**3 - 2*s**4 - 9*s - 2/15*s**6 + 0 - 4/5*s**5 - 2*s**2. Factor d(u).
-4*(u + 1)**4
Let b(j) = j**2 - 4*j - 8. Let a be b(6). Let i(f) be the third derivative of -f**2 + 0 - 1/210*f**5 + 0*f + 0*f**a + 0*f**3. Let i(d) = 0. Calculate d.
0
Let c(u) be the third derivative of -3*u**2 + 1/12*u**3 + 1/60*u**5 + 1/16*u**4 + 0*u + 0. Factor c(p).
(p + 1)*(2*p + 1)/2
Let v be 6/(-45)*1/(-2). Let r(q) be the first derivative of -1/12*q**4 - 2 + 1/6*q**2 + 0*q + 1/9*q**3 - v*q**5. Determine y so that r(y) = 0.
-1, 0, 1
Let y(m) be the third derivative of m**6/120 - m**5/30 + m**4/24 - 14*m**2. Solve y(a) = 0 for a.
0, 1
Let d = -122 - -122. Let l(q) be the second derivative of 1/2*q**3 - 1/5*q**4 - 3/5*q**2 + d - 3*q + 3/100*q**5. Factor l(n).
3*(n - 2)*(n - 1)**2/5
Suppose 8 = 4*z - 4. Factor -5 - 15*p**2 + 12*p + 6*p**3 + z + 0 - 1.
3*(p - 1)**2*(2*p - 1)
Let o(z) = 4*z**2 - 2*z + 1. Let m be o(1). Suppose 0 = 3*f + 5*v + 14, -m*f = 2*f - 3*v - 22. Factor -1/3*q + 1/3*q**3 + 1/3*q**f - 1/3.
(q - 1)*(q + 1)**2/3
Factor -4*z**3 + 4*z + 0*z + 25 - 28*z**2 + 3.
-4*(z - 1)*(z + 1)*(z + 7)
Let j(v) be the third derivative of 0 + 0*v**3 + v**2 + 0*v - 1/12*v**4 - 1/15*v**5. Let j(r) = 0. Calculate r.
-1/2, 0
Let a(b) = -9*b**2 + 6*b. Let k(q) = -17*q**2 + 11*q. Let l(u) = 11*a(u) - 6*k(u). Factor l(w).
3*w**2
Let 2/3*g**3 + 0 + 8/3*g**2 + 0*g = 0. What is g?
-4, 0
Factor -6/5*h - 3/5*h**2 + 3/5*h**3 + 0.
3*h*(h - 2)*(h + 1)/5
Let h = 2/139 - -268/695. Find k, given that 0*k + 0 + 0*k**2 + 0*k**3 + h*k**5 - 2/5*k**4 = 0.
0, 1
Let n be ((-4)/(-3))/((-14)/(-7)). Suppose -4/3*r + n + 2/3*r**2 = 0. Calculate r.
1
Let u(j) = 5*j**5 + 13*j**4 + 2*j**3. Let w(d) = -60*d**5 - 155*d**4 - 25*d**3. Let y(x) = 35*u(x) + 3*w(x). Find q, given that y(q) = 0.
-1, 0
Let n(a) = -a**2 + 5*a + 7. Let b be n(7). Let o = 7 + b. Factor -3/2*f**2 - 1/2*f**3 + o - f.
-f*(f + 1)*(f + 2)/2
Let i(v) be the first derivative of 1/21*v**6 + 0*v**2 - 2/35*v**5 + 0*v + 2 - 1/14*v**4 + 2/21*v**3. Factor i(j).
2*j**2*(j - 1)**2*(j + 1)/7
Let a(g) = 5*g**4 + 18*g**3 + 55*g**2 + 81*g + 36. Let q(n) = n**4 - n**2 + n. Let r(d) = a(d) - 3*q(d). Determine p, given that r(p) = 0.
-3, -2, -1
Factor 0*u - 1/4*u**4 + 0 + u**2 + 0*u**3.
-u**2*(u - 2)*(u + 2)/4
Suppose 24*x**2 - 52*x**2 + 3 + 25*x**2 = 0. What is x?
-1, 1
Let w(i) be the second derivative of -1/147*i**7 - 1/105*i**6 + 1/70*i**5 - i + 0*i**2 + 1/42*i**4 + 0 + 0*i**3. Find r such that w(r) = 0.
-1, 0, 1
Let w be (-3 - 70/(-16)) + -2. Let s = w - -9/8. Determine l so that 1/2*l + 3/2*l**3 - 3/2*l**2 + 0 - s*l**4 = 0.
0, 1
Factor 5*r**3 + 31 - 20*r + 1 - 5*r**2 - 12.
5*(r - 2)*(r - 1)*(r + 2)
Let t = 45 - 43. Let w(a) be the first derivative of -1 + 3/4*a**4 - 1/5*a**5 + 1/2*a**t + 0*a - a**3. Factor w(b).
-b*(b - 1)**3
Let i(q) = -q - 1. Let x be (6*-1)/((-3)/(-2)). Let d be i(x). Determine v so that 2*v**2 + 2*v - v - 2*v**3 + d*v**3 = 0.
-1, 0
Let r = -5 - -7. Factor -r*y - 12*y**3 - y**2 + 5*y**2 + 10*y**3.
-2*y*(y - 1)**2
Let u(a) be the first derivative of -5*a**3/3 + 5*a**2/2 + 17. Determine w so that u(w) = 0.
0, 1
Let l be -1 + (-2)/(-1) - -1. Let r = -17/6 - -10/3. Solve -1/2*b + 1/2*b**3 + r + b**4 - 3/2*b**l = 0.
-1, 1/2, 1
Suppose 0 = -3*a - 5*q - 16, -2*q = 3*a - 4*q - 19. Suppose -w = -5 + a. Factor -1/2 - 1/2*s**w + s.
-(s - 1)**2/2
Let c = 59 + -235/4. Let n = -18 + 20. Factor c*a**n + 0 - 1/2*a.
a*(a - 2)/4
Let n(b) be the second derivative of 2*b**5/35 + 11*b**4/42 - 19*b**3/21 + 4*b**2/7 - 22*b. Factor n(x).
2*(x - 1)*(x + 4)*(4*x - 1)/7
Let n(l) = -l - 4. Suppose -22 = 4*u + 2. Let p be n(u). Solve -2*w**5 - 5*w**5 + 6*w**5 + w**3 + w**4 - w**p = 0 for w.
-1, 0, 1
Let r(i) = 6*i**3 - 4*i**2 + 2*i + 8. Suppose -6*j = -9*j + 24. Let l = j - 4. Let a(q) = -13*q**3 + 8*q**2 - 5*q - 17. Let k(h) = l*a(h) + 9*r(h). Factor k(m).
2*(m - 2)*(m - 1)*(m + 1)
Let g(a) be the third derivative of a**9/7560 + 3*a**8/7840 + a**7/4410 + a**4/6 - a**2. Let p(i) be the second derivative of g(i). Factor p(q).
2*q**2*(q + 1)*(7*q + 2)/7
Let w(p) be the second derivative of -2/3*p**3 + 1/6*p**4 + 2*p - 1/60*p**5 + 0 + 4/3*p**2. Factor w(g).
-(g - 2)**3/3
Let d(j) be the first derivative of 5*j**4/2 - 5*j**3 + 5*j**2/2 - 12. Factor d(v).
5*v*(v - 1)*(2*v - 1)
Let b(p) be the third derivative of p**7/105 - p**6/20 + p**5/15 + 3*p**2. Factor b(c).
2*c**2*(c - 2)*(c - 1)
Let m(i) be the first derivative of i**6/5 - 3*i**5/25 - 3*i**4/10 + i**3/5 + 25. Suppose m(c) = 0. What is c?
-1, 0, 1/2, 1
Let h(v) be the second derivative of 0*v**3 + 1/15*v**6 + 1/10*v**5 + 0*v**2 + 0 + 0*v**4 + 2*v. Factor h(w).
2*w**3*(w + 1)
Let c(w) be the first derivative of 3*w**4/20 + w**3/5 - 2. Factor c(t).
3*t**2*(t + 1)/5
Let z be 2/6*37440/(-44). Let t = 284 + z. Factor 2/11*x**3 + 0 + t*x**2 + 2/11*x.
2*x*(x + 1)**2/11
What is c in 3*c**2 + 25/2 + 45/4*c + 1/4*c**3 = 0?
-5, -2
Let l(g) be the first derivative of -1/120*g**4 + 0*g**3 + g**2 + 0*g**5 + 4 + 1/600*g**6 + 0*g. Let c(x) be the second derivative of l(x). Factor c(p).
p*(p - 1)*(p + 1)/5
Let v(w) = 3*w**5 - 11*w**4 + w**3 + 9*w**2 + 6*w + 2. Let p(r) = 2*r**5 - 10*r**4 + 8*r**2 + 6*r + 2. Let k(n) = -5*p(n) + 4*v(n). Find j, given that k(j) = 0.
-1, 1
Suppose -32 = 2*i + 2*c, -3*i + 2 = -5*c + 10. Let n = -7 - i. Let -1/2*w**n + 1/2*w**5 + 0 + 0*w + 1/2*w**2 - 1/2*w**3 = 0. Calculate w.
-1, 0, 1
Let a(i) be the third derivative of -i**6/240 + i**5/40 + i**4/48 - i**3/4 - 14*i**2. Find q such that a(q) = 0.
-1, 1, 3
Let i be ((-108)/(-20) - 2) + -3. Factor 0 + i*b + 2/5*b**2.
2*b*(b + 1)/5
Suppose -3*o = 5*o - 8. Let -o + 7/2*k + k**4 - 1/2*k**5 - 4*k**2 + k**3 = 0. Calculate k.
-2, 1
Let u = 27/2 - 181/14. Factor 2*r**2 + 0 - u*r.
2*r*(7*r - 2)/7
Let w(l) = -23*l**3 - 64*l**2 - 21*l. Let n(s) = 12*s**3 + 32*s**2 + 10*s. Let d be -4 + 6 + -4 + 4. Let u(y) = d*w(y) + 5*n(y). What is z in u(z) = 0?
-2, -2/7, 0
Let g(j) be the first derivative of j**3/12 - j**2 + 4*j - 20. Factor g(u).
(u - 4)**2/4
Determine k, given that -9*k**2 + 192/5 - 3/5*k**3 - 144/5*k = 0.
-8, 1
Factor -3/4 + 3/4*p**2 - 1/4*p + 1/4*p**3.
(p - 1)*(p + 1)*(p + 3)/4
Let 3/4 - 3/8*w - 3/4*w**2 + 3/8*w**3 = 0. What is w?
-1, 1, 2
Let q(k) be the first derivative of 1/2*k**3 + 9/16*k**4 + 1 + 0*k**2 + 0*k. Suppose q(w) = 0. What is w?
-2/3, 0
Suppose -5*h = -3*b - 24, h - 3*b - 22 = -10. Factor 2/9*x**4 + 0*x + 0*x**2 + 0*x**h + 0.
2*x**4/9
Let c be -2 - ((-51)/(-90) - 3). Let v(t) be the third derivative of 1/12*t**6 + c*t**5 + 0*t + 3*t**2 + 0 + 1/3*t**4 - 4/3*t**3. Let v(z) = 0. What is z?
-2, -1, 2/5
Let m(i) be the third derivative of -i**6/40 + 3*i**5/20 - 3*i**4/8 + i**3/2 + 10*i**2. Factor m(s).
-3*(s - 1)**3
Suppose -8*y + 10*y = 0. Factor 0 + y*f - 2/9*f**2.
-2*f**2/9
Let c(o) be the third derivative of o**8/2016 - o**7/1260 - o**6/240 + o**5/360 + o**4/72 - 7*o**2. Find r, given that c(r) = 0.
-1, 0, 1, 2
Let x(q) be the first derivative of 2*q**3/3 - 4*q**2 - 10*q - 13. Factor x(o).
2*(o - 5)*(o + 1)
Let u(a) be the second derivative of -a**6/120 + a**4/8 + 2*a**3/3 + 6*a. Let h(b) be the second derivative of u(b). Determine r so that h(r) = 0.
-1, 1
Let b(c) = -16*c**3 - 16*c**2 + 11*c + 11. Let o(n) = 3*n**3 + 3*n**2 - 2*n - 2. Let p(d) = -2*b(d) - 11*o(d). Suppose p(t) = 0. Calculate t.
-1, 0
Let v(y) be the first derivative of y**6/180 - y**4/12 - 2*y**3/9 + y**2/2 + 4. Let g(k) be the second derivative of v(k). Factor g(d).
2*(d - 2)*(d + 1)**2/3
Let b = -18 - -21. Determine v, given that -2/9 - 4/9*v**b + 4/9*v**2 + 2/9*v + 2/9*v**5 - 2/9*v**4 = 0.
-1, 1
Suppose 47*w = 45*w + 4. Solve 0 + 0*n + 0*n**w + 2/3*n**3 + 2/3*n**4 = 0 for n.
-1, 0
Let c = 446 + -46829/105. Let v(n) be the second derivative of n + 0*n**3 + 1/42*n**4 + 0*n**2 + 0 + 0*n**5 - c*n**6. Factor v(l).
-2*l**2*(l - 1)*(l + 1)/7
Let s be 2 + 1 - (-8)/4. Let t(d) be the second derivative of 1/15*d**s + 1/63*d**7 - 1/15*d**6 - 2*d + 1/3*d**2 + 0 - 1/3*d**3 + 1/9*d**4. Factor t(v).
2*(v - 1)**4*(v + 1)/3
Suppose 4*y + b + 4 = 0, 4 = -y + 5*y - b. Find x such that y*x + 0*x**2 + 2/5*x**3 + 0 = 0.
0
Let g(l) be the second derivative of -l**5/20 - l**4/6 - 5*l**3/6 - 2*l**2 - 4*l. Let y(z) = -z**3 - 3*z**2 - 6*z - 5. Let x(v) = -5*g(v) + 4*y(v). Factor x(c)