Factor 2*k**4 - g*k**4 + r*k**4.
k**4
Let 10*x - 12*x**2 + 8 - 16*x**2 + 10*x + 0*x = 0. Calculate x.
-2/7, 1
Let m(i) be the second derivative of -i**5/60 + i**4/36 + i**3/9 + 11*i. Factor m(b).
-b*(b - 2)*(b + 1)/3
Suppose 8 = 4*v - 0. Let k = 0 + v. Factor -4*n**k + 2*n**2 - 2*n**3 + 4*n**3.
2*n**2*(n - 1)
Let q(f) = -5*f**4 + 3*f**3 + f**2 - 3*f + 4. Let b(w) = 14*w**4 - 9*w**3 - 3*w**2 + 9*w - 11. Let r(z) = 6*b(z) + 17*q(z). Factor r(c).
-(c - 1)*(c + 1)**2*(c + 2)
Let o(k) = 4*k**2 + 109*k + 790. Let u(m) = 36*m**2 + 980*m + 7112. Let s(f) = -28*o(f) + 3*u(f). Solve s(y) = 0.
-14
Solve -10/7 + 12/7*v - 2/7*v**2 = 0 for v.
1, 5
Suppose -3*q + 7 = -11. Suppose -2*v = -14 + q. Factor 0*p**4 - 2 + 4*p**2 - p**v - p**4.
-2*(p - 1)**2*(p + 1)**2
Suppose -5*u + 21 = 3*y, 3*u - 2*y - 3 = y. Let m be 3 + u + (-6)/3. Factor 0*f**2 + 0 - 5 + 3 - 2*f**4 + m*f**2.
-2*(f - 1)**2*(f + 1)**2
Let u = 3 + -1. Let f(n) be the third derivative of 0*n + 0*n**4 + 0 + 1/24*n**3 + n**u - 1/240*n**5. Factor f(s).
-(s - 1)*(s + 1)/4
Let t(h) = -10*h**5 + 40*h**3 + 15*h**2 - 35*h - 25. Let l(b) = -5*b**5 + 20*b**3 + 8*b**2 - 17*b - 12. Let d(w) = -5*l(w) + 2*t(w). Let d(r) = 0. Calculate r.
-1, 1, 2
Let a(d) = -6*d**2 + 5*d**2 + 1 - 2. Let i(c) be the first derivative of -c**4/2 + 8*c**3/3 + c**2 + 8*c + 2. Let h(w) = 8*a(w) + i(w). Solve h(q) = 0 for q.
-1, 0, 1
Suppose 3*o - 69 = -3. Let n be 7/o + 6/33. Factor 0 - 1/2*d**3 - 1/2*d**4 + n*d**2 + 1/2*d.
-d*(d - 1)*(d + 1)**2/2
Suppose 0 = -3*n - 3*j + 6, n - 3*j = -n - 16. Let m = 4 + n. Determine h so that m*h**4 + 0*h**4 + 0*h**4 - 2*h**5 = 0.
0, 1
Let g(j) = 14*j**3 - j + 0*j + 3*j**2 - 13*j**3 - 3. Let i be g(-3). Factor -1/3*p + i - 1/6*p**2.
-p*(p + 2)/6
Let h(w) be the first derivative of -w**5 + 15*w**4/4 + 5*w**3/3 - 15*w**2/2 + 26. Let h(n) = 0. What is n?
-1, 0, 1, 3
Let n(p) be the first derivative of 0*p**4 - 6/5*p**5 + 3/2*p**2 + 2*p**3 + 0*p - 1/2*p**6 + 3. Suppose n(m) = 0. Calculate m.
-1, 0, 1
Let w(s) be the first derivative of -7*s**4/2 - 4*s**3/3 + 7*s**2 + 4*s - 18. Factor w(g).
-2*(g - 1)*(g + 1)*(7*g + 2)
Let 72/7 + 12/7*l - 16/7*l**2 - 4/7*l**3 = 0. Calculate l.
-3, 2
Let w = 28 + -28. Factor -1/3*z**2 - 1/3*z + w.
-z*(z + 1)/3
Let u(q) = q**5 - q**2 + q. Let z(a) = -4*a**5 + 6*a**4 - 2*a**3 - 8*a**2 - 6*a + 8. Let y(v) = 6*u(v) + z(v). Suppose y(s) = 0. What is s?
-2, -1, 1
Let p(z) be the second derivative of z**8/26880 + z**7/2520 + z**6/720 + z**4/12 - 3*z. Let m(x) be the third derivative of p(x). Factor m(b).
b*(b + 2)**2/4
Let n be (3/(-9))/(2/3 + -2). Let z(y) be the third derivative of 0 - 3*y**2 - 2/3*y**3 + 0*y - 1/30*y**5 + n*y**4. What is w in z(w) = 0?
1, 2
Suppose -3*u = -0*u - 15. Suppose 4*j = -3*v + j + 21, -5*v + j = -u. Factor 0*x + v*x + 2*x**2 - 4*x.
2*x*(x - 1)
Let i be 9/2*(-48)/(-72). Let l(v) be the first derivative of 2 - 5/3*v**i + 2*v**2 + v. Factor l(f).
-(f - 1)*(5*f + 1)
Let w = 8 + -8. Let j(o) be the third derivative of 0*o**3 + 0*o + 1/36*o**4 + w - 1/180*o**6 + 0*o**5 + 2*o**2. Suppose j(c) = 0. Calculate c.
-1, 0, 1
Let c be (-6 - (-744)/132)*(0 - 2). Factor -6/11*k**2 + 0*k + c - 2/11*k**3.
-2*(k - 1)*(k + 2)**2/11
Let f = -35 + 71/2. Suppose c**2 + f*c**5 + 0*c**3 + 0 - c**4 - 1/2*c = 0. Calculate c.
-1, 0, 1
Let k = -15 - -12. Let u be 2*-2 + (-24)/k. Factor 2/7*w - 4/7*w**3 + 0*w**2 + 2/7*w**5 + 0 + 0*w**u.
2*w*(w - 1)**2*(w + 1)**2/7
Let l(a) be the first derivative of 2*a**5/5 - a**4/2 - 3. Factor l(k).
2*k**3*(k - 1)
Let s(z) be the third derivative of z**8/30240 - z**7/1260 + z**6/120 - z**5/60 - 3*z**2. Let n(x) be the third derivative of s(x). Factor n(t).
2*(t - 3)**2/3
Let g = 5216/28567 + -2/2597. Factor -2/11*d**2 + 4/11 + g*d.
-2*(d - 2)*(d + 1)/11
Suppose -n + 48 = 2*n. Let j be ((-15)/20)/((-9)/n). Factor -2/3*z**4 - 2/3 + j*z**2 - 4/3*z**3 + 2/3*z + 2/3*z**5.
2*(z - 1)**3*(z + 1)**2/3
Suppose -8*n = -6 - 10. Factor -n + 5*s - 7/2*s**2 + 3/4*s**3.
(s - 2)**2*(3*s - 2)/4
Let o(f) be the first derivative of -f**3 - 21*f**2/2 - 10. Solve o(i) = 0 for i.
-7, 0
Factor 31*a**2 + 4*a**4 - 6*a**4 - 29*a**2.
-2*a**2*(a - 1)*(a + 1)
Let h(j) = -5*j**2 - 3*j + 4. Let m(q) = 4*q**2 + 2*q - 3. Let l(k) = 3*h(k) + 4*m(k). Let y be l(2). Factor 2*o**3 + y + 8*o + 2*o**2 - 2*o + 4*o**2.
2*(o + 1)**3
Let s(t) = t**3 + 2*t**2 + t + 2. Let q be s(-2). Factor 3*z - 3 + q*z**2 - z - 2*z**3 + 5 - 2*z**2.
-2*(z - 1)*(z + 1)**2
Let j = 22/9 - 170/99. Factor 0 + j*w**2 + 2/11*w.
2*w*(4*w + 1)/11
Let i(o) = 8*o**2 + 12*o. Let r(a) = a - 1. Let h(n) = -n - 4. Let w be h(-6). Let p(c) = w*i(c) - 4*r(c). Factor p(s).
4*(s + 1)*(4*s + 1)
Suppose 5*y + 9 = -3*k, 0 = -4*k + y + y + 14. Let m be -1*(15/9 - k). Solve -1/3*t**2 - 2/3*t - m = 0 for t.
-1
Let p(t) be the third derivative of -t**5/80 - 3*t**4/32 - t**3/4 + 4*t**2. Factor p(h).
-3*(h + 1)*(h + 2)/4
Let x(n) be the first derivative of -n**4/12 - 3*n**3/8 - n**2/4 - n - 5. Let i(u) be the first derivative of x(u). Let i(v) = 0. What is v?
-2, -1/4
Let f(k) be the third derivative of -k**8/5376 + k**7/3360 + k**6/1440 + k**4/6 - k**2. Let d(y) be the second derivative of f(y). Factor d(p).
-p*(p - 1)*(5*p + 2)/4
Let d(g) be the third derivative of -g**5/12 - 5*g**4/8 + 22*g**2. Factor d(r).
-5*r*(r + 3)
Let n(w) be the second derivative of 0 - w - 3/2*w**2 + 0*w**3 + 0*w**4 - 1/120*w**5. Let z(y) be the first derivative of n(y). Factor z(u).
-u**2/2
Let l(t) = 7*t**3 - 3*t**2 + t - 1. Suppose -9 = c - 4. Let n(k) = -8*k**3 + 3*k**2 - 2*k + 2. Let b(i) = c*l(i) - 4*n(i). Solve b(g) = 0 for g.
-1, 1
Factor -9/2*g**4 + 9/2*g - 3/2*g**5 + 3*g**2 - 3*g**3 + 3/2.
-3*(g - 1)*(g + 1)**4/2
Let m be (-2)/(-8) + 5/(-4). Let f be -2 - 4*m/2. Factor f*k**2 - k + k**3 - 1/2*k**4 + 1/2.
-(k - 1)**3*(k + 1)/2
Let -16*d + 27*d**4 + 64*d**2 + 28*d**4 - 84*d**3 - 19*d**4 = 0. What is d?
0, 2/3, 1
Let j = -31 + 33. Let a(v) be the second derivative of 0 + 1/12*v**4 - 1/2*v**j - 1/6*v**3 + 1/20*v**5 - 2*v. Factor a(x).
(x - 1)*(x + 1)**2
Let n = -1/839 - 54533/1678. Let v = -32 - n. Factor 0 + 0*y - 1/2*y**5 + 1/2*y**4 - v*y**2 + 1/2*y**3.
-y**2*(y - 1)**2*(y + 1)/2
Let o(b) be the second derivative of -3*b**5/40 + 2*b**4/9 + 31*b**3/36 + b**2/2 + 42*b. Factor o(c).
-(c - 3)*(c + 1)*(9*c + 2)/6
Let u(d) be the second derivative of -d**5/100 + d**4/60 + d**3/15 + 2*d. Factor u(i).
-i*(i - 2)*(i + 1)/5
Let t(c) be the second derivative of -2/3*c**4 + 0*c**2 - 5*c + 0 - 4/3*c**3 + 3/10*c**5 + 4/15*c**6 + 1/21*c**7. Factor t(a).
2*a*(a - 1)*(a + 1)*(a + 2)**2
Let i = 91 - 91. Determine s so that 0*s**2 + 1/2*s**3 + i*s + 1/2*s**4 + 0 = 0.
-1, 0
Suppose -f = -108 + 28. Let x be (-1)/(-4) - 20/f. Determine q so that -5/4*q**3 + 1/4*q + x - 3/4*q**2 + 3/4*q**4 + q**5 = 0.
-1, 0, 1/4, 1
Let w = -16 + 19. Let t be 9/27 + 2/30. Factor -t*b**4 + 0*b**w + 2/5*b**2 + 0*b + 0.
-2*b**2*(b - 1)*(b + 1)/5
Let m = 8/3 - 2. Solve -1/3 - m*n**3 + 0*n + n**2 = 0 for n.
-1/2, 1
Suppose -5*i + 6*w - 2*w = -35, -3*w = -4*i + 27. Determine p, given that -3/2*p**i - 3/2*p + 0 - 3*p**2 = 0.
-1, 0
Let t(d) be the first derivative of d**4/20 - d**3/15 + 2. Factor t(m).
m**2*(m - 1)/5
Solve 0 - 8/3*a**2 + 2/3*a - 10/3*a**3 = 0 for a.
-1, 0, 1/5
Let m(u) be the first derivative of -u**4/11 + 6*u**3/11 + 6*u**2/11 - 10*u/11 - 15. What is d in m(d) = 0?
-1, 1/2, 5
Let i(l) be the third derivative of -l**7/630 - l**6/36 - 37*l**5/180 - 5*l**4/6 - 2*l**3 - 5*l**2 - 2. Suppose i(f) = 0. What is f?
-3, -2
Let r be (-2 + 2)/(-5 - -2). Suppose r = -t - 4*t. Factor -2 - y + 0*y**3 - 2*y + y**3 + t*y.
(y - 2)*(y + 1)**2
Let j(h) = h**4 + h**3 + 1. Let m(y) = -12*y**4 - 8*y - 4. Let t(g) = 8*j(g) + m(g). Factor t(z).
-4*(z - 1)**3*(z + 1)
Suppose c - 4*c - 18 = -5*y, -c + 4*y = 6. Let m = c - -9. Factor 3*k**2 - 2*k**4 + 2*k**m - 2*k**2 + 3*k**4.
k**2*(k + 1)**2
Factor 9*b - 4*b + 3*b - b**2 - b**2 - 8.
-2*(b - 2)**2
Let r(h) be the first derivative of -2/15*h**5 + 0*h - 3*h**2 - 2/3*h**3 + 5/6*h**4 - 3. Solve r(c) = 0.
-1, 0, 3
Suppose 2*c = 5*v + 29, 4*v - 1 = -4*c - 13. Let k = -3 - v. Solve 1/2*i**3 - 1/2*i**4 + 1/2*i**k + 0*i + 0 - 1/2*i**5 = 0 for i.
-1, 0, 1
Let u(g) be the second derivative of 7*g - 1/12*g**4 - 2/3*g**3 + 0 - 3/2*g**2. Suppose u(f) = 0. What