 25. Factor 4*l**5 - l**4 + 0*l**4 - g*l**p.
l**4*(l - 1)
Suppose 0 + 4 = 2*h. Let b(t) be the first derivative of 0*t**4 - 1/15*t**5 + 1/9*t**3 + 0*t**h + 0*t + 3. What is x in b(x) = 0?
-1, 0, 1
Let p(q) be the second derivative of -q**7/1680 + q**6/180 - q**5/48 + q**4/24 - q**3/2 - 4*q. Let i(r) be the second derivative of p(r). Factor i(n).
-(n - 2)*(n - 1)**2/2
Let q(d) = -3*d**2 - 6*d - 9. Let v(o) = -o - 1. Let x(w) = q(w) - 9*v(w). Factor x(t).
-3*t*(t - 1)
Let s be ((-4)/(-10))/((-1)/(-5)). Find a, given that a**2 + 8 + 4*a**2 + 0*a**s - 8*a - 3*a**2 = 0.
2
Suppose 3*x - 2*x + 22 = 2*b, b = 2*x + 14. Let n be b/(-9)*(-3)/5. Suppose n*z**2 + 0 - 2/3*z = 0. What is z?
0, 1
Suppose -42 = 7*j - 5*j. Let f be (7/(j/(-6)))/3. Factor i**2 - 5/3*i + f.
(i - 1)*(3*i - 2)/3
Let q(j) = -11*j**3 - j**2 + 17*j + 4. Let f(a) = 23*a**3 + 3*a**2 - 33*a - 8. Let p(c) = -3*f(c) - 5*q(c). Suppose p(r) = 0. What is r?
-1, -2/7, 1
Factor -2/7*i**3 - 2/7 + 2/7*i + 2/7*i**2.
-2*(i - 1)**2*(i + 1)/7
Suppose -5*p + j + 23 = 0, 5*j + 7 = -8. Let y(n) be the first derivative of 1 + 1/12*n**6 + 0*n**2 + 1/6*n**3 + 0*n - 1/8*n**p - 1/10*n**5. Factor y(l).
l**2*(l - 1)**2*(l + 1)/2
Let r = 1/57 - -166/285. Factor r*o**2 + 0 - 6/5*o.
3*o*(o - 2)/5
Let v(h) = h + 8. Let z be v(-8). Let l(d) be the first derivative of 0*d**3 - 1/6*d**6 + 0*d**2 + 0*d**5 + 1 + 0*d + z*d**4. Suppose l(y) = 0. What is y?
0
Let i be ((-24)/15)/(8/60). Let x be (-22)/i - 2/6. Determine k so that -x*k**2 - 1/2*k**3 - 1 + 5/2*k + 1/2*k**4 = 0.
-2, 1
Let v = -92 - -98. Let c(i) be the third derivative of 1/12*i**4 - 1/60*i**v - 2*i**2 + 0*i - 1/3*i**3 + 1/30*i**5 + 0. Let c(g) = 0. Calculate g.
-1, 1
Suppose 0 = u - k + 1, 1 + 2 = 3*u + 3*k. Let j(d) be the second derivative of 1/10*d**5 + 0 + 1/6*d**4 + u*d**2 - 2/3*d**3 + 3*d. Factor j(f).
2*f*(f - 1)*(f + 2)
Let u(y) = -19*y - 55. Let t be u(-3). Factor -5/4*b**3 + t*b**2 - b + 0 + 1/4*b**4.
b*(b - 2)**2*(b - 1)/4
Let a be (-286)/96 + (6 - 3). Let x(v) be the third derivative of 0 - 3*v**2 + 0*v**3 + 1/240*v**6 + 0*v**5 + 0*v - a*v**4. Factor x(u).
u*(u - 1)*(u + 1)/2
Let r be (18/27 + (-10)/12)*-4. Solve 4/3 - 2/3*m**2 - r*m = 0 for m.
-2, 1
Let v = -7 + 9. Suppose -3*g = -4*g + 4*r + 6, -v*r = -5*g + 12. Determine u so that 6 - 4 + 4*u**2 - 4*u - g*u**2 = 0.
1
Suppose -6 + 9/2*y + 3/2*y**2 = 0. Calculate y.
-4, 1
Factor -1/3*b**5 + 1/3*b**4 + 1/3*b**3 + 0 - 1/3*b**2 + 0*b.
-b**2*(b - 1)**2*(b + 1)/3
Factor -26*b**5 + b**3 - 2*b**3 - 3*b**3 + 30*b**5.
4*b**3*(b - 1)*(b + 1)
Factor 6*k - 1 + 1 + 3*k**2.
3*k*(k + 2)
Let d(w) = 12*w**3 + 52*w**2 + 36*w - 108. Let y(u) = -4*u**3 - 17*u**2 - 12*u + 36. Let j(v) = 3*d(v) + 8*y(v). Factor j(x).
4*(x - 1)*(x + 3)**2
Suppose 6 = -4*d + 26. Suppose 4*v + 6 = d*v. Factor 3/2*s**4 + v*s + 9*s**2 + 6*s**3 + 3/2.
3*(s + 1)**4/2
Let t(p) be the second derivative of p**6/120 + p**5/20 + 7*p**3/6 - 2*p. Let x(a) be the second derivative of t(a). Solve x(d) = 0.
-2, 0
Let i(b) be the first derivative of 3*b**4/28 - 3*b**3/7 + 9*b**2/14 - 3*b/7 + 47. Suppose i(m) = 0. Calculate m.
1
Let 4*x**5 - 12*x**3 - 6 + 85*x + 6*x**2 - 76*x - x**5 = 0. Calculate x.
-2, -1, 1
Suppose p - x - 20 = 4*x, -5*x = 0. Suppose 0 = -5*j - 0*j + p. Let q**2 + 5 - 2*q - 5 - 3 + j = 0. Calculate q.
1
Factor 0 + 6/5*c + 4/5*c**2 - 2/5*c**3.
-2*c*(c - 3)*(c + 1)/5
Let a(z) = 17*z**3 + 8*z**2 - 13. Let i(u) = 4*u**3 + 2*u**2 - 3. Let q be (6/(-5))/((-9)/(-45)). Let x(j) = q*a(j) + 26*i(j). Solve x(v) = 0.
-2, 0
Let p = 4301 + -21256/5. Let o = -47 + p. Determine z, given that -o*z + 4/5 - 18/5*z**2 = 0.
-1, 2/9
Let w(c) = 13*c - 128. Let m be w(10). Factor 0 + 49/2*j**5 + 0*j + 14*j**4 + 0*j**m + 2*j**3.
j**3*(7*j + 2)**2/2
Let n(f) = 2*f - 22. Let p be n(12). Factor u + 1/2*u**p + 1/2.
(u + 1)**2/2
Suppose 15 + 3 = 4*s + 2*t, -5*t = -5. Let k be (-10)/(-12) + s/(-12). Factor -3/2*i**3 + 3/2*i + 1/2 - k*i**2.
-(i - 1)*(i + 1)*(3*i + 1)/2
Determine u so that 1/5*u**2 - 1/5*u - 1/5 + 1/5*u**3 = 0.
-1, 1
Let l(y) be the third derivative of 13*y**5/36 + 35*y**4/18 + 10*y**3/9 - 2*y**2. Factor l(k).
5*(k + 2)*(13*k + 2)/3
Let j be -2*(4 - 12)*7/63. Factor -j - 1/9*c**2 + 8/9*c.
-(c - 4)**2/9
Let v(m) be the first derivative of -5*m**3/6 + 10*m - 11. Factor v(t).
-5*(t - 2)*(t + 2)/2
Let n(l) = -66*l**2 + 66. Let i(g) = -5*g**2 + 5. Let h(k) = -27*i(k) + 2*n(k). Factor h(f).
3*(f - 1)*(f + 1)
Let t be ((-42)/8)/(-4 - 0). Let q = 221/144 - t. Determine a so that -2/9*a**2 + q*a**4 - 2/9*a**3 + 2/9*a + 0 = 0.
-1, 0, 1
Let a(w) be the first derivative of w**6/600 - w**5/150 - 2*w**2 + 3. Let m(i) be the second derivative of a(i). Suppose m(p) = 0. Calculate p.
0, 2
Suppose -2*s = -7*s + 4*t + 18, 4*s - 4 = -2*t. Find u such that 0*u**s + 0*u - 2/5*u**4 - 2/5*u**3 + 0 = 0.
-1, 0
Suppose 4*a + 5 - 17 = 0. Suppose -2*b**2 + 3*b - a*b = 0. What is b?
0
Suppose -9*l - 2*v + 30 = -5*l, 5*v = l + 20. Let m be 2/((-2)/(-1)) - 1. What is p in -1/5*p**l + 0 + 1/5*p - 2/5*p**4 + 2/5*p**2 + m*p**3 = 0?
-1, 0, 1
Let w(b) be the first derivative of 3*b**4/8 + b**3/2 + 31. Suppose w(q) = 0. What is q?
-1, 0
Suppose -10 = -3*m + m. Let l(n) be the third derivative of 0*n**3 + 0 - n**2 + 1/84*n**4 + 1/210*n**m + 0*n. Solve l(o) = 0.
-1, 0
Suppose 5*h**3 - 4*h**3 - 3*h**2 - 1 + 6*h - 3*h = 0. What is h?
1
Determine q, given that 10/7*q**3 + 2/7*q**2 - 2/7*q**4 + 8/7 - 16/7*q - 2/7*q**5 = 0.
-2, 1
Let z(h) be the third derivative of h**5/480 - h**4/64 + h**3/24 - 5*h**2. Suppose z(a) = 0. Calculate a.
1, 2
Let x = 17 + -12. Suppose -u = 3 - x. Factor 2*h - u*h**3 + 4*h**2 - 5*h + h.
-2*h*(h - 1)**2
Solve 12 + 32*b - 12*b + 30*b - 18*b**2 = 0.
-2/9, 3
Let u = -312/2941 + -2/173. Let q = u + 27/85. Factor 1/5 + 0*x**3 - 2/5*x**2 + q*x**4 + 0*x.
(x - 1)**2*(x + 1)**2/5
Let p(k) = -k**5 + k**4 + k**3 - 3*k**2 - 2*k + 2. Let x(v) = -v**5 + v**3 - v**2 - v + 1. Let d(f) = -p(f) + 2*x(f). Determine c, given that d(c) = 0.
-1, 0, 1
Let x = 28 + -22. Let a(b) be the third derivative of -1/90*b**5 + 1/36*b**4 + 1/9*b**3 - 1/180*b**x + 0 + 0*b + b**2. Factor a(s).
-2*(s - 1)*(s + 1)**2/3
Suppose -125*h**3 + 180*h + 30*h**2 - 71*h**2 - 40 - 109*h**2 = 0. Calculate h.
-2, 2/5
Let z(d) be the third derivative of d**7/168 + 3*d**6/32 + 29*d**5/48 + 65*d**4/32 + 15*d**3/4 + 2*d**2. Factor z(v).
5*(v + 1)*(v + 2)*(v + 3)**2/4
Let j(w) = w**3 + w - 2. Let i(u) be the second derivative of -3*u**5/20 - u**4/12 - u**3/2 + 5*u**2/2 + 4*u. Let q(l) = 2*i(l) + 5*j(l). What is t in q(t) = 0?
-1, 0
Let p(z) be the first derivative of -1/7*z**2 + 0*z + 5 - 2/21*z**3. Factor p(l).
-2*l*(l + 1)/7
Find j, given that 14/11*j + 12/11 - 10/11*j**2 = 0.
-3/5, 2
Let t(i) be the second derivative of i**4/132 + 5*i**3/66 + 2*i**2/11 + 7*i. Determine n so that t(n) = 0.
-4, -1
Let g(i) = 6*i - 27. Let x be g(5). Factor 0*z**2 - 3*z**x + 0*z**4 + 3/2*z + 0 + 3/2*z**5.
3*z*(z - 1)**2*(z + 1)**2/2
Let n(v) be the first derivative of 5 + 0*v**2 + 2/15*v**5 - 1/6*v**4 + 0*v**3 + 0*v. Determine q, given that n(q) = 0.
0, 1
Let a(l) = l**3 - 4*l**2 + 2*l - 4. Let h be a(4). Factor -4*v**2 - 4*v**4 + 6*v**3 + 6*v**4 - h*v**3 + 0*v**3.
2*v**2*(v - 1)*(v + 2)
Let h(w) = w**3 - w. Let f(s) = 10*s**3 + 2*s**2 - 10*s - 2. Let b(i) = -f(i) + 2*h(i). Factor b(a).
-2*(a - 1)*(a + 1)*(4*a + 1)
Let m(t) be the third derivative of -t**6/24 + t**5/3 - 25*t**4/24 + 5*t**3/3 - 6*t**2. Factor m(z).
-5*(z - 2)*(z - 1)**2
Let f = -51 - -54. Let a(p) be the third derivative of 0 + 1/420*p**6 + 0*p - p**2 - 1/210*p**5 - 1/84*p**4 + 1/735*p**7 + 0*p**f. Factor a(w).
2*w*(w - 1)*(w + 1)**2/7
Let r(w) = 2*w**2 + 2*w. Let b(o) = -o**2. Let k(i) = -2*b(i) - 2*r(i). Solve k(v) = 0 for v.
-2, 0
Let b(d) = -d**4 - 6*d**3 - 18*d**2 + 13*d + 5. Let y(r) = r**4 + 3*r**3 + 9*r**2 - 7*r - 2. Let q(m) = -4*b(m) - 7*y(m). Factor q(o).
-3*(o - 2)*(o - 1)*(o + 1)**2
Let h(x) be the first derivative of 2*x**3/3 - 2*x - 4. Suppose h(r) = 0. What is r?
-1, 1
Let n(b) = -5*b + 10. Let y be n(2). Factor 0*j - 2/11*j**4 - 4/11*j**3 + y - 2/11*j**2.
-2*j**2*(j + 1)**2/11
Let h be 1 + (-250)/(-7) - 1. Let q be 2*(1 + 24/(-28)). Factor -q - 30/7*i - h*i**3 - 150/7*i**2.
-2*(5*i + 1)**3/7
Let o = 8 - 2. Let a be 2/7*7/o. Factor -1/3*g**2 - a*g 