5. Let z be k(5). Factor 0 - 1/6*r**4 - 1/6*r**3 + z*r + 1/3*r**x.
-r**2*(r - 1)*(r + 2)/6
Let s be (-196)/(-8) - (32 - 8). Suppose -s*f**3 - 1/2*f**4 + 2*f**2 + 0 + 2*f = 0. What is f?
-2, -1, 0, 2
Find f, given that -2/3*f**3 - 112/3*f**2 - 5408/3 - 1768/3*f = 0.
-26, -4
Let l be (-97)/(-5) - 11 - 9 - 21/(-15). Factor 1/5*x**4 - 3/5*x**2 + 0 + 18/5*x - l*x**3.
x*(x - 3)**2*(x + 2)/5
Let p(x) be the first derivative of -2/15*x**3 - 2/15*x**2 + 0*x - 17. Let p(t) = 0. What is t?
-2/3, 0
Let g(c) be the third derivative of c**8/1680 + c**7/1050 - c**6/200 - c**5/300 + c**4/60 + 3*c**2 - 5. Let g(w) = 0. What is w?
-2, -1, 0, 1
Suppose -i - 20 = -11*i. Factor 4*n + 2*n**2 - 4 - 12*n - 9*n**i + 3*n**2.
-4*(n + 1)**2
Let z = 44 + -21. Let c = z + -21. Factor 0 + 1/2*v**c + v.
v*(v + 2)/2
Suppose -11*w = -8*w - 21. Let o(t) = -t**2 + 5*t + 16. Let c be o(w). Find b such that 1/2*b**3 + 0 + b**c + 1/2*b = 0.
-1, 0
Let q(t) be the second derivative of 0 - 22*t + 0*t**2 + 1/14*t**3 - 1/28*t**4. Factor q(y).
-3*y*(y - 1)/7
Let l(b) be the second derivative of -5/24*b**4 + 5/6*b**3 - 22 + 0*b**2 + 1/12*b**6 - 1/4*b**5 + b. Factor l(m).
5*m*(m - 2)*(m - 1)*(m + 1)/2
Let i(g) = -g**3 + 6*g**2 - 4*g - 2. Let r be i(5). Let m(a) be the first derivative of 0*a**r + 0*a - 2 + 1/4*a**4 - 1/2*a**2. Factor m(s).
s*(s - 1)*(s + 1)
Solve -2/3*h - 1/6*h**2 - 1/2 = 0.
-3, -1
What is x in 1/2*x**2 - 16 - 2*x = 0?
-4, 8
Let t(b) be the second derivative of -b**6/30 + b**5/20 + b**4/12 - b**3/6 + 49*b. Factor t(l).
-l*(l - 1)**2*(l + 1)
Let w(n) be the second derivative of 2*n**7/105 + 2*n**6/15 + n**5/3 + n**4/3 - 2*n**2 - 3*n. Let a(d) be the first derivative of w(d). Factor a(i).
4*i*(i + 1)**2*(i + 2)
Let w = 38 + -34. Let 5*a**2 + a**5 - 2*a**4 + 5*a**4 + 0*a**w - 9*a**3 + 0*a**4 = 0. What is a?
-5, 0, 1
Let h(x) be the second derivative of -x**6/120 - 3*x**5/20 - x**4 + x**3 + 39*x. Let p(n) be the second derivative of h(n). Factor p(a).
-3*(a + 2)*(a + 4)
Let m = -32 - 3. Let l be (-6)/7*(-7 + m). Suppose 12 - 3*s**2 - 15*s**3 - 4*s**3 + l*s - 26*s**3 = 0. What is s?
-2/3, -2/5, 1
Let c = -5 - -7. Solve 3*s**4 + 15*s**2 + 19*s**2 - 34*s**c + 3*s**3 = 0 for s.
-1, 0
Let r(q) be the first derivative of -q**5/5 + 5*q**4/4 - q**3 - 5*q**2/2 + 4*q + 486. Factor r(g).
-(g - 4)*(g - 1)**2*(g + 1)
Let c be (-39)/(-45) + (-2)/(-15). Let -42*n**5 - 126*n**3 - 6*n - c + 84*n**2 + 69*n**4 - 8 + 30*n**5 = 0. What is n?
-1/4, 1, 3
Suppose 0 = 3*s + q + 124, q + 0*q + 4 = 0. Let f = -29 - s. Solve -f*g**4 - 6*g**3 - 16*g**5 + 4*g**2 - 2*g**3 + 13*g**5 = 0 for g.
-2, 0, 1/3
Let y(c) be the third derivative of c**7/105 - c**6/10 + 11*c**5/30 - c**4/2 + 32*c**2. Let y(v) = 0. What is v?
0, 1, 2, 3
Let w(d) = -d**2 + d + 11. Let a(l) = -2*l**2 + 5*l + 15. Let t(k) = k**2 - 2*k - 8. Let b(q) = -2*a(q) - 5*t(q). Let p(y) = 6*b(y) - 4*w(y). Factor p(s).
-2*(s - 2)*(s + 4)
Suppose -25*y + 33*y + 408 = 0. Let v be (17/y - (-14)/6) + -2. Determine n so that 1/2*n**5 + 0 + n**4 - 1/2*n - n**2 + v*n**3 = 0.
-1, 0, 1
Let o(x) = 12*x**2 + 10*x - 30. Let g(t) = t**3 - t**2 - t + 3. Let u(z) = -20*g(z) - 2*o(z). Factor u(b).
-4*b**2*(5*b + 1)
Let z(m) be the second derivative of -m**6/160 + 3*m**5/80 - m**3/2 - 13*m**2/2 - 3*m. Let a(k) be the first derivative of z(k). Factor a(n).
-3*(n - 2)**2*(n + 1)/4
Let g = 675 - 10124/15. Let u(v) be the second derivative of 1/2*v**4 - 1/3*v**3 - g*v**6 - 2*v**2 + 1/10*v**5 + 0 - v. Factor u(z).
-2*(z - 2)*(z - 1)*(z + 1)**2
Determine q so that 3/7*q**3 + 0*q - 3/7*q**4 + 0*q**2 + 0 = 0.
0, 1
Let m(j) = -j**3 + 2*j**2 - 3*j + 1. Let q(f) = -30*f**3 - 175*f**2 + 390*f - 210. Let y(l) = -25*m(l) + q(l). Let y(x) = 0. What is x?
-47, 1
Let o(h) be the second derivative of 1/147*h**7 + 1/14*h**4 + 36*h + 0 - 1/35*h**6 - 1/70*h**5 + 0*h**3 + 0*h**2. Solve o(r) = 0.
-1, 0, 1, 3
Let l(x) = x**3 + x**2 + x + 1. Let y(s) = -s + 15. Let t be y(14). Let v(c) = -c**3 + 6*c**2 - c + 1. Let f(m) = t*l(m) - v(m). Determine n so that f(n) = 0.
0, 1/2, 2
Suppose -g + 4*c = 18, 19 = -3*g - 0*g + 5*c. Suppose -p - 2 = -g. Find h such that -6/13*h**2 + p + 4/13*h = 0.
0, 2/3
Find m such that 968*m**2 - 1783*m**2 + 939*m**2 - 2*m**4 + 25*m**3 + 33*m**3 = 0.
-2, 0, 31
Let w(z) be the first derivative of -z**6/420 + z**5/70 + z**4/21 - 9*z**2/2 - 9. Let c(j) be the second derivative of w(j). Find p, given that c(p) = 0.
-1, 0, 4
Let l(s) be the second derivative of s**7/168 - s**6/120 - 3*s**5/40 + 75*s. Factor l(t).
t**3*(t - 3)*(t + 2)/4
Solve -16*t**2 + 34*t**4 - 82/5*t**3 + 0 - 8/5*t = 0 for t.
-2/5, -2/17, 0, 1
Let m(h) be the first derivative of -h**5/35 - h**4/28 + h**3/21 + h**2/14 + 421. Factor m(g).
-g*(g - 1)*(g + 1)**2/7
Let a(q) = -25*q**2 - 40*q + 45. Let w(c) = c**2 + 13 + 64*c + 10 - 84*c - 13*c**2. Let j(r) = -3*a(r) + 5*w(r). Factor j(h).
5*(h + 2)*(3*h - 2)
Let f(w) = 36*w**3 - 556*w**2 - 1784*w - 912. Let b(g) = 12*g**3 - 184*g**2 - 595*g - 304. Let d(y) = 8*b(y) - 3*f(y). Solve d(q) = 0.
-2, -2/3, 19
Let a(y) = y - 1. Suppose 3*p + 3 = 4*p. Let r be a(p). Factor 0*s + s**r + 4*s**3 - 2*s - 12*s**2 - 13*s**3.
-s*(s + 1)*(9*s + 2)
Let v(o) be the first derivative of o**6/10 + 18*o**5/25 + 39*o**4/20 + 12*o**3/5 + 6*o**2/5 + 38. Let v(n) = 0. Calculate n.
-2, -1, 0
Let j(a) = 41*a**2 - 367*a - 16. Let y be j(9). Factor -4/3*i + 2 - 2/3*i**y.
-2*(i - 1)*(i + 3)/3
Let o(r) be the first derivative of r**5/5 + 3*r**4/2 + 3*r**3 - 2*r**2 - 12*r - 127. Determine j, given that o(j) = 0.
-3, -2, 1
Let j = 421 + -421. Let r(i) be the first derivative of 0*i**3 + 0*i**2 + 0*i**4 - 1 + 1/18*i**6 + 0*i**5 + j*i. Factor r(d).
d**5/3
Suppose 12 = 2*y, -5*v + 4*y + 445 = 459. Find j, given that -21/5 + 24/5*j - 3/5*j**v = 0.
1, 7
Let 400 + 1/4*u**2 - 20*u = 0. What is u?
40
Factor 24/7 - 8/7*z - 2/7*z**2.
-2*(z - 2)*(z + 6)/7
Suppose 2*m - 31 = 65. Suppose 4 - 9 = -5*n + 2*j, -2*j = 5*n - 25. Solve -22*u**4 - m*u**n - 15*u**5 + 73*u**4 + 0*u**2 + 13*u**2 - u**2 = 0.
0, 2/5, 1, 2
Let h = 536 + -534. Let g(t) be the first derivative of h - t + 1/6*t**3 + 1/4*t**2. Factor g(s).
(s - 1)*(s + 2)/2
Let d(v) be the first derivative of v**7/14 - 2*v**6/5 + 3*v**5/4 - v**4/2 + 29*v + 6. Let f(b) be the first derivative of d(b). Factor f(u).
3*u**2*(u - 2)*(u - 1)**2
Factor 0 + 2*o**2 - 2/7*o**3 + 0*o.
-2*o**2*(o - 7)/7
Suppose 5*h - z - 191 = h, -5*h - 4*z = -244. Factor -o**3 + 3*o**3 + h*o + 18*o**2 + 25 + 7.
2*(o + 1)*(o + 4)**2
Let t be (-4)/(-28) - (0 + 100/(-84)). Factor -t*c**2 + 2/3*c**3 + 0 + 0*c.
2*c**2*(c - 2)/3
Suppose -3*t + 634 = -371. Suppose -b = 4*b - t. Factor -67*v - 3*v**4 + 6*v**3 + b*v.
-3*v**3*(v - 2)
Suppose -5*x - 5 = -6*x. Suppose h = x*h - 12. Factor 3/5*j**2 - 3/5 + 3/5*j - 3/5*j**h.
-3*(j - 1)**2*(j + 1)/5
Let c(w) = 2*w**3 - 27*w**2 - 68*w. Let o(h) = -h**3 + 25*h**2 + 68*h. Let i(u) = -2*c(u) - 3*o(u). Let i(l) = 0. Calculate l.
-17, -4, 0
Suppose -3*u + 4*t - 6 = 0, -3*u - 5 = -7*u + t. Factor 195*y**3 - 3*y - 12*y**u + 18*y - 198*y**3.
-3*y*(y - 1)*(y + 5)
Let f(h) be the second derivative of 4*h**7/105 - 43*h**6/75 - 11*h**5/50 - 3*h + 2. Determine w so that f(w) = 0.
-1/4, 0, 11
Let u be (42/(-28))/(2 + 642/(-320)). Factor -u*a**2 + 204*a**2 + 3 - 60*a + 97 - 4*a**3.
-4*(a - 1)*(a + 5)**2
Factor 11/3*s**2 - 3*s**3 + 0 - 2/3*s.
-s*(s - 1)*(9*s - 2)/3
Factor -5808 - 12*p + 41*p + 77*p - 34*p + 192*p - 3*p**2.
-3*(p - 44)**2
Factor 58*s - 27*s**2 - 2*s**3 - 2*s**3 - 7*s**3 + 10*s**3.
-s*(s - 2)*(s + 29)
Let n(s) be the second derivative of 8*s + 1/2*s**4 + 0 + 0*s**5 - 1/14*s**7 - 1/5*s**6 + 0*s**2 + 1/2*s**3. Factor n(y).
-3*y*(y - 1)*(y + 1)**3
Let v(j) be the second derivative of 0*j**3 + 0*j**2 + 0 + 1/12*j**4 + 1/8*j**5 + 1/21*j**7 - 23*j - 11/60*j**6. Find b such that v(b) = 0.
-1/4, 0, 1, 2
Let r = -25 - -33. Let b be (-14)/56 + 18/r. Factor 12*g + 65*g**2 + g + 2*g - 70*g**b.
-5*g*(g - 3)
Let b(s) be the third derivative of s**7/105 + 43*s**6/60 - s**2 - 288*s. Let b(z) = 0. Calculate z.
-43, 0
Suppose 5*r - 19 = 11. Let d(g) = 9*g**2 - 63*g + 71. Let z(x) = -3*x**2 + 21*x - 24. Let o(t) = r*d(t) + 17*z(t). Determine y, given that o(y) = 0.
1, 6
Suppose 24*d = 26*d + 4. Let f be -4 + 1 + d - -5. Solve 4/11*p + 2/11*p**3 + f + 6/11*p**2 