5. Let h be g(-5). Factor 0 + h*j + 1/2*j**2.
j**2/2
Let z(i) be the third derivative of -i**9/30240 + i**8/5040 + i**7/2520 - i**6/180 - i**5/15 + 5*i**2. Let d(f) be the third derivative of z(f). Factor d(n).
-2*(n - 2)*(n - 1)*(n + 1)
Factor 0*t**2 - 6/7*t**3 - 12/7 + 18/7*t.
-6*(t - 1)**2*(t + 2)/7
Let g(d) be the first derivative of -d**3/18 - d**2/2 - 4*d/3 - 23. Factor g(b).
-(b + 2)*(b + 4)/6
Let q(i) be the second derivative of -i**6/10 + i**5/10 + i**4/3 - i**3/3 - i**2/2 + 20*i. Factor q(a).
-(a - 1)**2*(a + 1)*(3*a + 1)
Let b(u) be the first derivative of -u**6/33 - 12*u**5/55 - 6*u**4/11 - 16*u**3/33 + 9. What is o in b(o) = 0?
-2, 0
Let s be 1 + -1 - (-15 + 13). Factor -b**s - 8*b**2 - 3*b**3 - 3 + 0*b**2 - 9*b.
-3*(b + 1)**3
Let q = 501/625 - 1/625. Determine p so that -16/5*p**4 - 16/5*p**2 - q*p - 4/5*p**5 - 24/5*p**3 + 0 = 0.
-1, 0
Suppose 2/3*u + 9*u**5 + 0 - 9*u**4 - 3*u**3 + 7/3*u**2 = 0. Calculate u.
-1/3, 0, 2/3, 1
Let r be (-4)/(-5)*(-85)/(-34). Factor 0*i**3 + 0*i + 3/4*i**r - 3/4*i**4 + 0.
-3*i**2*(i - 1)*(i + 1)/4
Let h(m) be the first derivative of -2/9*m**2 - 2/45*m**5 - 10/27*m**3 + 0*m - 2/9*m**4 + 2. Factor h(i).
-2*i*(i + 1)**2*(i + 2)/9
Let v(c) = -6*c**2 + 27*c + 12. Let i(l) be the second derivative of 0 - 53/6*l**3 + 13/12*l**4 - 23/2*l**2 - l. Let d(z) = 6*i(z) + 11*v(z). Factor d(k).
3*(k - 2)*(4*k + 1)
Suppose 4*d - 2*s = 4, s - 7 + 1 = -2*d. Let j(b) = 3*b**2 - b - 2. Let x(g) = -g**2 + 1. Let h(o) = d*j(o) + 5*x(o). Factor h(n).
(n - 1)**2
Let m(i) be the first derivative of -i**6/27 + 2*i**5/9 - i**4/6 - 2*i**3/3 - 31. Factor m(t).
-2*t**2*(t - 3)**2*(t + 1)/9
Suppose 0 = -2*t - t - 651. Let u = t - -1955/9. Let -2/9*z**2 + 0*z + u = 0. What is z?
-1, 1
Let d(w) be the second derivative of -3*w**5/100 - w**4/10 - w**3/10 + 7*w. Determine a, given that d(a) = 0.
-1, 0
Let v(u) be the third derivative of -u**6/80 + u**5/24 + u**4/24 - 20*u**2. Find s such that v(s) = 0.
-1/3, 0, 2
Let n(q) = q**3 - 7*q**2 + 7*q + 7. Let d(o) = -6*o**2 + 6*o + 6. Let w(m) = 4*d(m) - 3*n(m). Factor w(j).
-3*(j - 1)*(j + 1)**2
Factor 32*s + 8*s**2 + s**3 - 36*s - 5*s**3.
-4*s*(s - 1)**2
Suppose -3*v - 26 = 22. Let z be v/(-32)*(-1 + 1). Factor 0*a**2 - 2/5*a**3 + z + 6/5*a**4 + 0*a.
2*a**3*(3*a - 1)/5
Suppose -4 = q - 7. Let k = 8 - q. Solve -3*f + 3*f**2 + 3*f**3 + 29*f**4 + f - 12*f**2 - 21*f**k = 0 for f.
-1/3, -2/7, 0, 1
Let c(g) be the first derivative of -2*g**3/33 + g**2/11 - 6. Factor c(n).
-2*n*(n - 1)/11
Let i(t) = -t**3 - t**2 + 2*t. Let c be (-6 + 2)*2/4. Let d be i(c). Factor -15/2*h**4 + 7/2*h**3 - 1/2*h**2 + 9/2*h**5 + d*h + 0.
h**2*(h - 1)*(3*h - 1)**2/2
Suppose -9*j - 14*j + 46 = 0. Factor -4/3*p + 2/3*p**j + 2/3.
2*(p - 1)**2/3
Let v(c) be the third derivative of c**5/12 - 5*c**3/6 + 10*c**2. Factor v(j).
5*(j - 1)*(j + 1)
Let i(b) = b - 2. Let x be i(3). Let c(k) = -k - 1. Let o(j) be the first derivative of j**4/4 + j**2/2 + 2*j + 1. Let u(l) = x*o(l) + 2*c(l). Solve u(s) = 0.
-1, 0, 1
Factor 0*i - 2/9*i**2 + 0.
-2*i**2/9
Let u(g) be the third derivative of g**5/12 - 10*g**4/3 + 160*g**3/3 - 17*g**2. Solve u(n) = 0.
8
Let c(b) = -5*b**4 - b + b**2 + 6*b**4 - 1 - 2*b**4. Let z(f) = 38*f**4 - 82*f**3 + 52*f**2 - 12*f - 4. Let m(q) = -4*c(q) + z(q). Find d, given that m(d) = 0.
0, 2/7, 2/3, 1
Factor -x**3 + 2*x**4 - 4*x**5 - 2*x**2 + 5*x**5 + x**4 - x**4.
x**2*(x - 1)*(x + 1)*(x + 2)
Factor -1/5*g**4 + 0*g - 1/5*g**2 + 0 + 2/5*g**3.
-g**2*(g - 1)**2/5
Let h(k) be the third derivative of 0*k**4 + 0*k + k**2 - 1/120*k**5 + 0 + 0*k**3 - 1/240*k**6. Suppose h(n) = 0. What is n?
-1, 0
Let h(d) = -d**2 + 15*d + 2. Let s be h(15). Factor -1/4*x + 1/2*x**s - 1/4*x**3 + 0.
-x*(x - 1)**2/4
Let x(w) be the first derivative of 1/16*w**4 + 0*w**2 - 4 + 0*w + 1/12*w**3. Factor x(i).
i**2*(i + 1)/4
Let i = -65/4 - -49/3. Let u(b) be the first derivative of -2 + 0*b**2 + 1/15*b**5 + i*b**4 + 0*b**3 + 0*b. Let u(j) = 0. What is j?
-1, 0
Suppose 0 = -2*x - 2*x + 16. Let o(r) be the second derivative of -1/80*r**5 + 0*r**3 + 0 + 0*r**2 - r - 1/48*r**x. Factor o(p).
-p**2*(p + 1)/4
Let f(m) = m**2 + 9*m + 2. Let k be f(-10). Suppose -3*v - v = -k. Let -3*b + 2/3 + 16/3*b**2 + 2*b**4 - 14/3*b**v - 1/3*b**5 = 0. Calculate b.
1, 2
Let c(s) = -s**3 - 4*s**2 - s - 1. Let g be c(-4). Factor 0*y**g + y**2 - 2*y**4 + 0*y**4 - y**3 + 0*y**4.
-y**2*(y + 1)*(2*y - 1)
Let q(a) be the first derivative of a**3 - 3*a**2 + 3*a - 12. Suppose q(f) = 0. Calculate f.
1
Suppose 21 = -7*r + 49. Let b(s) be the second derivative of -1/5*s**3 + 2/5*s**2 - 3*s + 1/30*s**r + 0. Solve b(u) = 0 for u.
1, 2
Let j = 2 - 0. Suppose 21 = 4*r - 5*m, j*r + 5*m = -r + 7. Factor 1/5*x**5 + 0*x + 0 - 1/5*x**2 + 1/5*x**r - 1/5*x**3.
x**2*(x - 1)*(x + 1)**2/5
Factor 6/7*i**2 + 0*i - 2/7*i**3 - 8/7.
-2*(i - 2)**2*(i + 1)/7
Factor 0 + 122/13*z**2 - 4/13*z.
2*z*(61*z - 2)/13
Let v(y) be the third derivative of -2*y**7/105 + 7*y**6/30 + y**5/5 - 55*y**4/6 - 100*y**3/3 - 54*y**2. Factor v(d).
-4*(d - 5)**2*(d + 1)*(d + 2)
Let y = -4 - -12. Let 3 - y + 5 + 9*f**4 - 21*f**3 + 15*f**2 - 3*f = 0. Calculate f.
0, 1/3, 1
Let z(s) = 33*s**4 - 93*s**3 + 66*s**2 - 18*s + 6. Let i(t) = -65*t**4 + 185*t**3 - 133*t**2 + 35*t - 11. Let v(g) = 6*i(g) + 11*z(g). Factor v(h).
-3*h*(h - 2)*(h - 1)*(9*h - 2)
Let s(v) = -2*v**2 + v + 1. Let c(y) = -8*y**2 + 30*y - 22. Let n(w) = c(w) - 6*s(w). Let n(b) = 0. What is b?
-7, 1
Let k = -149/3 - -53. Factor -10/3*z**3 - 5/3*z + 5/3*z**4 - 1/3*z**5 + 1/3 + k*z**2.
-(z - 1)**5/3
Let t(y) be the second derivative of -y**6/120 + y**4/48 - 4*y. Solve t(l) = 0 for l.
-1, 0, 1
Let v(g) be the third derivative of 6*g**2 + 0*g + g**3 + 0 + 5/8*g**4 + 1/5*g**5 + 1/40*g**6. Factor v(z).
3*(z + 1)**2*(z + 2)
Let m(h) be the second derivative of 0*h**3 + 0 + 0*h**2 - 4*h + 1/6*h**4. Factor m(i).
2*i**2
Suppose -u - 2 = -1. Let q be ((-4)/4)/(u/7). Let b(a) = 8*a**2 - 6*a + 6. Let p(s) = 9*s**2 - 7*s + 7. Let z(g) = q*b(g) - 6*p(g). Factor z(y).
2*y**2
Let u(h) be the second derivative of h**2 + 0 - 5/6*h**3 + 1/4*h**4 + 8*h. Find o such that u(o) = 0.
2/3, 1
Let j be (-2*(-12)/16)/3. Factor 0 - j*n**5 - 3/2*n**4 - 1/2*n**2 + 0*n - 3/2*n**3.
-n**2*(n + 1)**3/2
Let s(m) be the first derivative of -m**7/280 + m**5/40 + 4*m**3/3 - 3. Let p(v) be the third derivative of s(v). Factor p(n).
-3*n*(n - 1)*(n + 1)
Let v be (-190)/(-105) - (-14)/(-21). Determine w so that 12/7*w + v + 4/7*w**2 = 0.
-2, -1
Let t(r) be the second derivative of r**7/1680 - r**6/144 + r**5/30 - r**4/12 - 5*r**3/6 - 5*r. Let x(c) be the second derivative of t(c). Solve x(p) = 0 for p.
1, 2
Let v = 89 + -124. Let g be (-10)/(-3)*(-7)/v. Let -2/3 + 2/3*u + 2/3*u**2 - g*u**3 = 0. Calculate u.
-1, 1
Suppose -2*w - 3*q - 2 = -11, 5*q - 15 = 0. Solve -2/11*f**2 + w - 2/11*f**3 + 0*f = 0 for f.
-1, 0
Let q(d) be the third derivative of d**7/2940 + d**6/1260 - d**5/420 - d**4/84 + d**3/6 - 3*d**2. Let c(v) be the first derivative of q(v). Factor c(s).
2*(s - 1)*(s + 1)**2/7
Suppose -4 = -5*a + 3*a. Let w(y) be the first derivative of -1/2*y**4 - 2/3*y**3 + 0*y**a + 0*y - 1. Factor w(r).
-2*r**2*(r + 1)
Suppose -5*f + 11 + 14 = 5*i, 4*f = -i + 14. Factor 1/2*d + 3/4*d**3 - 5/4*d**i + 0.
d*(d - 1)*(3*d - 2)/4
Let z(m) = -9*m**4 + 15*m**3 - 15*m**2 + 9*m + 4. Let o(t) = 55*t**4 - 90*t**3 + 90*t**2 - 55*t - 25. Let u(c) = 4*o(c) + 25*z(c). Factor u(d).
-5*d*(d - 1)**3
Let p be (-3 - 1)/4 - -1. Suppose 0*m + 3*m = p. Solve 0 + 2/5*x**2 - 2/5*x**4 + m*x + 0*x**3 = 0 for x.
-1, 0, 1
Let b(c) be the second derivative of 0*c**3 + 0*c**2 + 0 + 1/40*c**5 + 0*c**4 - 2*c + 1/30*c**6 + 1/84*c**7. Factor b(t).
t**3*(t + 1)**2/2
Let v(l) be the second derivative of l**5/20 + l**4/12 - l**3/6 - l**2/2 + 2*l. Factor v(j).
(j - 1)*(j + 1)**2
Suppose 5*p - p = 3*l - 12, -4 = -l - 3*p. Let f(j) be the first derivative of -2/5*j**5 + 0*j + 2 - 2*j**3 + j**2 + 3/2*j**l. Factor f(w).
-2*w*(w - 1)**3
Let t(b) be the third derivative of -1/60*b**4 - 4*b**2 + 0*b**3 + 1/150*b**5 + 0*b + 0. Factor t(o).
2*o*(o - 1)/5
Let g = -420 - -424. What is p in 30*p**3 + 0 + 125/2*p**5 + 75*p**4 + g*p**2 + 0*p = 0?
-2/5, 0
Let i(f) be the third derivative of f**7/735 - f**6/420 - f**5/210 + f**4/84 - 45*f**2. Factor i(k).
2*k*(k