 8. Let i = 1104 + -1102. Factor k*m**2 - 4*m**2 + 0*m**i.
3*m**2
Let q(d) be the first derivative of -d**6/18 + 5*d**4/6 - 20*d**3/9 + 5*d**2/2 - 4*d/3 - 148. Determine o, given that q(o) = 0.
-4, 1
Suppose 4*y + 20 = 0, -2*k - 5*y - 4 = -y. Factor -k - 4*z**5 + 16*z**4 - 20*z**3 + 8*z**2 + 8.
-4*z**2*(z - 2)*(z - 1)**2
Let w(x) be the first derivative of -7*x**5/15 + x**4/6 + 7*x**3/9 - x**2/3 - 75. What is i in w(i) = 0?
-1, 0, 2/7, 1
Let x = -16537/5 + 3311. Find l such that 2/5*l**5 + 0 + 44/5*l**3 + 16/5*l**4 + x*l + 48/5*l**2 = 0.
-3, -1, 0
Factor 18/5 - 12/5*d + 2/5*d**2.
2*(d - 3)**2/5
Suppose -16*j + 95 = -11*j. Factor 7*d**5 - d**4 + 4*d**3 - 5*d**2 + 3*d**3 - 3*d**5 + 2*d - j*d**3.
d*(d - 2)*(d + 1)**2*(4*d - 1)
Let i(h) be the first derivative of -h**4/2 - 4*h**3/3 + 45. What is b in i(b) = 0?
-2, 0
Let g(a) be the third derivative of 1/840*a**6 + 0*a**3 + 26*a**2 + 0*a + 1/420*a**5 + 0 - 1/1470*a**7 - 1/168*a**4. Factor g(n).
-n*(n - 1)**2*(n + 1)/7
Let t(q) be the second derivative of q**4/48 - 7*q**3/12 + 49*q**2/8 - 2*q - 26. Factor t(i).
(i - 7)**2/4
Let a(u) be the second derivative of u**7/1260 - u**6/540 - u**5/45 + u**4/9 + 37*u**3/6 - 38*u. Let m(p) be the second derivative of a(p). Factor m(g).
2*(g - 2)*(g - 1)*(g + 2)/3
Solve 0 - m**3 + 11/4*m**2 + 15/2*m - 1/4*m**4 = 0.
-5, -2, 0, 3
Factor -4*q**3 - q**4 + 5*q**4 + q**2 - 15*q**2 - 6*q**2 - 12*q.
4*q*(q - 3)*(q + 1)**2
Let r(j) = j**2 - 21. Let t be r(-5). Suppose -k - 6 = -t*i, 3*k - 10 = -22*i + 20*i. Solve 6/7*a + 1/7*a**k + 9/7 = 0 for a.
-3
Let r(k) be the second derivative of k**2 - 1/30*k**6 - 3*k + 1/2*k**3 + 0 - 1/12*k**4 - 3/20*k**5. Factor r(d).
-(d - 1)*(d + 1)**2*(d + 2)
Let 0 - 28*n + 4/3*n**2 = 0. Calculate n.
0, 21
Let g(a) = 3*a**2 - 10*a - 3. Let d be g(4). Let l be (-2)/(((-16)/12)/(d/3)). Let s**3 + l*s**4 + 0*s + 0 + 0*s**2 = 0. What is s?
-2/5, 0
Let m(g) be the second derivative of g**5/60 - g**4/12 + g**3/6 + 19*g**2/2 - 23*g. Let p(x) be the first derivative of m(x). Let p(d) = 0. What is d?
1
Suppose -12 = h - 5*x, -5*h - 5*x - 10 - 50 = 0. Let z be (0/4)/(h/(-6)). Factor -8/17*i + 2/17*i**3 + 0*i**2 + z.
2*i*(i - 2)*(i + 2)/17
Let g(h) = -5*h + 65. Let a be g(12). Let a*p**4 - 13*p**3 + 5*p**2 - 2059 + 2059 + 3*p**3 = 0. What is p?
0, 1
Let p = -2064 - -2064. Let a(b) be the second derivative of 0*b**2 + 4/3*b**3 + 4*b + p + 1/3*b**4. Factor a(r).
4*r*(r + 2)
Let b = 3122 - 3119. Factor -1/3 - 3/2*r - 1/2*r**2 + 2/3*r**b.
(r - 2)*(r + 1)*(4*r + 1)/6
Let z be (16/(-20) - 0)*430/(-602). Factor z*y**2 - 8/7 - 4/7*y.
4*(y - 2)*(y + 1)/7
Let v(n) = -n**2 - n. Let b(s) = 7*s**2 - 12*s + 81. Suppose -11*t + 180 = -5*t. Let y(k) = t*v(k) + 5*b(k). What is m in y(m) = 0?
9
Let h(f) = 10*f + 10*f**3 + 13*f**2 - 14*f**3 + 9*f**3. Let v(b) = 26*b**3 + 64*b**2 + 49*b. Let d(n) = 11*h(n) - 2*v(n). What is j in d(j) = 0?
-4, -1, 0
Let g(d) = d**3 - 6*d**2 - 11*d + 31. Let a be g(7). Factor 0 - 5/7*j**4 + 2/7*j**a + 0*j + 0*j**2.
-j**3*(5*j - 2)/7
Let a(z) be the third derivative of -z**6/90 - 184*z**5/45 - 4232*z**4/9 - 471*z**2. Factor a(o).
-4*o*(o + 92)**2/3
Let x(u) be the first derivative of -2*u**6/3 - 24*u**5/5 - 4*u**4 + 24*u**3 + 10*u**2 - 48*u - 251. Let x(h) = 0. Calculate h.
-4, -3, -1, 1
Let j(v) be the second derivative of -v**8/57120 + v**6/2040 - v**5/510 + 5*v**4/6 - v. Let g(a) be the third derivative of j(a). Factor g(w).
-2*(w - 1)**2*(w + 2)/17
Let k(i) be the first derivative of 1/3*i**3 + 3/2*i**2 + 2*i - 32. Factor k(n).
(n + 1)*(n + 2)
Suppose -4*m = -5*r - 114, -6*r = -r - 10. Factor -4*p**3 + p**5 + 2*p**2 - p**3 - p**4 + 3*p**3 + m - 32 + p.
(p - 1)**3*(p + 1)**2
Let r = -121 + -86. Let h = 2693/13 + r. Solve 2/13*s + 0 + 2/13*s**2 - h*s**4 - 2/13*s**3 = 0 for s.
-1, 0, 1
Let a = -744 + 746. Let w(k) be the second derivative of 0*k**a + 0 - 1/42*k**4 + 2/21*k**3 - 5*k. Solve w(h) = 0 for h.
0, 2
Suppose 128/13 - 12/13*h**2 + 2/13*h**3 - 48/13*h = 0. What is h?
-4, 2, 8
Let g be ((-164)/16 - -2)*(44 + -4)/(-4). Solve 6 + 12*d + g*d**4 - 75/2*d**5 - 57/2*d**3 - 69/2*d**2 = 0.
-2/5, 1
Let o(d) = -d**3 - 4*d**2 + 6*d - 7. Let f be o(-5). Let r = 18 + f. Factor -r*i**2 + 4*i**3 + i**3 - 2*i**3.
3*i**2*(i - 2)
Suppose -2*h + 9 = 3*b, 5*h = 4*b + 8*h - 11. Solve 21*y**2 + 2*y + 36*y**3 - 7*y**5 + y**b - 48*y**5 - 37*y**2 = 0 for y.
-1, 0, 1/3
Let s(g) be the second derivative of -g**5/10 - g**4/3 + 8*g**3/3 - 55*g - 2. Factor s(n).
-2*n*(n - 2)*(n + 4)
Let r = -3547 - -7095/2. Find u, given that 0*u + 0*u**4 - r*u**2 + 0 + 3/4*u**3 - 1/4*u**5 = 0.
-2, 0, 1
Suppose 0 = -13*j + 44 + 8. Factor -j - 59*y - 6 - 10*y**3 + 8*y**3 - 6*y**2 + 77*y.
-2*(y - 1)**2*(y + 5)
Let n = -13777/6 - -2290. Let i = n + 20/3. What is j in 1/2*j**2 - i + 0*j = 0?
-1, 1
Factor -35/2*u + 25 + 5/2*u**2.
5*(u - 5)*(u - 2)/2
Let y = 69 - 66. Factor 7*i**y - 15*i**3 - 2*i**2 - 2*i**4 + 13*i**3.
-i**2*(i - 2)*(2*i - 1)
Let r = 266518183/172 - 1549531. Let a = 3/43 - r. Solve -3/4*q**2 - a - 9/2*q = 0.
-3
Let h(i) = i + 8. Let o be h(10). Let r be (3/4)/(o/48). Factor -4*u - 9*u**r + 6*u + 0*u**2.
-u*(9*u - 2)
Suppose -2*v = -16*v + 14. Factor -6*m - v - 1147*m**2 - 2 + 1144*m**2.
-3*(m + 1)**2
Suppose 12*l - 85 = 7*l. Factor 44 + 21 - j**2 - l + 24*j + 4*j**2.
3*(j + 4)**2
Let z(r) be the first derivative of 5*r**6/6 + r**5 - 45*r**4/4 - 25*r**3/3 + 40*r**2 + 60*r + 206. Determine t so that z(t) = 0.
-3, -1, 2
Let y(k) be the second derivative of 5*k**7/6 + 5*k**6 + 2*k**5 - k + 1. Factor y(l).
5*l**3*(l + 4)*(7*l + 2)
Suppose 5*r = -2*a - 119, 3*a + 1 - 10 = 0. Let k = -71/3 - r. Factor -4/3*x**2 - k*x**3 + 0*x + 0 - 1/3*x**4.
-x**2*(x + 2)**2/3
Let y(m) be the second derivative of -m**6/180 + 2*m**5/45 - m**4/9 + 6*m**2 - 2*m. Let g(x) be the first derivative of y(x). Determine p, given that g(p) = 0.
0, 2
Let y(h) = -27*h**2 + 240*h - 984. Let j(a) = -11*a**2 + 96*a - 394. Let v(f) = 12*j(f) - 5*y(f). Determine k so that v(k) = 0.
8
Let p = 12 - 8. What is x in p*x**4 + 357 - 3*x**2 - x**2 - 353 - 4*x**2 = 0?
-1, 1
Factor -4/3*k**2 + 2/15*k**3 + 2/15*k**4 + 0 + 16/15*k.
2*k*(k - 2)*(k - 1)*(k + 4)/15
Suppose -5*g - 13 = 10*r - 6*r, 4*g = -20. Determine h so that 0*h + 0 - 4/13*h**2 - 2/13*h**r = 0.
-2, 0
Let i = -205598/3 + 67167. Let h = i + 1379. Solve 16/3*b + 4*b**3 - h*b**2 + 0 + 6*b**4 = 0.
-2, 0, 2/3
Let q(s) be the third derivative of -1/30*s**5 - 1/120*s**6 + 4/3*s**3 - 12*s**2 + 0 + 1/6*s**4 + 0*s. Solve q(u) = 0 for u.
-2, 2
Let i(p) = 6*p**2 - 113*p - 494. Let q(s) = -4*s**2 + 59*s + 248. Let d(u) = 6*i(u) + 10*q(u). Let d(j) = 0. What is j?
-11
Let y(g) = g**3 + g**2 - g + 117. Let z be y(0). Let n be (-26)/z - (-178)/72. Factor -3 + 3/4*r**3 + n*r**2 + 0*r.
3*(r - 1)*(r + 2)**2/4
Let o(s) = s**2 - s. Let x(t) = 1 + t**2 - 6 - 4 - 8*t. Let l(f) = -6*o(f) + 3*x(f). Find n, given that l(n) = 0.
-3
Suppose -b**3 - 5 - 31/2*b - 23/2*b**2 = 0. What is b?
-10, -1, -1/2
Let j(o) be the second derivative of -o**5/180 + o**4/72 + o**3/9 - 11*o**2/2 - 3*o. Let s(m) be the first derivative of j(m). Suppose s(h) = 0. Calculate h.
-1, 2
Let f be ((-2)/4)/(8/(-80)). Let s = f - -2. Suppose 4 - s + 3*c**2 + 0 = 0. What is c?
-1, 1
Let b(q) be the second derivative of 7/6*q**3 - 1/360*q**6 - 4*q + 1/120*q**5 + 0 + 1/12*q**4 + 0*q**2. Let g(l) be the second derivative of b(l). Factor g(s).
-(s - 2)*(s + 1)
Suppose -208*j = -259*j. Find s such that 0 + 3/2*s**2 - s + j*s**3 - 1/2*s**4 = 0.
-2, 0, 1
Let o(l) be the first derivative of 0*l**2 - 6 + 1/5*l**3 + 3/20*l**4 + 0*l. Factor o(i).
3*i**2*(i + 1)/5
Let t = 39 + -39. Suppose -4*q + 0*q = -2*c + 148, c + 5*q - 60 = t. Factor c*r**3 + 12*r**4 + 3*r**5 + 3*r + 12*r**2 + 0*r - 52*r**3.
3*r*(r + 1)**4
Let n(i) = -4*i**2 + 30*i - 11. Let b(a) = -2*a**2 + 32*a - 12. Let o(w) = -3*b(w) + 4*n(w). Factor o(z).
-2*(z - 2)*(5*z - 2)
Let v(h) = -7*h**3 - 88*h**2 + 10*h + 5. Let l(m) = -m**3 - 4*m**2 + 2*m + 1. Let i(w) = -5*l(w) + v(w). Find y such that i(y) = 0.
-34, 0
Suppose 1099*p - 6*p**4 - 1123*p - 34*p**3 + 16 + 6*p**2 - 66*p**2 = 0. Calculate p.
-2, 1/3
Solve -5/4*c**2 + 225/4*c - 55 = 0 for c.
1, 44
Let w(r) be the second derivative of r**6/15 + 13*r**5/10 + 8*r**4 + 12*r**3 - 3*r - 1. Factor w(h).
2*h*(h + 1)*