**2*(g + 2)**2
Let v be (18 - 14624/816)*(-3)/(-2). Factor 4/17*i**4 + 0 + 10/17*i**3 + v*i + 8/17*i**2.
2*i*(i + 1)**2*(2*i + 1)/17
Let f(h) be the third derivative of h**7/840 - h**6/480 - h**5/80 + 5*h**4/96 - h**3/12 + 7*h**2. Factor f(l).
(l - 1)**3*(l + 2)/4
Let w be (-4)/(-6 - -2)*3. Suppose 0 = -5*f - 2*j + 18, f - 2*j = -f - 4. What is d in -2/3*d**f + 5/3*d + 2/3 - 5/3*d**w = 0?
-1, -2/5, 1
Let t(b) be the third derivative of b**5/330 - b**4/132 - 3*b**2. Determine y so that t(y) = 0.
0, 1
Suppose -n = -5 + 2. Let k(p) be the second derivative of -1/6*p**n + 1/3*p**2 + 0 + 1/36*p**4 - 3*p. Let k(h) = 0. Calculate h.
1, 2
Let k(p) be the first derivative of 0*p - 1/6*p**3 - 3 + 0*p**2 + 1/8*p**4. Factor k(u).
u**2*(u - 1)/2
Let r(f) = f**2 - 5*f + 1. Let t be r(5). Factor 2*h + 2*h**2 - 2 - 2*h**2 + t - h**2.
-(h - 1)**2
Suppose -4*b + 5*j + 15 = 0, b + 6*j - 6 = 5*j. Factor 2/7*y**4 + 0*y**3 + 0*y + 0 + 0*y**2 - 2/7*y**b.
-2*y**4*(y - 1)/7
Let s(f) be the third derivative of f**6/180 - f**4/36 - 6*f**2. Find r, given that s(r) = 0.
-1, 0, 1
Let j = 994/5 - 198. Factor 2/5*c + 0*c**3 + 0 + 4/5*c**4 - 2/5*c**5 - j*c**2.
-2*c*(c - 1)**3*(c + 1)/5
Let u(r) = -1. Let l(x) = 2*x**2 - 6*x + 10. Let i(k) = -l(k) - 6*u(k). Let i(s) = 0. Calculate s.
1, 2
Let q(y) = -16*y**3 - 7*y**2 + 9*y + 7. Let i(h) = -11*h**3 - 5*h**2 + 6*h + 5. Let m(j) = -j + 9. Let r be m(4). Let f(b) = r*q(b) - 7*i(b). Factor f(x).
-3*x*(x - 1)*(x + 1)
Let i(w) = -2*w**2. Let c(y) = 2*y**2 - y. Let j be ((-8)/(-6))/(14/(-21)). Let o(n) = j*c(n) - 3*i(n). Solve o(h) = 0 for h.
-1, 0
Suppose -5*j - 7 = o + 3, -3*o + 2*j + 4 = 0. Suppose n + 3*n - 16 = o. Factor -6*u**3 - 2*u**5 + 6*u**n - 15 + 15 + 2*u**2.
-2*u**2*(u - 1)**3
Let x(y) = 2*y**2 + 2*y + 2. Suppose 5*t = 5*w + 3*t + 3, 4*t = 5*w + 11. Let r(f) = -4 - f**2 - 2*f - 2*f**2 + w. Let j(k) = -3*r(k) - 4*x(k). Factor j(a).
(a - 1)**2
Let k(c) be the first derivative of -c**4/4 + 7*c**3/6 - 2*c**2 + 3*c/2 + 30. Find d, given that k(d) = 0.
1, 3/2
Factor 12/7*j**2 + 8/7*j + 0 + 4/7*j**3.
4*j*(j + 1)*(j + 2)/7
Let a(g) be the third derivative of g**7/525 + g**6/300 - 10*g**2. Solve a(c) = 0.
-1, 0
Let o(n) be the first derivative of n**7/21 - 17*n**6/75 + 21*n**5/50 - 11*n**4/30 + 2*n**3/15 + 2*n - 2. Let p(v) be the first derivative of o(v). Factor p(r).
2*r*(r - 1)**3*(5*r - 2)/5
Let h(j) = -12*j**3 + 2*j**2 - 10. Let a(x) = x**3 + 1. Let m(g) = -20*a(g) - 2*h(g). Factor m(z).
4*z**2*(z - 1)
Let j be 4/(-4 - (0 + -3)). Let b be 15/28 - j/(-14). Solve 0 - b*o**2 + 0*o = 0 for o.
0
Let f(r) be the second derivative of 8*r**6/75 - 8*r**5/25 + r**4/3 - 2*r**3/15 + 6*r. Let f(l) = 0. What is l?
0, 1/2, 1
Determine x, given that -12/5*x**3 + 0 - 3/5*x**4 - 6/5*x - 3*x**2 = 0.
-2, -1, 0
Suppose -h + 1 + 1 = 0. Let -2*f - 3*f + h*f - 3*f**2 = 0. What is f?
-1, 0
Determine m, given that -55*m**2 - 59*m**2 + 117*m**2 + 12 + 15*m = 0.
-4, -1
Suppose -2*h = -v - 2, -4*h = -2*h - 2*v. Factor 0 - 2/7*q**h + 6/7*q**3 + 0*q.
2*q**2*(3*q - 1)/7
Factor 22/5*o**3 + 2*o**4 + 2/5*o + 0 + 14/5*o**2.
2*o*(o + 1)**2*(5*o + 1)/5
Solve 10*x**4 + 2*x**2 - 317*x**5 + 10 + 10*x**3 + 312*x**5 - 5*x - 22*x**2 = 0 for x.
-1, 1, 2
Let o = -40 - -46. Factor -3/2 + 6*b**3 - 9*b**2 - 3/2*b**4 + o*b.
-3*(b - 1)**4/2
Let y(s) be the first derivative of s**4 - 4*s**3/3 + 3. Find b such that y(b) = 0.
0, 1
Let t(c) = -c**2 - 10*c - 4. Suppose -2*k = -3 + 21. Let h be t(k). Determine r so that 2/3*r**2 + 1/3*r**h + 2/3*r**3 - r**4 + 1/3 - r = 0.
-1, 1
Let t(o) be the second derivative of -15*o**7/56 - o**6/2 + o**5/8 + 5*o**4/12 - 5*o**3/24 + 22*o. Let t(x) = 0. Calculate x.
-1, 0, 1/3
Let d = -390 + 1561/4. Factor -j**2 + 5/4*j - 1/2 + d*j**3.
(j - 2)*(j - 1)**2/4
Factor -2/9 + 0*f + 2/9*f**2.
2*(f - 1)*(f + 1)/9
Let k(j) be the second derivative of 0 - 2*j + 0*j**3 + 0*j**4 + 0*j**2 - 1/20*j**5. Suppose k(x) = 0. What is x?
0
Suppose -18 = -3*t - 0*t. Suppose 4*k - t - 14 = 0. Factor -z**k - 3*z**5 + 3*z**5 + z**3.
-z**3*(z - 1)*(z + 1)
Let t(f) be the third derivative of f**6/40 - f**4/8 - 57*f**2. Factor t(u).
3*u*(u - 1)*(u + 1)
Let k(j) = 29*j**2 - 16*j + 4. Let z(g) = 28*g**2 - 17*g + 4. Let a(u) = 3*k(u) - 4*z(u). Solve a(q) = 0.
2/5
Let l(n) be the third derivative of -n**6/90 - 2*n**5/15 - 2*n**4/3 - 16*n**3/9 - 2*n**2 - 9. Factor l(b).
-4*(b + 2)**3/3
Let j = -33 + 233/7. Factor 0 - j*x + 6/7*x**2.
2*x*(3*x - 1)/7
Let q(n) = 36*n + 219. Let o be q(-6). Determine s, given that 6/5*s - 2/5 + 2/5*s**o - 6/5*s**2 = 0.
1
Let k(n) = n**3 + 2*n**2 - 3*n + 3. Let a be k(-3). Let o(l) be the second derivative of -1/12*l**4 + 0*l**2 + 1/6*l**a + 0 - l. Factor o(x).
-x*(x - 1)
Suppose 0 = -2*s - 3*l + 4 - 3, s + 2*l = 0. Find x, given that -1/4*x**3 + 0 + 0*x - 1/4*x**s = 0.
-1, 0
Let a(j) = -j**2 - 2*j - 3. Let b be a(-5). Let l = b + 20. Factor -2/9 + 0*y + 2/9*y**l.
2*(y - 1)*(y + 1)/9
Let b(z) be the third derivative of 1/72*z**4 - 1/18*z**3 - 1/360*z**6 + 0*z - 2*z**2 + 1/180*z**5 + 0. Factor b(u).
-(u - 1)**2*(u + 1)/3
Let y = -11 + 15. Suppose -2*a + y = -a. Determine s, given that -5*s + 9*s**2 - s**5 - 13*s**3 + 3*s**2 + s + 6*s**a = 0.
0, 1, 2
Suppose 3*b = -p + 6 + 8, -4*b - 24 = -4*p. Suppose -u + p = -5*j, 3*j + 2*j - 4 = -3*u. Find v, given that -1/3*v**2 + 0 + 1/3*v**5 - v**4 + 0*v + v**u = 0.
0, 1
Suppose -2*j = -2*v - 11 + 1, 4*v = -3*j + 8. Let q(s) be the third derivative of 1/24*s**j + 0 + 0*s + 1/3*s**3 - 1/60*s**5 - 3*s**2. Factor q(z).
-(z - 2)*(z + 1)
Let x(u) = u**2 - 8*u + 1. Let h(k) = -3*k**2 + 33*k - 3. Let q(b) = -b**2 - 3*b + 9. Let t be q(-6). Let d(y) = t*x(y) - 2*h(y). Factor d(g).
-3*(g - 1)**2
Factor -5 + 4*h - 4*h**4 + 67*h**3 - 144*h**3 + 3*h**4 + 73*h**3 + 6*h**2.
-(h - 1)**2*(h + 1)*(h + 5)
Let m(k) be the second derivative of -1/24*k**4 + 0 - k - 1/4*k**2 - 1/6*k**3. Find o, given that m(o) = 0.
-1
Let b(p) be the second derivative of 0*p**5 - 1/2520*p**7 + 0*p**4 + 0 - 1/6*p**3 + 0*p**6 + p + 0*p**2. Let t(c) be the second derivative of b(c). Factor t(r).
-r**3/3
Let l = -2 + 4. Factor -12*o**2 + 18*o**3 + 4*o - l*o + 2*o**4 - 10*o**4.
-2*o*(o - 1)**2*(4*o - 1)
Factor -1/2*i + 1/2*i**2 - 3.
(i - 3)*(i + 2)/2
Let p(g) = 5*g**4 - 10*g**3 - 22*g**2 + 8*g + 13. Let o(c) = -15*c**4 + 30*c**3 + 67*c**2 - 23*c - 38. Let y(u) = 2*o(u) + 7*p(u). Factor y(j).
5*(j - 3)*(j - 1)*(j + 1)**2
Let 1/5*x**3 - 1/5*x - 2/5 + 2/5*x**2 = 0. What is x?
-2, -1, 1
Find y such that 0*y**4 + 2/9*y**5 + 0*y + 4/9*y**2 + 0 - 2/3*y**3 = 0.
-2, 0, 1
Let r(t) be the third derivative of 0*t - t**2 + 0 - 1/60*t**5 + 1/12*t**4 + 0*t**3. Find l such that r(l) = 0.
0, 2
Suppose 0 = 25*n - 40*n. Find o such that -2/3*o**3 + 0 + n*o + 2/3*o**2 = 0.
0, 1
Let g(l) be the first derivative of -121*l**6/36 + 33*l**5/5 - 37*l**4/24 - 2*l**3 - l**2/3 + 1. Factor g(r).
-r*(r - 1)**2*(11*r + 2)**2/6
Solve -1/4*w**2 - w**3 - 7/8*w**4 - 1/4*w**5 + 1/4*w + 1/8 = 0 for w.
-1, 1/2
Factor 16*o**2 - 8*o**3 + 5*o**4 - o**5 - 5*o**2 - 7*o**2.
-o**2*(o - 2)**2*(o - 1)
Let x(i) be the third derivative of 0*i - 1/180*i**6 - 1/9*i**4 + 0*i**3 + 2/45*i**5 + 3*i**2 + 0. Let x(v) = 0. Calculate v.
0, 2
Suppose 0*s = -3*s - 6. Let c = s + 5/2. Factor -2 - 2*y - c*y**2.
-(y + 2)**2/2
Suppose 2*g + 0*g - 3*g**2 - 5*g + 2*g**2 = 0. Calculate g.
-3, 0
Let i(p) be the third derivative of 0*p - 1/3*p**3 - 1/24*p**4 + 0 + 1/120*p**6 + 5*p**2 + 1/30*p**5. Factor i(c).
(c - 1)*(c + 1)*(c + 2)
Suppose 0 = -3*g + 2*h - 0*h - 6, 0 = -4*h + 12. Let s(p) be the first derivative of 1 + 0*p**3 + g*p - 1/4*p**2 + 0*p**5 + 1/4*p**4 - 1/12*p**6. Factor s(i).
-i*(i - 1)**2*(i + 1)**2/2
Let s(j) = -9*j**4 - 17*j**3 - 5*j**2 + 3*j. Let n(p) = -18*p**4 - 35*p**3 - 11*p**2 + 6*p. Let u(b) = -2*n(b) + 5*s(b). Factor u(o).
-3*o*(o + 1)**2*(3*o - 1)
Suppose 14*x = 22 + 6. Find z such that -9/4*z**3 + 9/4*z**5 + 0 + 3/2*z**4 + 0*z - 3/2*z**x = 0.
-1, -2/3, 0, 1
Let n(h) be the first derivative of 5*h**6/3 + 18*h**5/5 + 12*h**4/5 + 8*h**3/15 - 8. Find x, given that n(x) = 0.
-1, -2/5, 0
Let p(y) be the third derivative of y**8/360 - 2*y**7/1575 - 7*y**6/300 + 2*y**5/45 - y**4/45 + 4*y**2. What is m in p(m) = 0?
-2, 0, 2/7, 1
Let c = -668 + 6020/9. Factor -8/3*i + 20/3*i**3 + 22/9*i**2 - c - 50/9*i**4