3*s**4 - s**3 + 2/3*s + 1/3*s**5 + 1/3*s**2.
s*(s - 2)*(s - 1)*(s + 1)**2/3
Let b = 353/13800 - -1/920. Let h(f) be the second derivative of 0*f**2 - 1/15*f**3 - 2*f + b*f**6 - 1/15*f**4 + 0 + 0*f**5 + 1/105*f**7. Factor h(q).
2*q*(q - 1)*(q + 1)**3/5
Factor 4*a**3 - 4 + 0 + 5 + a**4 + 6*a**2 + 4*a.
(a + 1)**4
Let v(b) = -4*b**2 - 23*b - 9. Let p(h) = -2*h**2 - 12*h - 4. Let r(g) = 7*p(g) - 4*v(g). Factor r(s).
2*(s + 2)**2
Let d be ((-4)/(-8))/(3/18). Let f(i) be the first derivative of -2*i - 2/3*i**d + 2*i**2 + 2. Solve f(m) = 0 for m.
1
Let g(f) be the third derivative of -3/70*f**5 + 0*f - 1/12*f**4 + 2/21*f**3 + f**2 + 0. Factor g(a).
-2*(a + 1)*(9*a - 2)/7
Suppose -2*x = 2*a, 0 = -5*x + a + 5 + 7. Factor 2/3 + 2*r + x*r**2 + 2/3*r**3.
2*(r + 1)**3/3
Factor 24*k**2 + 4*k**3 - 3*k + 14*k + 9*k.
4*k*(k + 1)*(k + 5)
Suppose 4 = -2*d + 5*d + 4*u, d - 2 = -2*u. Let a = -2 + 5. Factor 1/2*c**2 + d*c + 0 + 1/2*c**a.
c**2*(c + 1)/2
Let f(z) be the first derivative of 0*z - z**2 - 2 - 1/2*z**4 - 4/3*z**3. Factor f(p).
-2*p*(p + 1)**2
Let v = -498/13 - -16079/416. Let t = v - 3/32. Let 1/4*m**4 - 1/4*m**2 + 0 + t*m - 1/4*m**3 = 0. What is m?
-1, 0, 1
Let n(a) be the first derivative of -a**4/7 + 4*a**3/21 + 1. Find t such that n(t) = 0.
0, 1
Let h(f) be the second derivative of 10/21*f**7 + 0 + 0*f**4 + 6*f + 0*f**2 + 0*f**3 - 2/5*f**5 - 2/5*f**6. Factor h(l).
4*l**3*(l - 1)*(5*l + 2)
Suppose -4 = -3*v + 2. Determine j, given that 2*j**3 - v*j - 5*j**3 + 15*j**3 - 2*j**2 = 0.
-1/3, 0, 1/2
Let q(r) be the first derivative of -5*r**6/18 + 17*r**5/15 - 7*r**4/4 + 11*r**3/9 - r**2/3 + 2. Suppose q(c) = 0. What is c?
0, 2/5, 1
Let t = 459/2 - 229. Factor -t*q + 1/4 + 1/4*q**2.
(q - 1)**2/4
Let d(t) be the second derivative of t**7/126 + 4*t. Determine f, given that d(f) = 0.
0
Suppose 0 = -5*x + 9 + 16. Let n(a) be the second derivative of -1/27*a**3 + 4*a + 1/90*a**x + 0*a**2 + 0 + 0*a**4. Find g, given that n(g) = 0.
-1, 0, 1
Let i(o) be the second derivative of -o**4/48 - o**3/12 + 5*o. Factor i(w).
-w*(w + 2)/4
Let u(w) = 3*w. Let o(b) = 4*b. Let l(p) = 5*o(p) - 8*u(p). Let d be l(-2). Factor 2*z**2 + 4*z - 8*z**2 - 2*z**4 - 8*z**3 + 4*z + d.
-2*(z - 1)*(z + 1)*(z + 2)**2
Let k(t) be the second derivative of -t**6/135 + t**5/18 - 4*t**4/27 + 4*t**3/27 - 7*t. Factor k(v).
-2*v*(v - 2)**2*(v - 1)/9
Let q = 208 - 205. Factor 0 - 3/5*z**q - 3/5*z**2 + 0*z.
-3*z**2*(z + 1)/5
Let o be (-450)/(-80)*20/(-3). Let j = 38 + o. Let -j - 1/4*s + 1/4*s**2 = 0. Calculate s.
-1, 2
Suppose 4*t - 5*n = 287, 131 = 2*t + 5*n + 10. Let i = -474/7 + t. Let 2/7*p**4 + i*p**2 + 6/7*p**3 - 4/7 - 6/7*p = 0. What is p?
-2, -1, 1
Suppose 5*v - 2*j = 2*j + 28, 4 = -2*j. Factor 6*f**2 + 0*f + 2*f**v + 0*f**4 - f**4 + 1 - 4*f**3 - 4*f.
(f - 1)**4
Let m(y) be the third derivative of 0*y - 1/3*y**4 + 4/9*y**3 + 1/36*y**6 + 0 - 4*y**2 + 1/30*y**5. Factor m(h).
2*(h - 1)*(h + 2)*(5*h - 2)/3
Let m(d) be the second derivative of 4*d + 0 - 1/10*d**5 - 1/4*d**2 - 1/3*d**3 - 1/4*d**4 - 1/60*d**6. Factor m(h).
-(h + 1)**4/2
Let r(y) be the first derivative of y**6/600 - y**5/50 + y**4/10 + 2*y**3/3 + 2. Let f(b) be the third derivative of r(b). Solve f(m) = 0 for m.
2
Determine x so that -3*x**2 - 7*x + 2*x + 0*x**2 - 3 - x = 0.
-1
Let a(u) be the first derivative of -2*u**5/25 + u**4 - 42. Factor a(r).
-2*r**3*(r - 10)/5
Let h(r) be the first derivative of -4*r**3/3 + 6*r**2 - 8*r - 31. Find i, given that h(i) = 0.
1, 2
Factor 10/9*b**2 + 8/9*b + 0 + 2/9*b**3.
2*b*(b + 1)*(b + 4)/9
Let j be 4 - 0/(3 - 4). Suppose -z - 2 = 3*a, -z - j = -3*a + z. Factor 0*l - 2/3*l**4 - 4/3*l**3 + 0 + a*l**2.
-2*l**3*(l + 2)/3
Let t(m) = -4*m**4 + 6*m**3 + 5*m**2 - 3*m - 4. Let a = 18 - 13. Let u(o) = 3*o**4 - 7*o**3 - 5*o**2 + 4*o + 5. Let y(n) = a*t(n) + 4*u(n). Factor y(k).
-k*(k - 1)*(2*k + 1)*(4*k + 1)
Suppose 0 = f - 1 + 13. Let i be 6/(-14)*8/f. Let -2/7*n + i*n**2 + 0 - 2/7*n**4 + 2/7*n**3 = 0. What is n?
-1, 0, 1
Find s such that -2/9*s**2 + 2/9 + 0*s = 0.
-1, 1
Let a(v) be the third derivative of -1/480*v**6 + 0*v + 0 - 1/24*v**4 + 3*v**2 + 0*v**3 - 1/60*v**5. Factor a(i).
-i*(i + 2)**2/4
Let p(q) be the third derivative of -q**5/120 - q**4/48 - 16*q**2. Factor p(z).
-z*(z + 1)/2
Let s(n) be the third derivative of 4*n**2 + 0*n**4 - 1/120*n**5 + 0*n**3 + 0 + 0*n. Solve s(o) = 0.
0
Let v(o) be the second derivative of o**5/50 - o**4/10 + 2*o**3/15 - 8*o. Determine i so that v(i) = 0.
0, 1, 2
Let n = 4 + -4. Suppose -4*d - v - 2*v + 7 = n, 2*d + 5*v + 7 = 0. Factor -5 + 0*z - 2*z**2 - d*z + 3.
-2*(z + 1)**2
Let r(i) = -23*i - 89. Let o be r(-4). Factor 2/3*v - 2/3*v**o - 4/3*v**2 + 4/3.
-2*(v - 1)*(v + 1)*(v + 2)/3
Let w(k) = k**2 + 10*k + 11. Let h(s) = -2*s - 3. Let d be h(3). Let u be w(d). Suppose -30*p**u + 30*p**2 + 3*p**3 = 0. Calculate p.
0
Let z(t) be the second derivative of 0*t**4 + t + 1/3*t**3 - 1/10*t**5 + 0*t**2 + 0. Factor z(x).
-2*x*(x - 1)*(x + 1)
Let z(k) be the first derivative of 2*k**6/21 - 32*k**5/35 + 13*k**4/7 + 88*k**3/21 - 64*k**2/7 - 128*k/7 + 19. Find p, given that z(p) = 0.
-1, 2, 4
Factor 225/2*v - 45/2*v**2 + 3/2*v**3 - 375/2.
3*(v - 5)**3/2
Let h(r) be the first derivative of 3*r**5/80 - 3*r**3/8 + 3*r**2/4 - r - 2. Let p(k) be the first derivative of h(k). Solve p(g) = 0.
-2, 1
Let y(i) be the third derivative of i**6/900 - i**5/225 + i**4/180 - 5*i**2. Determine z so that y(z) = 0.
0, 1
Let h(i) = i**3 - 5*i**2 + 2*i - 6. Let z be h(5). Solve 20*v**3 + 70*v**4 - 22*v**4 + z*v**3 - 3 - 24*v - 45*v**2 = 0.
-1, -1/4, 1
Factor 5*r**2 - 2*r**2 + 5*r - 2*r.
3*r*(r + 1)
Factor 4/5*d**3 - 2/5*d**5 + 0 + 2/5*d**4 + 0*d + 0*d**2.
-2*d**3*(d - 2)*(d + 1)/5
Let j(y) = -4*y**5 - 32*y**4 - 24*y**3 - 28*y**2 + 16*y + 12. Let h(x) = -x**4 + x**3 + 2*x + 1. Let v(d) = -12*h(d) + j(d). Determine k, given that v(k) = 0.
-2, -1, 0
Let w(y) be the third derivative of -y**7/420 + y**6/60 - y**5/20 + y**4/12 + 5*y**3/6 - y**2. Let d(x) be the first derivative of w(x). Factor d(p).
-2*(p - 1)**3
Let w(k) be the first derivative of k**4/8 + k**3/2 + 3*k**2/4 + k/2 + 20. Factor w(p).
(p + 1)**3/2
Let i(f) = -f**3 + 1. Let w(u) = -25*u**3 + 27*u**2 - 6*u + 4. Let m(l) = -4*i(l) + w(l). Suppose m(q) = 0. Calculate q.
0, 2/7, 1
Let t(k) = -k - 1. Let i = -14 + 9. Let s(b) = b**4 + 3*b**3 + b**2 + 2*b + 3. Let j(a) = i*t(a) - s(a). Solve j(g) = 0 for g.
-2, -1, 1
Factor 3/4*s**5 + 3/4*s**4 + 0 + 0*s + 0*s**2 + 0*s**3.
3*s**4*(s + 1)/4
Let g(t) = -2*t - 16. Let v be g(-10). Let x(q) be the first derivative of 18/5*q**5 - 4*q**2 + 2*q + 1 - 4/3*q**3 + 6*q**v. Factor x(s).
2*(s + 1)**2*(3*s - 1)**2
Find u such that 84*u - 3*u**2 - 2*u**2 - 39*u = 0.
0, 9
Factor -3/2*x + 0 + 3*x**2 - 3/2*x**3.
-3*x*(x - 1)**2/2
Let q be (-1 - -6) + -12 + 9. Factor 2/7*u**3 - 6/7*u + 0*u**q + 4/7.
2*(u - 1)**2*(u + 2)/7
Let d(b) = -b**2 + b + 1. Let j(x) = -12*x**2 + 6*x + 17. Let s(z) = -44*d(z) + 4*j(z). Factor s(q).
-4*(q - 1)*(q + 6)
Let w(p) = p**3 + 8*p**2 + 7*p + 3. Let x be w(-7). Factor -2/7*j**x - 4/7*j - 6/7*j**2 + 0.
-2*j*(j + 1)*(j + 2)/7
Let k(y) be the second derivative of 8*y + 1/33*y**3 + 1/165*y**6 + 0*y**2 + 0 - 1/66*y**4 - 1/110*y**5. Find z such that k(z) = 0.
-1, 0, 1
Let p(z) be the third derivative of z**2 - 1/30*z**5 + 0*z + 0 + 1/3*z**3 + 0*z**4. Find l, given that p(l) = 0.
-1, 1
Find m, given that 4/7 + 0*m**4 - 4/7*m**2 - 8/7*m**3 + 2/7*m**5 + 6/7*m = 0.
-1, 1, 2
Let l = 16 - 22. Let p be 0 + l/(-2) + 0. Factor 0 + 2/7*u**p + 0*u**2 - 2/7*u.
2*u*(u - 1)*(u + 1)/7
Factor -2/9*r - 32/9*r**2 - 52/9*r**4 + 68/9*r**3 + 4/9 + 14/9*r**5.
2*(r - 1)**4*(7*r + 2)/9
Let u(d) be the third derivative of -d**6/24 + 5*d**5/12 - 35*d**4/24 + 5*d**3/2 - 11*d**2. Let u(z) = 0. What is z?
1, 3
Let d(p) be the first derivative of -2/3*p**3 + 7/4*p**4 - 7/2*p**2 + 2*p - 5. Factor d(o).
(o - 1)*(o + 1)*(7*o - 2)
Let c(s) be the first derivative of -s**4/4 + s**3/3 - 2. Determine g, given that c(g) = 0.
0, 1
Let t(m) = m**3 + m - 1. Let x(v) = 4*v**4 + 20*v**3 + 4*v - 16. Let s(c) = -12*t(c) + x(c). Factor s(k).
4*(k - 1)*(k + 1)**3
Suppose 3*q - 8 = -4*u + 6, 3*q + u = 8. Factor -3*a**q - 1 + a**2 + 2*a + a**2 + 0*a.
-(a - 1)**2
Let k = 10 + -13. Let j be (k/6)/(5/(-30)). Suppose -4/5*w**2 + 0 - 2/5*w*