/5. Factor -c - 2/3*d**2 + 16/3*d.
-2*(d - 4)**2/3
Let a(o) be the second derivative of o**5/20 - o**4/2 + 3*o**3/2 + 3*o**2/2 + 2*o. Let z(q) be the first derivative of a(q). Factor z(r).
3*(r - 3)*(r - 1)
Let a(q) = q + 8. Let g be a(-5). Let t be (3/2)/((-1)/(-2)). Factor 16 - 3*j**2 + 3*j**4 - 16 - 3*j**t + g*j**5.
3*j**2*(j - 1)*(j + 1)**2
Let y(t) be the first derivative of -3*t**5/5 - t**4 - t**3/3 + 2. Factor y(x).
-x**2*(x + 1)*(3*x + 1)
Let j(m) = -11*m**4 - 10*m**3 + 15*m**2 + 14*m - 14. Let u(f) = -f**4 - f + 1. Let b(c) = j(c) - 6*u(c). Find x, given that b(x) = 0.
-2, 1
Let q(d) be the first derivative of -d**7/525 + d**6/150 - d**4/30 + d**3/15 + 4*d**2 + 7. Let a(g) be the second derivative of q(g). Factor a(p).
-2*(p - 1)**3*(p + 1)/5
Suppose 104*h = 120*h - 32. Factor -2/11 - 12/11*n**h - 14/11*n.
-2*(n + 1)*(6*n + 1)/11
Let o(s) = -5*s - 1. Let l be o(-1). Suppose -16 = l*g + 5*i - i, g = 3*i + 12. Factor g*f + f**3 + f**4 + 0*f.
f**3*(f + 1)
Let v(m) be the third derivative of m**6/40 + m**5/4 + m**4 + 2*m**3 + 6*m**2. Factor v(l).
3*(l + 1)*(l + 2)**2
Find k such that 11*k**2 + 11*k**2 - 25*k**2 - 3*k**3 = 0.
-1, 0
Let m(x) be the third derivative of x**8/336 - x**7/210 - x**3/6 + 3*x**2. Let n(o) = 3*o**5 - 3*o**4 - 2. Let k(c) = 2*m(c) - n(c). Let k(j) = 0. Calculate j.
0, 1
Suppose -6/13*d**3 + 0 + 0*d**4 + 0*d + 2/13*d**5 - 4/13*d**2 = 0. Calculate d.
-1, 0, 2
Let i = 141 + -88. Let m = -263/5 + i. Factor -2/5*w**3 - 2/5 + m*w**2 + 2/5*w.
-2*(w - 1)**2*(w + 1)/5
Let y(j) be the second derivative of j**5/20 + 5*j**4/12 + 4*j**3/3 + 2*j**2 - 20*j. Suppose y(a) = 0. Calculate a.
-2, -1
Let i = -66 + 66. Factor 1/6*o**4 + 1/6*o**2 + i + 1/3*o**3 + 0*o.
o**2*(o + 1)**2/6
Let c = 1/74 - 373/222. Let l = c + 13/6. Find t such that -l*t + 0*t**2 + 1/2*t**3 + 0 = 0.
-1, 0, 1
Let f(y) = -30*y**2 + 40*y + 40. Let i(h) = 6*h**2 - 8*h - 8. Let x(q) = 2*f(q) + 11*i(q). Factor x(l).
2*(l - 2)*(3*l + 2)
Let p(h) = -h**3 + 8*h**2 - 3*h - 1. Let n be p(6). Factor 36 - n*r - 4*r**2 + r**2 - 7*r - 4*r**3 + 31*r**2.
-4*(r - 3)**2*(r - 1)
Factor 16*m**2 - 4 + 11*m - 10*m - 7*m - 2*m**3 - 4*m**3.
-2*(m - 2)*(m - 1)*(3*m + 1)
Let b be (6/(-4))/(2/(-4)). Let a be (-24)/(-9) - (-8)/(-12). Suppose 1/4 - 3/4*c + c**b + 0*c**a = 0. What is c?
-1, 1/2
Let y(r) be the second derivative of 0*r**3 + 1/480*r**6 + 1/24*r**4 + r**2 + 0 + 3*r + 1/60*r**5. Let s(k) be the first derivative of y(k). Factor s(p).
p*(p + 2)**2/4
Let d(j) be the third derivative of -j**8/84 + 4*j**7/105 + j**6/15 - 8*j**5/15 + 7*j**4/6 - 4*j**3/3 + 8*j**2. Suppose d(f) = 0. What is f?
-2, 1
Let z(m) be the first derivative of 0*m + 3 + 0*m**2 + 1/12*m**3. Factor z(q).
q**2/4
Let a(u) be the third derivative of 1/160*u**6 + 0 + 1/80*u**5 + 0*u**3 + 0*u - 3*u**2 - 1/32*u**4 - 1/280*u**7. Solve a(c) = 0 for c.
-1, 0, 1
Let q = 36 - 33. Let j(r) be the first derivative of 3/8*r**2 - q - 1/4*r - 1/6*r**3. Find v, given that j(v) = 0.
1/2, 1
Suppose 2/3*a**2 + 0 - 4/3*a = 0. What is a?
0, 2
Factor 4 - 2*w**3 + 2/3*w**4 - 2*w**2 + 14/3*w.
2*(w - 3)*(w - 2)*(w + 1)**2/3
Let -12*l**2 + 8*l**2 + 2*l**4 - 4*l**3 + 6*l**2 = 0. What is l?
0, 1
Let s(v) be the second derivative of v - 1/50*v**5 + 0 - 1/15*v**4 + 0*v**2 + 0*v**3. Suppose s(u) = 0. What is u?
-2, 0
Determine y, given that -4/7 - 2/7*y + 2/7*y**2 = 0.
-1, 2
Factor -26/7*r**3 - 2/7*r**5 + 12/7*r**4 + 0 - 8/7*r + 24/7*r**2.
-2*r*(r - 2)**2*(r - 1)**2/7
Suppose -10 + 16 = 2*p. Let z be (-1)/((-9)/24) - 2. Factor 0*y**2 + y - z - 1/3*y**p.
-(y - 1)**2*(y + 2)/3
Let h(u) be the third derivative of u**5/30 - u**4/12 - 2*u**3/3 + 5*u**2. Determine p so that h(p) = 0.
-1, 2
Let r(v) be the first derivative of 0*v**2 - 3 + 6/55*v**5 + 0*v**3 + 0*v + 5/33*v**6 - 1/11*v**4. Factor r(a).
2*a**3*(a + 1)*(5*a - 2)/11
Let q(d) be the first derivative of -d**3/3 + 22. Factor q(i).
-i**2
Let b(n) be the second derivative of 0 + 1/2*n**4 - n - 1/3*n**3 + 0*n**2 - 3/10*n**5 + 1/15*n**6. Factor b(r).
2*r*(r - 1)**3
Suppose -2*z = -b - 4, 8*b + 6 = 3*z + 5*b. Factor 1/2*i**z - 1/4*i**3 + 0 - 1/4*i.
-i*(i - 1)**2/4
Let u = 8 - 4. Find i such that 2 - u*i + 3*i**2 + 8*i + 3*i = 0.
-2, -1/3
Factor -426*p**2 + 20 + 490*p**3 - 62*p - 38*p + 391*p**2.
5*(2*p + 1)*(7*p - 2)**2
Factor 0 - 2/7*r**4 - 4/7*r - 8/7*r**3 - 10/7*r**2.
-2*r*(r + 1)**2*(r + 2)/7
Let n(m) = -m - 4. Let o be n(-7). Factor -12*h**4 + 2*h**o - 5*h**3 - 6*h**3 - 2*h**2 - 5*h**5.
-h**2*(h + 1)**2*(5*h + 2)
Suppose -10*z + 12 + 8 = 0. Let x(v) be the first derivative of 0*v**2 + 2/5*v**5 + z*v + 2 - 4/3*v**3 + 0*v**4. Suppose x(b) = 0. Calculate b.
-1, 1
Let d = 59/52 + -5/13. Let f(l) be the first derivative of -l**3 + 2 - 1/2*l**2 + 0*l - d*l**4 - 1/5*l**5. Factor f(v).
-v*(v + 1)**3
Let y(d) be the first derivative of -3*d**2 - 4/3*d**3 - 1 - 2*d. Let x(k) = 5*k**2 + 7*k + 2. Let r(z) = -3*x(z) - 4*y(z). Factor r(f).
(f + 1)*(f + 2)
Let h be ((-4)/10*4)/(12/(-50)). Solve -h*i**2 + 2/3*i**5 + 10/3*i + 20/3*i**3 - 2/3 - 10/3*i**4 = 0.
1
Let q(s) be the first derivative of s**6/2 - 36*s**5/5 + 171*s**4/4 - 134*s**3 + 234*s**2 - 216*s + 19. Factor q(r).
3*(r - 3)**2*(r - 2)**3
Let b(j) be the second derivative of -j**6/270 - j**5/180 + j**4/18 + 2*j**3/27 - 4*j**2/9 - 53*j. Factor b(o).
-(o - 2)*(o - 1)*(o + 2)**2/9
Factor 0 - 2/7*i**2 - 1/7*i - 1/7*i**3.
-i*(i + 1)**2/7
Let w(h) be the second derivative of h**6/50 + 3*h**5/10 + 5*h**4/4 + 7*h. Let w(o) = 0. What is o?
-5, 0
Let u(j) be the first derivative of j**4/60 - j**3/15 + j**2/10 - j - 8. Let d(l) be the first derivative of u(l). Find i, given that d(i) = 0.
1
Let f(b) = -6*b**2 - 3*b + 3. Let z(m) = 13*m**2 + 6*m - 7. Let c = -16 - -7. Let q be (-38)/(-9) + 2/c. Let w(x) = q*z(x) + 9*f(x). Solve w(l) = 0.
-1, -1/2
Factor -19/5*b**3 + 216/5 - 324/5*b + 126/5*b**2 + 1/5*b**4.
(b - 6)**3*(b - 1)/5
Let k be 196/(-21)*(-20)/(-7). Let q = -26 - k. Solve 2/3*d**2 + 0*d - q = 0.
-1, 1
Let u(c) be the first derivative of 2/9*c**3 + 1/3*c**2 - 4/3*c - 1. Determine g so that u(g) = 0.
-2, 1
Suppose 8 = r - 5*k, r + 4*k - 8 = -3*r. Let c(l) be the second derivative of -1/30*l**r - 1/150*l**6 + 0 + 0*l**2 + 1/60*l**4 - l + 1/100*l**5. Factor c(j).
-j*(j - 1)**2*(j + 1)/5
Suppose -5*b - 20 = 0, 0 = 5*l + 4*b + 47 - 11. Let a = 7 + l. Find k, given that -4/7*k**a + 2/7*k**5 + 2/7*k + 2/7*k**4 - 4/7*k**2 + 2/7 = 0.
-1, 1
Find o, given that -53*o**2 + 30*o**2 + 4*o**5 - 69*o**2 - 32*o + 28*o**3 + 64 + 28*o**4 = 0.
-4, -1, 1
Let a(r) be the second derivative of -r**5/5 + 2*r**3 + 4*r**2 + r. Solve a(g) = 0 for g.
-1, 2
Let h(c) be the second derivative of -1/4*c**4 + 0 - 1/6*c**3 + 2*c + 0*c**2. Determine b, given that h(b) = 0.
-1/3, 0
Let s(x) = -x**3 + x**2 + x + 1. Let g(p) = -5*p**3 + 8*p**2 - p + 4. Let c(l) = g(l) - 3*s(l). Suppose c(w) = 0. What is w?
1/2, 1
Let v be (-360)/252*7/(-4). Suppose 1/2*d**5 + v*d - 1/2 - 5/2*d**4 - 5*d**2 + 5*d**3 = 0. What is d?
1
Factor 0*x**4 + 3*x**4 + 6*x**3 - x**2 + 4*x**2.
3*x**2*(x + 1)**2
Let c(b) be the first derivative of -3*b**4/4 + 25*b**3/9 - 2*b**2 - 4*b/3 - 4. Factor c(h).
-(h - 2)*(h - 1)*(9*h + 2)/3
Let f(p) be the second derivative of -p**4/90 + 2*p**3/45 + p**2/5 + 8*p. Find y, given that f(y) = 0.
-1, 3
Factor -170*j**3 - 3*j**4 + 170*j**3.
-3*j**4
Let t(b) be the first derivative of -16/3*b**3 - 3 + 4/3*b**6 - 6*b**2 - 2*b + 18/5*b**5 + b**4. Find z such that t(z) = 0.
-1, -1/4, 1
Let g be 3 - 5 - 4*-2. Let k(c) be the second derivative of 1/150*c**g + 1/30*c**3 - 1/50*c**5 - 1/30*c**4 + 1/210*c**7 + 3*c + 1/10*c**2 + 0. Factor k(w).
(w - 1)**2*(w + 1)**3/5
Let p(q) be the first derivative of 2*q**3/15 - 6*q**2/5 + 2*q + 18. Factor p(b).
2*(b - 5)*(b - 1)/5
Suppose -9 = y + 1. Let r = y - -14. Factor -4*g**2 - 2*g**r - g**5 - 2 + 6*g - 4*g**3 + 8*g**4 - g**5.
-2*(g - 1)**4*(g + 1)
Let b be 341/4278 + 4/46. What is y in -b*y + 1/6 - 1/6*y**2 + 1/6*y**3 = 0?
-1, 1
Let j(h) be the second derivative of 2*h**6/105 + 4*h**5/35 + 2*h**4/7 + 8*h**3/21 + 2*h**2/7 - 43*h. Determine n so that j(n) = 0.
-1
Let n(m) be the second derivative of -3*m**5/25 - 4*m**4/15 + 8*m**3/15 + 8*m. Factor n(u).
-4*u*(u + 2)*(3*u - 2)/5
Let u = -1844/5 - -370. Let t(b) be the first derivative of -2 - u*b**5 + 1/