*6/15 + a**5/2 + a**4/3 - 11*a. Factor u(f).
2*f**2*(f + 1)**2*(f + 2)
Let g(h) be the second derivative of h**8/560 + h**7/168 + h**6/180 - 2*h**3/3 - 4*h. Let r(z) be the second derivative of g(z). Suppose r(u) = 0. Calculate u.
-1, -2/3, 0
Let h(k) be the second derivative of -10/3*k**3 + 0 - 5/3*k**4 + 3*k - 1/2*k**5 - 4*k**2 - 1/168*k**7 - 1/12*k**6. Suppose h(n) = 0. Calculate n.
-2
Let q be -4*2/(-10) + 96/30. Let s(l) be the third derivative of 4*l**2 - 1/300*l**5 + 0*l - 1/60*l**q + 0 - 1/30*l**3. Factor s(n).
-(n + 1)**2/5
Let t(d) = -31*d**3 + 16*d**2 + 16*d + 2. Let f(g) = -11*g**3 + 17*g**2 + 1 + 1 - 21*g**3 + 17*g. Let r(s) = -3*f(s) + 4*t(s). Factor r(j).
-(j - 1)*(4*j + 1)*(7*j + 2)
Suppose -4*k - k = w - 32, 3*k + 3*w = 12. Find a, given that 2*a**3 + 3*a - a**2 + 5*a - k*a**2 = 0.
0, 2
Let d = 4 - 2. Let o = 1/156 - -305/1092. Find m such that 0 + 0*m + o*m**d = 0.
0
Suppose 2*k - 18 = -4*k. Solve -2*n**4 - 18*n**3 + 15*n**3 + k*n**5 + 6*n**2 - 4*n**4 = 0 for n.
-1, 0, 1, 2
Factor -3*b**3 - 6*b**2 + 18*b**3 - 12*b**4 + 3*b**5 + 0*b**4.
3*b**2*(b - 2)*(b - 1)**2
Let q(j) = -j**2 + 3*j**3 - 3*j**3 - 1 + j**3 + 2. Let m be q(0). What is p in -1/4*p**2 - m - p = 0?
-2
Let y(n) = 36*n**3 - 519*n**2 + 804*n - 267. Let z(k) = -5*k**3 + 74*k**2 - 115*k + 38. Let f(h) = 4*y(h) + 27*z(h). Find o, given that f(o) = 0.
2/3, 1, 7
Factor -4/7 + 8/7*i**2 + 2*i.
2*(i + 2)*(4*i - 1)/7
Let t be 3 + (1 - -3 - -14). Let a be (-4 + t/6)*0. Factor 0 + 2/3*n**3 + a*n**2 - 2/3*n.
2*n*(n - 1)*(n + 1)/3
Let k(f) be the second derivative of f**6/35 - f**5/70 - 20*f. Factor k(r).
2*r**3*(3*r - 1)/7
Let m(i) = -5*i**4 + 8*i**3 + 4. Let x(a) = -6*a**4 + 9*a**3 + 5. Let u(t) = 5*m(t) - 4*x(t). Factor u(b).
-b**3*(b - 4)
Let q(n) be the third derivative of -n**6/360 - n**5/180 + n**4/72 + n**3/18 + 4*n**2. Factor q(s).
-(s - 1)*(s + 1)**2/3
Let w = 86 - 83. Factor 1/4*x**5 - 2 + 11/4*x**3 + 3/2*x**4 - w*x + 1/2*x**2.
(x - 1)*(x + 1)*(x + 2)**3/4
Factor -26*k**2 + 42*k**3 + 4*k + k**2 - 35*k**2 + 20*k - 9*k**4.
-3*k*(k - 2)**2*(3*k - 2)
Let n = 3125/3 - 1041. Factor -1/3*g**5 - n*g**2 + 1/3*g + 2/3*g**4 + 0 + 0*g**3.
-g*(g - 1)**3*(g + 1)/3
Let q(y) be the third derivative of -y**6/1440 - y**5/240 - y**4/96 + y**3/3 - 3*y**2. Let a(i) be the first derivative of q(i). What is p in a(p) = 0?
-1
Let v(x) = x**3 + x**2 - 1. Let o(z) = -z**3 - z**2 - z. Let a(j) = -j**3 - 4*j**2 - 7*j. Let d(i) = a(i) + 2*o(i). Let w(m) = -d(m) - 6*v(m). Factor w(g).
-3*(g - 2)*(g + 1)**2
Let y = 34 + -34. Factor -4/5*d**4 + 2/5*d - 2/5*d**5 + 4/5*d**2 + 0 + y*d**3.
-2*d*(d - 1)*(d + 1)**3/5
Let k(d) = -60*d**2 + 80*d - 11. Let a(c) = 15*c**2 - 20*c + 3. Let r(n) = 9*a(n) + 2*k(n). Factor r(x).
5*(x - 1)*(3*x - 1)
Let h(m) be the second derivative of m**6/60 + 7*m**5/150 + m**4/30 - 2*m**2 - 4*m. Let y(f) be the first derivative of h(f). Solve y(t) = 0 for t.
-1, -2/5, 0
Let r(p) = 4*p**3 - 16*p + 8. Let y = -7 + 8. Let l(w) = w**2 - w + 1. Let x(c) = y*r(c) + 4*l(c). Factor x(d).
4*(d - 1)**2*(d + 3)
Let a(x) = -x**3 + 45*x**2 - 43*x - 42. Let o be a(44). Find f, given that 2/3*f + 2/3*f**4 + 2*f**3 + 0 + 2*f**o = 0.
-1, 0
Let y = 17 + -17. Suppose 1 = 3*t - 5. Find n, given that y*n - n**3 - 4*n**t + 2 + n - 2*n**3 = 0.
-1, 2/3
Let k = 16 + -13. Suppose 3*q + 3*v - 12 = 0, 0 = q + k*q + v - 10. Suppose -2/3*z**5 + q*z - 4/3*z**3 + 2/3 + 4/3*z**2 - 2*z**4 = 0. What is z?
-1, 1
Let r(f) = 24*f**4 - 7 - 10*f + 7 - 4*f**3 + 4*f**2. Let o(k) = -5*k**4 + k**3 - k**2 + 2*k. Let m(q) = 14*o(q) + 3*r(q). Factor m(h).
2*h*(h - 1)*(h + 1)**2
Let d = -251/12 - -89/4. Let u(x) be the first derivative of -1/2*x + 5/6*x**3 + 5/4*x**2 + 2 - 25/8*x**4 - 4*x**5 - d*x**6. Let u(p) = 0. Calculate p.
-1, 1/4
Let z be 5 - (2 - 1) - (10 + -8). Factor 0 + 1/2*u - 7/4*u**4 + 7/4*u**z - 1/2*u**3.
-u*(u - 1)*(u + 1)*(7*u + 2)/4
Let k(a) be the third derivative of -3*a**5/20 - a**4/4 - 23*a**2 + 2*a. Factor k(b).
-3*b*(3*b + 2)
Let v(r) be the first derivative of -2*r**5/5 + 2*r**4 - 2*r**3/3 - 6*r**2 - 22. Let v(d) = 0. Calculate d.
-1, 0, 2, 3
Let r be ((-2)/(-5))/((-2)/(-30)). Find x, given that -r*x + 4*x**3 + 4*x**2 - 8*x**2 + 4 + x + x = 0.
-1, 1
Suppose 39*s - 40*s + 4 = 0. Let h(m) be the first derivative of -7/2*m**4 + 2*m**5 - 2*m**3 + 7*m**2 - s*m + 1. Suppose h(y) = 0. What is y?
-1, 2/5, 1
Let y(b) = -b**2 + 2*b + 2. Let q be 9/(-15) + (-26)/(-10). Let j be y(q). Let 0 - 2/5*c - 18/5*c**3 - 12/5*c**j = 0. Calculate c.
-1/3, 0
Let j(a) = 3*a - 19. Let b be j(11). Let o = 72/5 - b. Solve -o - 2/5*n**2 + 4/5*n = 0.
1
Suppose 0*g = 2*g - l - 32, -2*g + 4*l + 32 = 0. Let w be (1 + 1)*2/g. Determine u so that -1/2*u + w + 1/4*u**2 = 0.
1
Let k(f) = f - 6. Let t be k(8). Suppose -g - 1 - 2 = -2*r, -4*g - r = -15. Suppose -2*x + x**g - t*x + 3*x = 0. Calculate x.
-1, 0, 1
Let u(w) be the third derivative of w**8/1008 + w**7/90 + w**6/45 - 4*w**5/45 + 31*w**2. Factor u(a).
a**2*(a - 1)*(a + 4)**2/3
Suppose -5*p = -5 - 5. Factor 5*x**2 + 12 + 21*x - 3*x**p + x**2 - 9*x.
3*(x + 2)**2
Let s be (-52)/(-14) + 12/42. Let 4*x**2 + s*x**3 - 4*x**4 - 4*x + 4*x**4 - 5*x**4 + x**4 = 0. What is x?
-1, 0, 1
Let u(d) = 16*d**2 + 5*d + 3. Let i(n) = -n**3 - 48*n**2 - 15*n - 8. Let w(l) = 3*i(l) + 8*u(l). Factor w(x).
-x*(x + 5)*(3*x + 1)
Let n(o) = o + 8. Let j be n(0). Suppose -4*l - j = -6*l. Determine q so that -10/7*q**l + 4/7*q**3 + 2/7*q - 2/7 + 12/7*q**2 - 6/7*q**5 = 0.
-1, 1/3, 1
Let d(v) = -v**2 + 2. Let t be d(0). Suppose -2*u + 4 = -y, -y + u - 2 = -2*y. Let y - 1/2*r**t + 0*r = 0. What is r?
0
Let r(b) = -b + 8. Let k be r(5). Determine g, given that -g**2 + 5*g + 3*g**2 - 5*g - 6*g**k = 0.
0, 1/3
Let c(v) be the second derivative of v**7/10080 - v**6/2880 - 5*v**4/12 + 5*v. Let l(o) be the third derivative of c(o). Let l(k) = 0. Calculate k.
0, 1
Let m(c) = c**2 - 7*c - 2. Let f be m(8). Let a(s) be the first derivative of 2/3*s**3 + 0*s**4 - 2/5*s**5 + 1 + 0*s - 1/2*s**2 + 1/6*s**f. Factor a(g).
g*(g - 1)**3*(g + 1)
Suppose -5*s + 4*y + 33 = 0, 2*s + 1 - 3 = -4*y. Factor -4/3*j**2 - 1/3*j**s + 0 - 1/3*j - 4/3*j**4 - 2*j**3.
-j*(j + 1)**4/3
Let x(i) be the second derivative of -5*i**7/84 + i**6/4 - i**5/4 - 5*i**4/12 + 5*i**3/4 - 5*i**2/4 - 7*i. Factor x(n).
-5*(n - 1)**4*(n + 1)/2
Let h = 9 - 6. Solve n**3 + 0*n**3 + 0 - 3*n**h - 6*n + 2 + 6*n**2 = 0.
1
Let g be (176/11)/(1 - -1). Let m be (-6)/4*g/(-6). Factor 0 + 2/5*f**m - 2/5*f**5 + 0*f + 2/5*f**3 - 2/5*f**4.
-2*f**2*(f - 1)*(f + 1)**2/5
Suppose z + 5*i = 13, 0 = 2*z + 3*i + 8 - 20. Suppose -4*d = 5*r - 10, 3*d - z*r - r = -8. Factor d - 2/3*v - 2*v**3 + 2/3*v**4 + 2*v**2.
2*v*(v - 1)**3/3
Let u(a) = -a + 10. Let y be u(7). Solve -1/2*k**4 + 1/2*k**y + 0 + 0*k + 0*k**2 = 0.
0, 1
Suppose -4*y + 4 = -3*d - 23, 4*y + 3*d = -3. Factor -12*j + 4*j**y + 21*j - 10*j**2 + 27*j + 34*j**2.
4*j*(j + 3)**2
Suppose 0 = 5*f + 5*y + 15, 5*f - 8 - 1 = 3*y. Let t(m) be the first derivative of -2/5*m**5 + f*m**2 - 2*m + 1 + 0*m**4 + 4/3*m**3. Factor t(w).
-2*(w - 1)**2*(w + 1)**2
Suppose 0 = 2*r + r. Suppose -2*l + v + v - 6 = 0, -l - v + 7 = r. Suppose 2 + 0 - 5*c + 5*c**2 - 2*c**l = 0. Calculate c.
2/3, 1
Suppose 5*c - c = 8. Solve 0 + 3*s**2 - s**c - 4 - 2 - 4*s = 0.
-1, 3
Let k = 1236/7 + -176. Solve 2/7*z - 2/7*z**2 + k = 0 for z.
-1, 2
Let u be 9/(-2)*10/(-15). Let j(f) be the first derivative of -2*f + 2*f**u + 1/2*f**2 - 4/5*f**5 + 1/2*f**6 + 3 - f**4. Factor j(x).
(x - 1)**3*(x + 1)*(3*x + 2)
Let r(o) be the second derivative of o**7/84 - o**6/15 + o**5/10 + o**4/12 - 5*o**3/12 + o**2/2 - 6*o. Suppose r(n) = 0. What is n?
-1, 1, 2
Let n be 2*(-1)/2 - 2. Let k(a) = 4 - 3*a**2 - a**2 + 2*a**2 + a. Let i(d) = -5*d**2 + 2*d + 11. Let x(r) = n*i(r) + 8*k(r). Let x(l) = 0. Calculate l.
1
Suppose -4*v + 2*i = -2, -5*i = -2*v - 0*v - 3. Let s be (-20)/(-6) - (v - 1). Factor -1/3*g**5 - 5/3*g - s*g**3 - 1/3 - 10/3*g**2 - 5/3*g**4.
-(g + 1)**5/3
Let u(g) = -g**3 - g**2 + g + 1. Let i(z) = -8*z**3 - 32*z**2 - 34*z - 10. Let q(y) = i(y) + 2*u(y). Solve q(a) = 0 for a.
-2, -1, -2/5
Solve 3*d + 5*d - 7*d**3 + 5*d**2 - 3*d + 2*d**3 - 5*d**4 = 0.
-1, 0, 1
Let k be (-325)/(-125) - 2/(-5). Let g(n) be the first derivative of -16*n**k - 4*n**2 + 0*n - 10*n**5 - 1 - 45/2*