**5.
-p*(p + 1)**3*(3*p + 1)/2
Suppose 14*t = 17*t. Suppose t = g - 0*g - 2. Factor -g*a**3 + 16/3*a**2 + 4/9 - 26/9*a.
-2*(a - 2)*(3*a - 1)**2/9
Let x(j) be the second derivative of j**7/1260 - j**6/360 - j**5/30 - j**4/3 + 3*j. Let h(c) be the third derivative of x(c). Factor h(k).
2*(k - 2)*(k + 1)
Let o(s) be the third derivative of s**6/72 - s**5/18 + 6*s**2. Factor o(i).
5*i**2*(i - 2)/3
Let s(m) be the second derivative of -m**5/4 - 10*m**4/3 - 65*m**3/6 - 15*m**2 - 29*m. Determine g so that s(g) = 0.
-6, -1
Suppose -4 = 4*p, 3*h - 4*h - p + 2 = 0. Let r be (-4)/14 + 6/21. Factor -2/7*l**2 - 2/7*l**4 + 4/7*l**h + r*l + 0.
-2*l**2*(l - 1)**2/7
Factor -2/7*f - 4/7 + 2/7*f**2.
2*(f - 2)*(f + 1)/7
Suppose -3 = 2*b - f, 9 = 3*b - 2*b + 3*f. Let w(m) be the second derivative of m + 1/36*m**4 - 1/60*m**5 + 0*m**2 + b + 1/9*m**3. Factor w(l).
-l*(l - 2)*(l + 1)/3
Let o(q) be the second derivative of 7/6*q**3 + 2/3*q**4 - 2*q + 0 + 3/20*q**5 + q**2. Let o(n) = 0. What is n?
-1, -2/3
Let d(m) = -9*m**3 + 24*m**2 - 24. Let t(v) = 2*v**3 - 5*v**2 + 5. Let a be 10*((-32)/(-20) - 4). Let z(h) = a*t(h) - 5*d(h). Determine w so that z(w) = 0.
0
Let r(b) be the third derivative of -b**7/840 - b**6/240 + b**4/48 + b**3/24 - b**2. Suppose r(d) = 0. What is d?
-1, 1
Let n(c) be the first derivative of c**6/6 - c**4/4 + 1. Factor n(s).
s**3*(s - 1)*(s + 1)
Let l(d) be the second derivative of d**8/1680 - 2*d**3/3 - 2*d. Let q(j) be the second derivative of l(j). Factor q(i).
i**4
Let v(n) = -9*n**4 - 7*n**3 + 0*n**3 + 3*n - 5*n. Let q(j) = 0*j**3 + j - 2*j**3 + j**4 + j**2 + 3*j**3. Let c(t) = 2*q(t) + v(t). Factor c(k).
-k**2*(k + 1)*(7*k - 2)
Factor -4*d**5 + 2*d**4 + 6*d**5 - 7*d**4 + 3*d**4.
2*d**4*(d - 1)
Let s(r) = r**3 + r - 4. Let f be s(0). Let t be (f - -2)/(-1 + 0). Determine z so that 1/5*z + z**3 - 8/5*z**t + 2/5 = 0.
-2/5, 1
Let s(t) be the first derivative of 2*t**5/85 + t**4/34 - 2*t**3/17 - t**2/17 + 4*t/17 - 25. Let s(k) = 0. Calculate k.
-2, -1, 1
Let i(t) = 3*t - 46. Let o be i(16). Let 13/3*p**3 + 0 + o*p**2 + 4/3*p**5 + 1/3*p + 4*p**4 = 0. What is p?
-1, -1/2, 0
Suppose -5*z - 4*v + 72 = 0, -18 = 5*z + 3*v - 92. Factor -6*c**5 + 3*c**4 + z*c - 15*c**2 + 9*c**3 + 3*c**5 - 10*c.
-3*c*(c - 1)**3*(c + 2)
Let o(l) = l**3 + 8*l**2 + 7*l + 4. Let r be o(-7). Factor 4 - 2*d**2 + 0 - r + 2.
-2*(d - 1)*(d + 1)
Factor 5*m**2 + 11 - 4 - 10*m - 2.
5*(m - 1)**2
Let j(x) be the second derivative of 0 - x**2 - 1/12*x**4 + 10*x + 1/2*x**3. Solve j(f) = 0.
1, 2
Let f = -17 + 19. Let p = 8 + -6. What is z in f - p - 2*z**2 = 0?
0
Let k(g) be the first derivative of 2*g**3/45 - g**2/15 + 1. Factor k(r).
2*r*(r - 1)/15
Suppose 0 = 23*g - 20*g - 9. Let f(r) be the first derivative of 26/5*r**5 + 0*r + 2 - 8*r**2 + r**6 - 8/3*r**g + 7*r**4. Find c, given that f(c) = 0.
-2, -1, 0, 2/3
Factor -2*n**5 + 3*n**5 + n - 2*n**3 - 2*n + 2*n.
n*(n - 1)**2*(n + 1)**2
Let y = -72 - -77. Let s be (-90)/(-21) + (-4)/14. Factor 2*d**2 - d**y + d + 4*d - 4*d**s + 0*d**4 - 4*d**3 + 2.
-(d - 1)*(d + 1)**3*(d + 2)
Let g be 32/55 + 8/(-44). Let l = -256 + 1284/5. Determine r, given that g*r + 0 - l*r**2 + 2/5*r**3 = 0.
0, 1
Let o = 6 - 2. Suppose 0*n = -2*n - 2*b, -2*n + o*b = -12. Factor -2*v**2 + 0*v**2 - 2*v + 0*v**n.
-2*v*(v + 1)
Let y be 36/15*(-20)/3. Let c be 1*(-2)/y*2. Let -5/4*z**2 + 0 - 1/2*z - 3/4*z**3 + 1/4*z**4 + c*z**5 = 0. What is z?
-1, 0, 2
Let a(x) be the first derivative of x**6/1260 - x**5/210 + x**4/84 + x**3/3 + 4. Let n(u) be the third derivative of a(u). Let n(i) = 0. Calculate i.
1
Solve -4/5*o**2 - 1/5*o**3 + 1/5*o + 4/5 = 0 for o.
-4, -1, 1
Let b(v) = -5*v**3 - 4*v**2 - 3*v - 4. Let f(l) = 9*l**3 + 7*l**2 + 5*l + 7. Suppose 3*x - 4 - 17 = 0. Let m(w) = x*b(w) + 4*f(w). Let m(p) = 0. Calculate p.
-1, 0, 1
Factor -78/7*m**2 + 72/7*m + 36/7*m**3 - 6/7*m**4 - 24/7.
-6*(m - 2)**2*(m - 1)**2/7
Suppose -2*h - 8 = -6*h - 5*k, -2*h + 4 = -k. Let r(w) be the third derivative of -1/180*w**6 + 0*w - h*w**2 + 0*w**3 + 1/90*w**5 + 0*w**4 + 0. Factor r(y).
-2*y**2*(y - 1)/3
Let x(j) = -j**3 - 7*j**2 + j + 7. Let g be x(-7). Factor 2*p - 5*p + g*p**2 - 6*p**2.
-3*p*(2*p + 1)
Let q(w) be the second derivative of 1/24*w**3 + 0*w**2 + 1/48*w**4 - 1/120*w**6 - w + 0 - 1/80*w**5. Find b, given that q(b) = 0.
-1, 0, 1
Suppose -427 + 21*n**3 + 32*n**2 + 2*n - 51*n**3 + 423 = 0. Calculate n.
-1/3, 2/5, 1
Factor 1/3*s + 1/3*s**2 - 2/3.
(s - 1)*(s + 2)/3
Let i(r) be the third derivative of -r**5/60 + r**4/24 - 12*r**2. Factor i(b).
-b*(b - 1)
Factor 2/3*s**4 + 2/3 - 2/3*s + 4/3*s**3 - 2/3*s**5 - 4/3*s**2.
-2*(s - 1)**3*(s + 1)**2/3
Let n be (-2)/20*(-4)/42. Let o(z) be the third derivative of -1/30*z**5 + 0*z + 0*z**4 + n*z**7 + 0*z**6 - 4*z**2 + 0*z**3 + 0. Factor o(f).
2*f**2*(f - 1)*(f + 1)
Let t(w) be the second derivative of -w**8/6720 - w**7/840 - w**6/240 - w**5/120 - w**4/12 - w. Let o(m) be the third derivative of t(m). Factor o(j).
-(j + 1)**3
Factor 0 + 3/4*t**3 + 1/2*t**2 + 1/4*t**4 + 0*t.
t**2*(t + 1)*(t + 2)/4
Suppose 3*h - 5*w - 27 = -0*h, 2*h - 4*w = 20. Let n = h - 2. Find d such that 9*d**3 - 4*d**2 - 5*d**5 + 2*d**5 + 5*d**2 + 5*d**n = 0.
-1, 0, 2
Suppose x + 0 - 2 = 0. Suppose x*k - 3*y = 4, 0 = 2*k - 2*y - 1 - 5. Factor 3/5*f**3 + 2/5*f - 1/5*f**k - f**2 + 1/5*f**4 + 0.
-f*(f - 1)**3*(f + 2)/5
Let k = 18 - 18. Let v(o) be the third derivative of 0*o**4 + k*o**6 + o**2 - 1/252*o**8 + 0*o**3 - 1/315*o**7 + 0*o + 0 + 0*o**5. What is z in v(z) = 0?
-1/2, 0
Let n(k) = k + 7. Let q be n(-7). Suppose b - 2*y = -q - 6, y - 12 = -4*b. Factor u + 6*u**3 - b*u**4 + 4*u**4 + u + 6*u**2.
2*u*(u + 1)**3
Let x = 3 + 0. Suppose 39*q**4 + 16*q**3 + 15*q**5 - q**2 + 11*q**x - 2*q**2 - q - 5*q = 0. Calculate q.
-1, 0, 2/5
Let m(d) = 2*d**2 + 1. Let b be m(-1). Factor -3*f - 3*f**3 + 2*f + f**b + 3*f.
-2*f*(f - 1)*(f + 1)
Suppose -6*x - 36 = -10*x. Find i, given that 0*i**2 - 3*i**2 + 0 - 3 + x*i - 3 = 0.
1, 2
Let p = 9 - 7. Solve 5*k**2 + 2*k**5 - 1 + 9 + 6*k**4 - 19*k**p - 2*k**3 = 0 for k.
-2, -1, 1
Let v = 13 + -9. Let j(g) be the first derivative of 0*g**5 - 1/6*g**2 + 0*g**3 + 1/6*g**v + 1 + 0*g - 1/18*g**6. Let j(p) = 0. Calculate p.
-1, 0, 1
Suppose 1 = -w + 5. Factor -i**3 + 0*i**2 + w*i**2 - i**3 + 3*i - 5*i.
-2*i*(i - 1)**2
Let n(u) = 9*u**4 - 12*u**3 - 30*u**2 + 12*u + 21. Let g(a) = -8*a**4 + 13*a**3 + 29*a**2 - 13*a - 21. Let l(s) = -6*g(s) - 5*n(s). Factor l(h).
3*(h - 7)*(h - 1)*(h + 1)**2
Let x(q) = -q**2 + q. Let f(g) be the third derivative of 1/60*g**5 + 0*g - 1/6*g**3 + 2*g**2 + 0 + 0*g**4. Let r(m) = -f(m) - 2*x(m). Solve r(j) = 0 for j.
1
Let s(f) be the first derivative of 3*f**4/20 - f**3/3 + f**2/5 - 8. Determine x, given that s(x) = 0.
0, 2/3, 1
Let v(n) = -n**2 - 10*n - 11. Let i be v(-9). Let s = 4 + i. Determine r so that -2*r**2 + 0 + s*r**3 + 2 - 2 - 4*r = 0.
-1, 0, 2
Let w(r) be the first derivative of -r**7/98 + r**6/35 - 3*r**5/140 - 2*r - 8. Let f(i) be the first derivative of w(i). Factor f(x).
-3*x**3*(x - 1)**2/7
Let y(m) be the second derivative of m**4/48 + m**3/4 + 9*m**2/8 - 9*m. Factor y(q).
(q + 3)**2/4
Let s(y) be the third derivative of -y**7/1260 + y**6/360 + y**5/120 - y**4/18 + y**3/9 + 5*y**2. Let s(l) = 0. What is l?
-2, 1, 2
Let n(p) be the third derivative of -1/150*p**5 + 0*p + 0*p**3 - 2*p**2 + 1/60*p**4 + 0 + 1/525*p**7 - 1/300*p**6. Factor n(q).
2*q*(q - 1)**2*(q + 1)/5
Let u be (-2)/(-15) - (868/15)/(-31). Find p, given that -16/7*p - 10/7*p**4 + 2/7*p**5 + 2*p**3 + 2/7*p**u + 8/7 = 0.
-1, 1, 2
Let m(p) = 6*p**3 - 6*p**2 - 9*p + 3. Let x(n) = 7*n**3 - 6*n**2 - 9*n + 4. Let r(f) = 4*m(f) - 3*x(f). Let r(v) = 0. Calculate v.
-1, 0, 3
Let r(n) be the second derivative of -4/3*n**4 - 1/2*n**2 + 4/3*n**3 + 0 - n. Factor r(y).
-(4*y - 1)**2
Let r(g) be the second derivative of -1/24*g**4 + 0*g**2 + 0*g**3 + 0 + 1/40*g**5 - 1/84*g**7 + 1/60*g**6 - 3*g. Find n, given that r(n) = 0.
-1, 0, 1
Let r(w) = -14*w - 52. Let m be r(-4). Let g(s) be the second derivative of 0*s**5 + 1/105*s**7 + 0*s**2 + 0*s**3 + 0*s**m + 0 - 4*s - 1/75*s**6. Factor g(v).
2*v**4*(v - 1)/5
Find u, given that 2 - 4*u**2 - 2*u + u + 3*u**2 - 2*u**2 = 0.
-1, 2/3
Let h = -10 - -14. Let f(z) = z**2 - 3*z. Let a be f(h). Factor 3*s**4 + s + 3*s**3 - a*