**8. Suppose u(a) = 0. What is a?
-1, 2
Let 12/5*z + 0 + 36/5*z**2 - 93/5*z**3 - 36/5*z**4 + 81/5*z**5 = 0. Calculate z.
-1, -2/9, 0, 2/3, 1
Suppose -l + 0 = -3. Factor -2/5*a**2 - 2/5*a**5 + 2/5*a**l + 2/5*a**4 + 0*a + 0.
-2*a**2*(a - 1)**2*(a + 1)/5
Let d be (-216)/(-1280) + 1/(-6). Let w(c) be the third derivative of 0*c - 1/120*c**5 - c**2 - d*c**6 + 0 + 0*c**3 - 1/96*c**4. Factor w(a).
-a*(a + 1)**2/4
Let i(t) = t**2 + t - 2. Suppose z = a - 7, a + a - 4*z - 24 = 0. Let v(w) = w**2 - w. Let n(h) = a*i(h) + 2*v(h). Find b such that n(b) = 0.
-1, 1
Let o(i) be the first derivative of -i**4/24 + 7*i**3/18 - 5*i**2/6 + 22. Factor o(z).
-z*(z - 5)*(z - 2)/6
Let i(p) be the second derivative of 0*p**3 + 3*p + 0 - 1/16*p**4 + 0*p**2. Factor i(f).
-3*f**2/4
Let y = 4878 - 14806/3. Let j = y - -58. Factor 2/3*a**5 + 0*a**3 - j*a + 4/3*a**4 + 0 - 4/3*a**2.
2*a*(a - 1)*(a + 1)**3/3
Let o(p) be the third derivative of p**7/35 - 7*p**6/120 - p**5/6 + 17*p**4/24 - p**3 + 4*p**2. Find c, given that o(c) = 0.
-3/2, 2/3, 1
What is b in -22*b**3 + 4*b**3 - 27*b**2 + b**4 - 4*b**4 = 0?
-3, 0
Factor -3*l**4 + 0*l**4 + 510*l**3 - 519*l**3.
-3*l**3*(l + 3)
Let f(a) be the second derivative of -1/15*a**6 + 0 + 1/10*a**5 + 0*a**4 + 0*a**3 + 4*a + 0*a**2. Let f(r) = 0. Calculate r.
0, 1
Let p(t) be the first derivative of -1 + 0*t**2 + 2/33*t**3 + 0*t. Determine d, given that p(d) = 0.
0
Let r(k) be the second derivative of -k**4/12 + k**3/10 + k**2/5 - 4*k. Factor r(f).
-(f - 1)*(5*f + 2)/5
Let c = -128/5 + 26. Let m = -3/10 + 7/10. Let c*u + m - 2/5*u**3 - 2/5*u**2 = 0. Calculate u.
-1, 1
Let p(n) be the second derivative of -n**6/30 + 9*n**5/20 - 2*n**4 + 8*n**3/3 - 6*n. Determine j, given that p(j) = 0.
0, 1, 4
Let j(g) be the second derivative of g**7/2520 + g**6/540 - g**5/360 - g**4/36 - 2*g**3/3 + 3*g. Let a(y) be the second derivative of j(y). Factor a(x).
(x - 1)*(x + 1)*(x + 2)/3
Let g(c) be the third derivative of 3/8*c**4 + 0 - c**3 - 1/20*c**5 - 9*c**2 + 0*c. Factor g(q).
-3*(q - 2)*(q - 1)
Let g(q) be the first derivative of -2*q**5/35 - 5*q**4/14 - 2*q**3/3 - 3*q**2/7 - 39. Factor g(b).
-2*b*(b + 1)**2*(b + 3)/7
Let -46/19*c**4 - 8/19*c**2 + 60/19*c**3 - 16/19*c + 0 + 10/19*c**5 = 0. Calculate c.
-2/5, 0, 1, 2
Let u(m) be the first derivative of 0*m**2 + 0*m + 0*m**5 + 0*m**4 + m**3 + 3 + 1/840*m**7 - 1/360*m**6. Let v(p) be the third derivative of u(p). Factor v(f).
f**2*(f - 1)
Let w(o) = -o**4 - o**3 - o**2 + o. Let a(b) = 14*b**4 + 14*b**3 + 10*b**2 - 14*b. Let y(k) = -a(k) - 12*w(k). Factor y(j).
-2*j*(j - 1)*(j + 1)**2
Suppose -5*z - 2*a + 3 = 0, -3*a - 2 = z - 0*a. Suppose 2 = i - z. Factor -i*p - 5*p**2 + 4*p**2 + 5*p.
-p*(p - 2)
Let z(y) be the third derivative of y**5/15 + y**4 + 6*y**3 + 12*y**2. Let z(r) = 0. Calculate r.
-3
Let a(t) be the second derivative of 2/9*t**3 - 3*t + 1/6*t**4 - 2/5*t**5 + 7/45*t**6 + 0*t**2 + 0. Determine n so that a(n) = 0.
-2/7, 0, 1
Let o(f) be the third derivative of -f**6/210 + f**5/105 + f**4/42 - 2*f**3/21 - 2*f**2. Find u such that o(u) = 0.
-1, 1
Factor 2/9*f**4 + 0 - 2/9*f**5 + 0*f**2 + 0*f + 0*f**3.
-2*f**4*(f - 1)/9
Suppose -j + h + 2 + 2 = 0, 5*j = h + 16. Suppose -3*t**3 + 7*t**j + 6*t - 8*t - 2*t**3 = 0. Calculate t.
-1, 0, 1
Let m be (29/(-25) - -1)/((-32)/80). Determine k so that -m*k**2 + 2/5*k**3 + 0 + 0*k - 2/5*k**5 + 2/5*k**4 = 0.
-1, 0, 1
Let u = 19 + -17. Let d(l) be the first derivative of u + 0*l + 1/6*l**3 - 1/4*l**2 + 1/4*l**4. Factor d(k).
k*(k + 1)*(2*k - 1)/2
Let r(s) be the third derivative of -4*s**2 - 1/300*s**6 + 1/25*s**5 + 0*s**3 + 0*s - 3/20*s**4 + 0. Factor r(y).
-2*y*(y - 3)**2/5
Solve 0*p**3 + 3*p**2 - p**3 - 4 + 2*p**3 = 0 for p.
-2, 1
Factor 45*j + 38*j - 98*j - 18 - 3*j**2.
-3*(j + 2)*(j + 3)
Let r = 132 - 130. Let q(s) be the first derivative of 0*s - 3/2*s**r - 4 - s**3. Find y such that q(y) = 0.
-1, 0
Let d(j) be the second derivative of 3*j**5/20 + j**4/4 - j. Determine h so that d(h) = 0.
-1, 0
Let o(l) be the third derivative of -l**5/60 - l**4/4 + 27*l**2. Solve o(s) = 0.
-6, 0
Suppose -3*c + 4*l = -4*c + 11, -5*l = -4*c + 2. Let v(z) be the first derivative of 0*z + 1 + 2/3*z**c + 0*z**2. Factor v(p).
2*p**2
Let h(n) be the first derivative of 1/2*n**4 + 0*n + 6/25*n**5 - 1/5*n**2 - 5 + 2/15*n**3. Find w, given that h(w) = 0.
-1, 0, 1/3
Let h(n) = -n**4 + n**3 - n**2 + n. Suppose 4*s = 7 + 13. Let k(z) = -7*z**4 + 5*z**3 - 3*z**2 + 5*z. Let x(w) = s*h(w) - k(w). Suppose x(g) = 0. Calculate g.
-1, 0, 1
Let o = 20 + -15. Suppose 23 = 5*f + 2*v, -o*f + v - 6 = -17. What is r in 0*r**2 + 0 - 1/2*r**5 - 1/2*r**f - r**4 + 0*r = 0?
-1, 0
Let v(y) be the second derivative of 5*y**4/48 + 5*y**3/8 + 5*y**2/4 + 2*y + 5. Let v(w) = 0. Calculate w.
-2, -1
Let b(n) be the second derivative of n**4/6 - n**2 - 3*n. Solve b(i) = 0 for i.
-1, 1
Let k = -9 + 11. Let f(y) be the third derivative of -y**k + 1/90*y**5 + 0 + 1/315*y**7 + 0*y**4 + 0*y - 1/90*y**6 + 0*y**3. Factor f(u).
2*u**2*(u - 1)**2/3
Let y be 4 + 3 + -1 + -4. Let w be -3 - (-92)/16 - y. Find h such that -w*h**3 - 1/4*h**2 + 3/4*h + 1/2 - 1/4*h**4 = 0.
-2, -1, 1
Let u(r) be the second derivative of -3/20*r**5 + 1/14*r**7 + 4*r + 0*r**3 - 1/30*r**6 + 0 + 0*r**2 + 1/12*r**4. Let u(h) = 0. What is h?
-1, 0, 1/3, 1
Let p(s) be the second derivative of -s**7/21 + s**6/15 + s**5/10 - s**4/6 + 5*s. Find u such that p(u) = 0.
-1, 0, 1
Let x = -51/16 - -409/48. Let 28*u**3 - x*u - 8/3*u**4 + 0 - 32/3*u**2 - 28/3*u**5 = 0. Calculate u.
-2, -2/7, 0, 1
Suppose 10*b = 7*b + 6. Factor -1/4*t**4 + b*t**3 + 8*t - 4 - 6*t**2.
-(t - 2)**4/4
What is q in -25/6*q**3 - 4*q - 15/2*q**2 - 2/3 = 0?
-1, -2/5
Let x be (-6)/2 - (-10)/3. Let 1/3*r**3 - x*r**2 + 0 - 2/3*r = 0. What is r?
-1, 0, 2
Let g(p) be the second derivative of -55*p**4/12 + 5*p**3/3 - p. Solve g(z) = 0.
0, 2/11
Determine b so that 0 + 3/2*b - 3/2*b**2 = 0.
0, 1
Let f(l) be the first derivative of 4*l**3/15 - 16*l/5 - 13. Factor f(s).
4*(s - 2)*(s + 2)/5
Suppose 6 = -3*t + 9. What is l in 5/2*l - 7/2*l**2 + t = 0?
-2/7, 1
Let q(f) = -4*f + 24. Let v be q(6). Factor 0 + 0*o - 1/3*o**3 + v*o**2.
-o**3/3
Let c(f) = -f**5 + 4*f**3 - f - 4. Let q(w) = -w**5 - 1 - 3 - 1 - w**2 + 4*w**3 + 0*w**5. Let d(r) = -3*c(r) + 2*q(r). Factor d(x).
(x - 2)*(x - 1)*(x + 1)**3
Let u(b) be the first derivative of b**7/2940 + b**6/420 + b**5/140 + b**4/84 - b**3/3 - 1. Let f(j) be the third derivative of u(j). Factor f(y).
2*(y + 1)**3/7
Let m(j) be the third derivative of -1/135*j**5 + 0*j**4 + 0*j**3 - 1/945*j**7 + 0 + 0*j - 1/180*j**6 - j**2. Factor m(w).
-2*w**2*(w + 1)*(w + 2)/9
Let v(b) be the first derivative of -b**4/12 + 2*b**3/9 - b**2/6 - 2. Factor v(n).
-n*(n - 1)**2/3
Let w be (4/30)/(2/6). Factor 0*l - 2/5*l**4 - w + 0*l**3 + 4/5*l**2.
-2*(l - 1)**2*(l + 1)**2/5
Suppose -8/9*i - 4/3*i**2 - 2/9 - 8/9*i**3 - 2/9*i**4 = 0. Calculate i.
-1
Let q(f) = -2*f**4 + 8*f**3 + 2*f**2. Let z(i) = -3*i**4 + 9*i**3 + 3*i**2 + i. Suppose b + 4*b = -25. Let w(p) = b*q(p) + 4*z(p). Factor w(s).
-2*s*(s - 1)*(s + 1)*(s + 2)
Let a(v) = -v + 2. Let k be a(-5). Factor 3*t - k*t + t**3 + 3*t.
t*(t - 1)*(t + 1)
Let f be (1/1)/(24/18). Factor -3/4*w - 9/4*w**3 + 0 + 9/4*w**2 + f*w**4.
3*w*(w - 1)**3/4
Let f be 3 + (6 + -2)*2. Let w(z) = z**3 - 11*z**2 + 2. Let s be w(f). Determine q, given that 0*q**2 + 2*q**3 - s*q**3 - 3*q**4 - 3*q**3 + 3*q**2 + 3*q = 0.
-1, 0, 1
Let t(i) be the first derivative of -2/3*i + 11 - 1/2*i**2 - 1/9*i**3. Factor t(n).
-(n + 1)*(n + 2)/3
Let f(l) be the second derivative of l**4/36 - l**3/9 + l**2/6 + 6*l. Determine u, given that f(u) = 0.
1
Factor z**2 + 0 - 6*z**2 + 1 + 4.
-5*(z - 1)*(z + 1)
Let a(s) = 5*s**4 - 28*s**3 + 62*s**2 - 38*s. Let x(f) = 135*f**4 - 755*f**3 + 1675*f**2 - 1025*f. Let q(g) = 55*a(g) - 2*x(g). Solve q(n) = 0 for n.
0, 2
Let g = -172 + 175. Factor 0*d**g - 2/3*d**2 + 1/3*d**4 + 1/3 + 0*d.
(d - 1)**2*(d + 1)**2/3
What is c in -10*c**5 - 4*c**2 - 10*c + 23*c**3 + 2*c**4 - 9*c**3 + 2 + 6*c**3 = 0?
-1, 1/5, 1
Let s(q) = q - q**3 + 5 - 3*q**2 - 2 + 2*q**2. Let p be s(0). Factor -5*h**4 - 7*h**5 - 11*h**p - 7*h**4 - 4*h**4 - 2*h**2.
-h**2*(h + 1)**2*(7*h + 2)
Let z(i) be the second derivative of -i**7/11340 + i**6/3240 + i**4/3 + 3*i. Let j(w) be 