.
3*j*(j - 2)*(j - 1)*(j + 1)**2
Let v(n) be the third derivative of n**8/336 - n**7/84 + n**6/80 + n**5/120 - n**4/48 + 23*n**2. Factor v(t).
t*(t - 1)**3*(2*t + 1)/2
Let p(y) be the second derivative of y**5/100 - y**4/10 + 2*y**3/5 - 4*y**2/5 + 5*y. Factor p(l).
(l - 2)**3/5
Suppose -4*i + 4*t = -7*i + 8, 3*t - 15 = 0. Let z be i/6*18/(-4). Factor 0 - 4*j**2 + z*j**2 - 1 + 2*j.
-(j - 1)**2
Let c be 106862/(-770) + (-4)/(-22). Let h = c + 139. Factor 2/5*f - h*f**2 + 4/5.
-2*(f - 2)*(f + 1)/5
Let h be (-1)/(-2)*-1*1/(-4). Let y(v) be the second derivative of 3/40*v**5 + h*v**4 + 1/60*v**6 + 0 + 0*v**2 + 3*v + 1/12*v**3. Suppose y(l) = 0. What is l?
-1, 0
Let b be (-6)/2 + (-6)/(-3). Let u(p) = -3*p**3 + 2*p**2 - 1. Let c be u(b). Factor -3*s + c - 6*s**2 - s + 2*s**2 + s**2.
-(s + 2)*(3*s - 2)
Let a(r) be the first derivative of r**8/1680 + r**7/420 + r**6/360 + r**3 - 3. Let x(f) be the third derivative of a(f). Factor x(u).
u**2*(u + 1)**2
Let w(h) be the second derivative of -4/5*h**2 + 7/30*h**4 + 8/15*h**3 + 0 - 1/10*h**5 - 3*h. Solve w(k) = 0.
-1, 2/5, 2
Let c(o) = -o**5 - o**4 - o + 1. Let g(f) = 8*f - f**3 + 5*f**3 - 6*f**4 + 2*f**4 - 8 + 12*f**2. Let r(b) = 6*c(b) + g(b). Solve r(u) = 0.
-1, 1/3, 1
Suppose -14 = 3*y - 0*t - 5*t, -t = -3*y + 2. Factor -c**y + 1 + 9*c - 9*c.
-(c - 1)*(c + 1)
Suppose 0 = -3*z + z - 4. Let w be z + (8/6 - -2). Factor 1/3*a**2 + 4/3 + w*a.
(a + 2)**2/3
Find d, given that 6/11*d**2 - 12/11*d + 0 = 0.
0, 2
Let j(z) = 7*z**2 - 9*z + 7. Let v(w) = -3*w**2 + 4*w - 3. Let l(q) = 2*j(q) + 5*v(q). Let l(p) = 0. What is p?
1
Let s(h) be the first derivative of 1/3*h**3 + 1/4*h**4 - h - 1 - 1/2*h**2. Factor s(f).
(f - 1)*(f + 1)**2
Let l(w) be the third derivative of w**6/120 + w**5/60 - 24*w**2. Factor l(g).
g**2*(g + 1)
Let k(o) = -6*o**4 + 6*o**2 + 2*o + 2. Let r(j) = j**5 - 25*j**4 + 25*j**2 + 8*j + 9. Let z(c) = 9*k(c) - 2*r(c). Find b such that z(b) = 0.
-1, 0, 1
Factor -2/11 - 2/11*m**4 + 0*m + 4/11*m**2 + 0*m**3.
-2*(m - 1)**2*(m + 1)**2/11
Let s(d) = d. Let h(i) = -i**2 - 7*i - 8. Let f(g) = h(g) - 2*s(g). Let r be f(-8). Factor -1/3*c**3 + r + 0*c**2 + 1/3*c.
-c*(c - 1)*(c + 1)/3
Suppose 5*f = 4 - 19. Let x be f/5 + 91/35. Factor -1/4*j**3 + 0*j + 0 + 1/4*j**x.
-j**2*(j - 1)/4
Let p(c) = -3*c**3 - 15*c**2 - 6. Let v(h) = -h**3 - h - 2*h**2 - 1 + 0*h + h**2. Let d(j) = -p(j) + 6*v(j). Factor d(y).
-3*y*(y - 2)*(y - 1)
Let l(s) be the first derivative of s**2 - s + 3. Let y be l(2). Find g, given that -1 - y - 2*g**2 + 2 + 4*g = 0.
1
Let b(f) = 2*f. Let c be b(1). Suppose 0 = c*w - w - 2. Let 0*p**w + 0 + 2/3*p**3 - 2/3*p = 0. Calculate p.
-1, 0, 1
Let p(o) be the second derivative of 0 + 2/5*o**2 - 1/5*o**3 - 6*o + 1/50*o**5 + 0*o**4. Suppose p(z) = 0. Calculate z.
-2, 1
Let j(g) = -g**2 - 47*g. Let t be j(-47). Suppose -1/2*r**3 + 1/2*r + 0 + t*r**2 = 0. Calculate r.
-1, 0, 1
Let u(f) be the second derivative of 7*f - 1/14*f**7 + 1/2*f**4 + 3/2*f**2 - 3/10*f**5 + 0 + 3/2*f**3 - 3/10*f**6. Factor u(l).
-3*(l - 1)*(l + 1)**4
Let b = 3 - -3. Factor t + 3*t**3 + 3*t**4 - 6*t + 3*t**2 - b*t**4 + 2*t.
-3*t*(t - 1)**2*(t + 1)
Let l(a) be the first derivative of -1/14*a**6 - 1/7*a**3 + 3/35*a**5 + 0*a + 4 + 3/28*a**4 + 0*a**2. Factor l(x).
-3*x**2*(x - 1)**2*(x + 1)/7
Suppose 0 = 4*d - 8*d - 4*d. Factor 6/7*q**3 - 2/7*q**2 + 2/7*q**5 + 0 - 6/7*q**4 + d*q.
2*q**2*(q - 1)**3/7
Determine u so that -3/8*u**2 - 15/8*u - 3/2 = 0.
-4, -1
Let j(w) be the third derivative of w**6/1260 - w**4/84 + w**3/6 + w**2. Let d(i) be the first derivative of j(i). What is r in d(r) = 0?
-1, 1
Let a(d) be the second derivative of -1/2*d**2 + 0 + 5*d - 2/15*d**6 + 1/2*d**3 + 5/12*d**4 - 3/20*d**5. Factor a(b).
-(b - 1)*(b + 1)**2*(4*b - 1)
Suppose 4*r - 5*l - 23 = 0, 10 = -3*r + 2*r - 4*l. Suppose -4*f = -b - 6, 5*b - f - 4 = r*b. Factor -b*a**2 - a + 2*a - 3*a + 3*a + 2*a**4 - a**5.
-a*(a - 1)**3*(a + 1)
Let f(m) be the first derivative of m**4/22 + 14*m**3/33 + m**2 + 10*m/11 + 7. Let f(g) = 0. What is g?
-5, -1
Let f = -173/3 + 59. Let 2/3*m**2 + 2/3 - f*m = 0. What is m?
1
Let k(f) be the second derivative of -4*f + 0*f**2 + 0*f**3 + 0*f**4 + 0 - 1/126*f**7 + 0*f**6 + 1/60*f**5. Factor k(c).
-c**3*(c - 1)*(c + 1)/3
Let w(h) = h**5 - h**2 + 1. Let x(a) = -9*a**5 - 4*a**4 + 12*a**3 + 9*a**2 - 8*a - 5. Let r(d) = 5*w(d) + x(d). Determine u, given that r(u) = 0.
-2, -1, 0, 1
Let p(s) be the first derivative of -2*s**3/21 + 2*s**2/7 - 2*s/7 + 13. Factor p(w).
-2*(w - 1)**2/7
Let b(a) be the second derivative of -2*a**6/15 + 2*a**4/3 - 2*a**2 - a. Factor b(u).
-4*(u - 1)**2*(u + 1)**2
Let a = -8 - -10. Factor g**2 - g**3 - 11*g**2 - g**3 - 24*g - a*g**2 - 16.
-2*(g + 2)**3
Let h(t) be the second derivative of -2/147*t**7 + 0 + 1/42*t**4 + 1/21*t**3 + 0*t**2 - 1/21*t**6 - 4*t - 3/70*t**5. Determine u, given that h(u) = 0.
-1, 0, 1/2
Let m(r) be the first derivative of r**6/30 + 2*r**5/25 - r**4/20 - 2*r**3/15 - 29. Factor m(y).
y**2*(y - 1)*(y + 1)*(y + 2)/5
Let g(p) be the first derivative of -p**7/735 - p**6/420 - 2*p**2 - 3. Let w(m) be the second derivative of g(m). Factor w(o).
-2*o**3*(o + 1)/7
Let x(y) = -270*y**3 + 579*y**2 - 99*y + 21. Let p(n) = 27*n**3 - 58*n**2 + 10*n - 2. Let b(q) = -21*p(q) - 2*x(q). Solve b(u) = 0.
0, 2/9, 2
Let a(q) = 3*q**2 + 1. Let z be a(-1). Suppose 0 = 4*d - 2*u - 7 + 1, -d + 5 = 3*u. Factor -l + d*l**z - 3*l**4 - 4*l**2 + 6*l + 7*l**2 + 2 - l**3.
-(l - 2)*(l + 1)**3
Let t be (-72)/(-30)*(-3 - 7). Let p be ((-9)/t)/(3/24). Determine c, given that -1/6*