Let g(f) be the first derivative of 8/35*f**5 - 4/21*f**3 + 1/21*f**6 - 10 - 4/7*f - 5/7*f**2 + 2/7*f**4. Factor g(z).
2*(z - 1)*(z + 1)**3*(z + 2)/7
Let v be 12/66 + (-26)/22. Let p be (13/5 + v)/((-252)/(-90)). Factor 2/7*z**3 + 0*z + 0 + p*z**2.
2*z**2*(z + 2)/7
Let o(v) be the first derivative of 1/2*v**2 + 1/5*v**5 - 1/4*v**4 - 25 + 0*v - 1/3*v**3. Factor o(n).
n*(n - 1)**2*(n + 1)
Let a(y) be the second derivative of y**6/8 + 11*y**5/10 + 7*y**4/2 + 4*y**3 - 11*y**2 - 6*y. Let c(f) be the first derivative of a(f). Factor c(u).
3*(u + 2)**2*(5*u + 2)
Let s(a) = -4*a**2 + 35*a - 25. Let b(c) = -5*c**2 + 37*c - 24. Let q(n) = 3*b(n) - 4*s(n). Find r, given that q(r) = 0.
1, 28
Let u(l) be the third derivative of l**5/330 - 49*l**4/132 - 50*l**3/33 + 203*l**2 - 2. Factor u(t).
2*(t - 50)*(t + 1)/11
Let l(c) = -15*c**4 - 9*c**3 + 3*c**2 + 33*c - 24. Let o(i) = -2*i**4 - i**2 + 2*i - 1. Let s(u) = -l(u) + 6*o(u). Factor s(m).
3*(m - 1)**2*(m + 2)*(m + 3)
Factor -30*h**2 - 36*h**2 + 10*h - 29*h**2 + 96*h**2.
h*(h + 10)
Find j, given that 42*j - 110*j**2 + 80*j**2 + 35 - 2*j - 5*j**4 - 40*j**3 = 0.
-7, -1, 1
Factor -18*w**2 + 20*w**4 + 7*w**2 - 21*w**4 + 8*w - 8*w**3 + 16 - 4*w**2.
-(w - 1)*(w + 1)*(w + 4)**2
Suppose 0 = -o - 3*c - 5, -6 = 5*c + 9. Suppose 3*m - 35 = -o*a, 5*a - 3*a - 5*m = -15. Determine v so that -10*v**5 - 4*v**5 + 12*v**4 - 16*v**2 + 10*v**a = 0.
-1, 0, 2
Let p = 142/23 + -380/69. Factor -p*r**2 - 2/3*r + 0.
-2*r*(r + 1)/3
Suppose 3*c = -0*c + 15, -25 = 3*v - 5*c. Let z be 2 - (2 + v + -2). Factor -3*b**2 + 13*b**4 + 3*b**3 - 14*b**4 + b**z.
-b**2*(b - 2)*(b - 1)
Let k(b) = 70*b + 352. Let i be k(-5). Let c(a) be the first derivative of -1/7*a**3 - 5 + 0*a**i + 0*a - 3/35*a**5 - 3/14*a**4. Factor c(y).
-3*y**2*(y + 1)**2/7
Let o(d) be the third derivative of d**6/60 - 14*d**5/15 + 49*d**4/12 + 26*d**3 - 549*d**2. Determine i so that o(i) = 0.
-1, 3, 26
Let f = -26 + 31. Let n(m) be the second derivative of 0*m**2 + 2*m - 3/20*m**f + 0 + 0*m**4 + 0*m**3. Factor n(x).
-3*x**3
Let g be (-156)/4134 + 10742/954 + -11. Suppose -12 = -4*q - 0*q. Determine r, given that g*r + 0 + 2/3*r**q + 2/9*r**4 + 2/3*r**2 = 0.
-1, 0
Let k(n) = -14*n - 4. Let s be k(-4). Let c = s - 27. Factor 4 - 12 - 36*x - 30*x**2 + 2 - 2 + c*x**3.
(x - 2)*(5*x + 2)**2
Factor 5/6*k**2 + 5/6*k - 5/6 - 5/6*k**3.
-5*(k - 1)**2*(k + 1)/6
Suppose n - d - 13 = -1, -4*d = 8. Determine q, given that -14*q**4 - 15*q**3 + n*q**4 - q**3 = 0.
-4, 0
Suppose 0 + 45 = 5*c + l, 4*c - 5*l - 65 = 0. Factor -c*h**2 + 21*h**3 + 19*h**4 - 25*h**3 - 9*h**4 + 4*h.
2*h*(h - 1)*(h + 1)*(5*h - 2)
Let h(a) = 24*a + 26. Let y(j) = 3*j**2 + 3*j - 3. Let o(v) = -2*v**2 - 2*v + 2. Let p(i) = 7*o(i) + 5*y(i). Let f(w) = h(w) + 2*p(w). Factor f(t).
2*(t + 1)*(t + 12)
Let p(m) be the second derivative of 18*m + 0 - 6*m**2 - 3/2*m**3 + 1/4*m**4. What is b in p(b) = 0?
-1, 4
Suppose 0 = -l - l - 12. Let v = l + 13. Let 11*n**4 + 10*n**3 - 10*n + v*n**4 - 4*n**4 + 4 - 18*n**2 = 0. Calculate n.
-1, 2/7, 1
Let r(s) be the first derivative of -s**7/560 + s**6/80 - s**4/4 - 5*s**3/3 - 10. Let j(q) be the third derivative of r(q). What is f in j(f) = 0?
-1, 2
Let a(z) be the second derivative of z**9/18144 + z**8/1008 + 7*z**4/4 + 35*z. Let x(l) be the third derivative of a(l). Factor x(r).
5*r**3*(r + 8)/6
Suppose 17*f + 109 = 194. Let b(k) be the first derivative of -3/10*k**f + 0*k**2 + k**3 + 0*k**4 + 13 - 3/2*k. Solve b(j) = 0 for j.
-1, 1
Let g(c) be the second derivative of c**4/32 + 19*c**3/8 + 274*c. Solve g(i) = 0 for i.
-38, 0
Let g(n) be the first derivative of 2*n**3/3 + 72*n**2 + 2592*n + 431. Factor g(d).
2*(d + 36)**2
Let q be 1/(22/(-732))*(-663)/(-26). Let u = q + 849. Factor 2/11*n**2 - 4/11*n - u.
2*(n - 3)*(n + 1)/11
Let o(w) = -3. Let l(g) = -7 + 2*g**2 - 4*g**2 + 3*g**2 - 2*g**2 + g. Let a(n) = -n**2 + 4*n + 2. Let d be a(5). Let b(u) = d*l(u) + 7*o(u). Factor b(m).
3*m*(m - 1)
Let s(z) be the second derivative of -z**6/90 + 2*z**5/15 - 7*z**4/12 + z**3 + 127*z. Suppose s(v) = 0. What is v?
0, 2, 3
Let h be 3/2*1/6. Let x be 1*(1 + -3)/(-1). Factor h*g**x + 1/4*g + 0.
g*(g + 1)/4
Let c be (-3)/1 + -1 + 6. Factor 52*s**3 - 2*s - 20*s**4 + 12*s + 13*s**3 - 55*s**c.
-5*s*(s - 2)*(s - 1)*(4*s - 1)
Let w be (-40)/(-96)*2*(-2 - -8). Let z(k) be the third derivative of 0*k**w - 1/8*k**4 - k**2 + 1/40*k**6 + 0 + 0*k**3 + 0*k. Find o such that z(o) = 0.
-1, 0, 1
Let g(p) be the second derivative of 1/42*p**7 + 5/6*p**4 + 1/2*p**5 + 1/2*p**2 - 13*p + 5/6*p**3 + 1/6*p**6 + 0. Solve g(y) = 0 for y.
-1
Solve -10/3*v**2 - 1/3*v**3 + 64/3 - 8/3*v = 0.
-8, -4, 2
Let q(x) be the first derivative of -1/8*x**4 + 0*x + 1/12*x**6 + 0*x**2 - 1/3*x**3 + 1/5*x**5 + 10. Determine h so that q(h) = 0.
-2, -1, 0, 1
Suppose 24 = -5*a - 4*l + 18, 4*a - 2*l = 16. Find v, given that 6/7 + 3/7*v**3 - 6/7*v**a - 3/7*v = 0.
-1, 1, 2
Let b(f) = f**3 - 10*f**2 + 2*f - 4. Let i be b(10). Let u = i - 14. Factor -6*l**u - 6*l**2 + 2 + 10*l**2.
-2*(l - 1)*(l + 1)
Let j(c) be the third derivative of c**9/22680 - c**8/3360 - 7*c**4/8 + 21*c**2. Let q(y) be the second derivative of j(y). Factor q(b).
2*b**3*(b - 3)/3
Let b(z) be the second derivative of -z**5/30 + 4*z**4/3 - 64*z**3/3 - 3*z**2/2 - 24*z. Let a(j) be the first derivative of b(j). Factor a(w).
-2*(w - 8)**2
Let i(c) be the third derivative of -1/15*c**4 + 0 + 0*c - c**2 + 1/150*c**5 + 0*c**3. Determine k, given that i(k) = 0.
0, 4
Let x(g) be the second derivative of -g**7/105 - 11*g**6/75 - 3*g**5/50 + 83*g**4/30 + 136*g**3/15 + 12*g**2 - 635*g. Let x(w) = 0. Calculate w.
-10, -2, -1, 3
Suppose 18 = -3*v, -34*i + 31*i - 18 = 4*v. Factor 0 + 0*w + 2/3*w**3 - 2/3*w**2 + 10/3*w**4 + i*w**5.
2*w**2*(w + 1)**2*(3*w - 1)/3
Let z(q) be the second derivative of q**4/20 - 13*q**3/5 + 507*q**2/10 - 119*q. Find c, given that z(c) = 0.
13
Let x(i) = -i**3 + 20*i**2 + 22*i + 7. Let t be x(21). Let -t*v + v**2 + 24 + 8*v - 5*v**2 = 0. What is v?
-6, 1
Factor -64/3 + 136/3*l - 10/3*l**3 + 64/3*l**2.
-2*(l - 8)*(l + 2)*(5*l - 2)/3
Factor 276/17*l - 2/17*l**2 - 9522/17.
-2*(l - 69)**2/17
Factor -653*a**3 - 26*a**2 - 657*a**3 - 6*a + 1290*a**3.
-2*a*(a + 1)*(10*a + 3)
Let w(i) be the third derivative of -i**7/70 + 3*i**6/20 - i**5/20 - 3*i**4 - 8*i**3 - i**2 + 36*i. Determine c, given that w(c) = 0.
-1, 4
Factor -27/2*v + 27 + 3/2*v**2.
3*(v - 6)*(v - 3)/2
Let k(t) be the first derivative of 0*t - 5/2*t**4 + 0*t**2 - 6 - 1/3*t**6 - 8/5*t**5 - 4/3*t**3. What is j in k(j) = 0?
-2, -1, 0
Suppose 7*c - 28 = -14. Factor 20*w**3 - 25*w**2 + 9*w + 6*w + 5*w**4 + c*w**3 - 17*w**3.
5*w*(w - 1)**2*(w + 3)
Suppose 5*w + 13 = -5*v - 12, 2*w + 45 = 5*v. Let f be 1/((-6)/(-27)) - (-5)/w. Solve 0*b**3 + 1/4*b**5 + 1/2*b**f - 1/4*b + 0 - 1/2*b**2 = 0 for b.
-1, 0, 1
Let q(h) be the second derivative of h**4/6 + 16*h**3/3 - 86*h. Factor q(b).
2*b*(b + 16)
Let s(h) = -h**4 - h**3 + h**2 + 2*h + 1. Let x(r) = 2*r**4 + 14*r**3 + 2*r**2 + 4*r + 2. Let m(n) = 2*s(n) - x(n). Let m(g) = 0. What is g?
-4, 0
Let m(w) = -w**3 + 3*w**2 + 12*w - 7. Let g be m(5). Factor 2*s**2 - 13*s**3 - 8 - 13*s + 2 - 10*s**2 + 12*s**g.
-(s + 1)**2*(s + 6)
Determine x, given that -9/10*x + 0 + 1/10*x**2 = 0.
0, 9
Factor -2/13*h**2 - 400/13*h - 20000/13.
-2*(h + 100)**2/13
Let b(s) = -s - 2. Let j be b(-7). What is h in h**2 + 4*h**4 - 27*h**5 + 23*h**j + 4*h**3 - 5*h**2 = 0?
-1, 0, 1
Suppose 6*l = 8*l + 6. Let t(z) = -2*z**4 + 2*z**3 - z**2 + 4*z - 3. Let u(b) = -b**4 + b**3 - b**2 + 3*b - 2. Let n(j) = l*u(j) + 2*t(j). Factor n(f).
-f*(f - 1)**2*(f + 1)
Let m = 569 + -2841/5. Suppose -1/5*b**4 + m*b - 2/5*b**2 + 3/5 - 4/5*b**3 = 0. Calculate b.
-3, -1, 1
Let u(l) be the third derivative of l**7/42 - l**6/12 - 7*l**5/12 - 5*l**4/6 + 22*l**2 - l. Let u(i) = 0. Calculate i.
-1, 0, 4
Let w(u) be the third derivative of 0*u - 1/4*u**3 + 1/160*u**6 - 1/20*u**5 + 5/32*u**4 + 0 - 3*u**2. Factor w(j).
3*(j - 2)*(j - 1)**2/4
Let r(x) be the first derivative of -2/15*x**3 + 24 - 1/5*x**2 + 0*x. Factor r(q).
-2*q*(q + 1)/5
Let a = 84 + -84. Let r be a - (-6 + 96/18). Factor -r*g + 0 + 2/3*g**2.
2*g*(g - 1)/3
Suppose 4*o - 25 = -i, 3*o - 8 = i + 2. Factor 5/2*t**2 + i*t + 0 - 5/2*t**4 - 5*t**3.
-5*t*(t - 1)*(t + 1)*(t + 2)/