8. Let s be u(8). Let a(x) be the second derivative of 0*x**3 - 2*x - 1/6*x**4 + s*x**2 + 0. What is g in a(g) = 0?
0
Let d(h) be the first derivative of -25*h**4 - 40*h**3 - 18*h**2 + 3. Factor d(v).
-4*v*(5*v + 3)**2
Let p(x) = -x**3 + 7*x**2 + 11*x + 4. Let r be p(8). Factor 20*q**2 - 5*q + r*q**3 - 5*q + 7*q - 5*q.
4*q*(q + 1)*(7*q - 2)
Let o(h) = h**3 + h**2 - h - 1. Let u(f) = 18*f**3 + 12*f**2 - 45*f - 39. Let c(q) = 15*o(q) - u(q). Let c(s) = 0. Calculate s.
-2, -1, 4
Let o(a) = -6*a**2 + 9*a - 15. Suppose 0 = 5*j, 4*d + 0*j + 3*j = 8. Let x(h) = -2*h**2 - 4*h**2 - h - 1 + 4*h**2 + h**d. Let r(z) = o(z) - 3*x(z). Factor r(k).
-3*(k - 2)**2
Let j = 85 + -83. Let h(n) be the second derivative of -5/42*n**4 + 2/21*n**3 - 11/70*n**5 - 3*n + 0*n**j + 0 - 4/105*n**6. Find w such that h(w) = 0.
-2, -1, 0, 1/4
Let i = 233 + -233. Find x, given that -4/7*x + 2/7*x**4 - 2/7 + 4/7*x**3 + i*x**2 = 0.
-1, 1
Suppose 4*q**2 - 2*q + 0 - 5/2*q**3 + 1/2*q**4 = 0. Calculate q.
0, 1, 2
Let f(n) = 13*n**2 - 5*n + 6. Let q be f(3). Factor 2 + 64*y**4 + 3*y - 19*y - 9*y - 176*y**3 + q*y**2.
(y - 2)*(4*y - 1)**3
Let v be (-9)/(-12)*(-24)/(-30). Let 1/5*o**3 + 2/5*o + v*o**2 + 0 = 0. Calculate o.
-2, -1, 0
Suppose -5 + 5*y**2 + 5 - 17*y + 2*y = 0. What is y?
0, 3
Let z(h) be the first derivative of 6*h + 2/3*h**3 - 4*h**2 - 5. Factor z(b).
2*(b - 3)*(b - 1)
Let b(d) be the first derivative of 25/2*d**4 + 28*d**2 + 1/3*d**6 - 16*d - 16/5*d**5 - 76/3*d**3 + 1. Determine h so that b(h) = 0.
1, 2
Let j = -1/794 - -3179/2382. Factor j - 2/3*a**2 - 2/3*a.
-2*(a - 1)*(a + 2)/3
Suppose -6 = -5*r + 24. Find w, given that 4*w**3 + w**3 - r*w**3 = 0.
0
What is z in -38*z**4 - 3 + 6*z**2 + 35*z**4 + 0 = 0?
-1, 1
Suppose 278*w - 272*w = 24. Let 0 + 15/7*h**3 + 6/7*h**2 + 3/7*h**5 + 0*h + 12/7*h**w = 0. Calculate h.
-2, -1, 0
Suppose -7 = -3*a - 4*w, -2*a = -2*w - 3*w - 20. Let j be ((-4)/6)/(2 - a). Factor -2/9*y**3 + j*y + 2/9*y**2 - 2/9.
-2*(y - 1)**2*(y + 1)/9
Let v(q) be the third derivative of 0 - 1/20*q**5 + 3/4*q**4 - 9/2*q**3 + 8*q**2 + 0*q. Let v(f) = 0. What is f?
3
Find q such that 3*q**3 - 136*q**2 + 20 + 2*q**3 - 20*q + 131*q**2 = 0.
-2, 1, 2
Let t(y) be the second derivative of -y**5/80 - y**4/48 + y**3/24 + y**2/8 + 5*y. Factor t(d).
-(d - 1)*(d + 1)**2/4
Let d be (2/24)/(24/1024). Let b(s) be the first derivative of 0*s + 4/3*s**2 + 10/3*s**5 - 2 + 5/6*s**4 - d*s**3. Find f such that b(f) = 0.
-1, 0, 2/5
Let m(t) be the second derivative of -t**9/120960 + t**7/10080 - t**5/960 + t**4/4 + 6*t. Let s(d) be the third derivative of m(d). Factor s(y).
-(y - 1)**2*(y + 1)**2/8
Let g(r) be the first derivative of r**6/21 - 12*r**5/35 + r**4 - 32*r**3/21 + 9*r**2/7 - 4*r/7 + 5. Find w such that g(w) = 0.
1, 2
Let j(z) = -8*z**2 + 6*z + 9. Let l(t) = -2 - 6 + 7*t**2 - 5*t + 0*t. Let o(f) = -6*j(f) - 7*l(f). Suppose o(p) = 0. What is p?
-2, 1
Let r(f) be the third derivative of -f**7/42 + f**6/24 + f**5/3 - 5*f**4/6 - 10*f**2. Solve r(n) = 0.
-2, 0, 1, 2
Let w(u) be the third derivative of 0*u**5 + 2*u**2 + 0*u + 0*u**3 + 1/420*u**6 + 0 - 1/84*u**4. Factor w(f).
2*f*(f - 1)*(f + 1)/7
Let h(w) be the third derivative of -w**6/24 + w**5/6 + 16*w**2. Solve h(m) = 0.
0, 2
Let p(r) = 16*r**2 - 4*r + 2. Let q be p(2). Let u = q - 172/3. Solve 2*y**3 + u - 1/3*y**2 - 5/3*y = 0.
-1, 1/2, 2/3
Let d be 1*(-6)/15*-15. Let t be d/9 + (-8)/(-6). Factor 0*o**4 - t*o**4 - 4*o**2 + 7*o**3 - o**3.
-2*o**2*(o - 2)*(o - 1)
Let v(k) be the second derivative of 3/5*k**5 + 0 - k + 5/4*k**4 + 0*k**2 + 1/2*k**3. Let v(w) = 0. What is w?
-1, -1/4, 0
What is n in 0 - 1/8*n**3 + 0*n**2 + 1/8*n = 0?
-1, 0, 1
Let z(i) = i**3 - i**2 - i - 1. Let m(v) = v**3 - v**2 - 2*v - 2. Let b(n) = m(n) - 2*z(n). Factor b(h).
-h**2*(h - 1)
Suppose -4*d + 22 - 6 = 0. Factor 5*u**d + 11*u**2 - u**2 - 2*u**4 - 12*u**3 + 2*u**2.
3*u**2*(u - 2)**2
Factor -8/3 + 20/3*f + 4/3*f**4 - 4*f**2 - 4/3*f**3.
4*(f - 1)**3*(f + 2)/3
Let z(i) = i**2 - 3*i + 4. Let q be z(3). Factor 2*d**2 - 3 - q*d + 1 + 4.
2*(d - 1)**2
Suppose -4*g = -15*g + 22. Let 2/3*n**g + 4/3 - 2*n = 0. What is n?
1, 2
Factor -2/3*i**4 + 8/9*i**3 + 0*i**2 - 2/9*i**5 + 0 + 0*i.
-2*i**3*(i - 1)*(i + 4)/9
Let v = 16 + -13. Let y(c) = -5*c**4 + 2*c**3 - 5*c**2 + 4*c. Let w = 1 + -5. Let a(t) = -4*t**4 + t**3 - 4*t**2 + 3*t. Let f(q) = v*y(q) + w*a(q). Factor f(s).
s**2*(s + 1)**2
Suppose -4*x = -7 - 5. Factor x*t**2 + 2*t**3 - 5*t**3 + 3*t + 3*t.
-3*t*(t - 2)*(t + 1)
Factor 24/7*i**3 + 16/7*i**4 + 4/7*i + 0 + 16/7*i**2 + 4/7*i**5.
4*i*(i + 1)**4/7
Let t(a) be the third derivative of 5*a**8/336 - 5*a**7/42 + 5*a**6/12 - 5*a**5/6 + 25*a**4/24 - 5*a**3/6 - 16*a**2. Determine m, given that t(m) = 0.
1
Let u(j) be the first derivative of 2*j**5/85 + 4*j**4/17 + 26*j**3/51 + 6*j**2/17 + 34. Factor u(l).
2*l*(l + 1)**2*(l + 6)/17
Suppose -4*s = 135 - 7. Let y be ((-8)/s)/((-10)/(-8)). Determine w, given that 1/5 - 2/5*w**2 + 0*w**3 + 0*w + y*w**4 = 0.
-1, 1
Let u(s) be the first derivative of -2*s**5/45 - s**4/18 - 5. Suppose u(d) = 0. Calculate d.
-1, 0
Let r(g) be the third derivative of g**7/245 + g**6/420 - g**5/105 + 7*g**2. Factor r(c).
2*c**2*(c + 1)*(3*c - 2)/7
Let t(f) be the first derivative of -1/9*f**3 - 2 + 1/6*f**2 + 0*f. Factor t(u).
-u*(u - 1)/3
Suppose -3*q - 3 = -3*o, -2*o - 1 + 0 = -3*q. Suppose -4*g + v = -2*v, -2*g + v = 0. Factor -x**q + g*x + 0*x.
-x**3
Let a(m) = -m - 1. Let k be a(-6). Suppose 3*y = k*c + 21, -4*y + c + 0 + 11 = 0. Solve -4*g**3 + 3*g**3 + 3*g**3 - y*g**4 = 0.
0, 1
Let a(j) be the third derivative of j**7/280 - j**6/160 - j**5/80 + j**4/32 - 46*j**2. Let a(k) = 0. Calculate k.
-1, 0, 1
Factor 15*q**2 - 2*q**3 - 12*q**2 - 32*q + 13*q**2.
-2*q*(q - 4)**2
Suppose 4*k = 3*k. Let i(x) be the third derivative of 0*x**5 - 1/84*x**4 + k*x**3 + 0 + 0*x - 2*x**2 + 1/420*x**6. Let i(v) = 0. Calculate v.
-1, 0, 1
Let y(o) be the third derivative of -o**7/105 + o**5/30 - 16*o**2 + 2*o. Factor y(b).
-2*b**2*(b - 1)*(b + 1)
Let z(o) = -o**2 + 7*o + 5. Let k be z(7). Suppose 0 = 5*f + d - 80, f - d - k = d. Factor f*s + 1 + 21*s**2 - 2 - 5.
3*(s + 1)*(7*s - 2)
Let g = -200323/325140 + -3/5419. Let u = 1/20 - g. Determine s so that 0 - 8/3*s**2 - 8/9*s + 2/3*s**5 + 20/9*s**4 + u*s**3 = 0.
-2, -1/3, 0, 1
Let v(b) be the third derivative of b**6/600 + b**5/50 + b**4/10 + 4*b**3/15 - 13*b**2. Factor v(p).
(p + 2)**3/5
Find v such that -6*v**3 - 296*v**2 - 2*v**5 - 2*v**4 + 306*v**2 - 4*v + 4*v**5 = 0.
-2, 0, 1
Let j(n) = n**4 - n**3 + n - 1. Let w(y) = 8*y**4 - 20*y**3 + 30*y**2 - 12*y - 6. Let z(v) = -12*j(v) + 2*w(v). Factor z(k).
4*k*(k - 3)**2*(k - 1)
Let a(i) = -11*i**2 + 6*i + 11. Let f(r) = -23*r**2 + 13*r + 23. Let u(q) = -13*a(q) + 6*f(q). Determine v, given that u(v) = 0.
-1, 1
Let 3/4*j**2 + 0 - 3/4*j = 0. What is j?
0, 1
Suppose -3*j = 2*n - 7, 4*j = 3*n - 0*n - 2. Suppose 2/5*r + 4/5 - 2/5*r**n = 0. Calculate r.
-1, 2
Let a(i) be the second derivative of 0 + 5*i - 1/10*i**2 - 2/15*i**3 - 1/20*i**4. Factor a(f).
-(f + 1)*(3*f + 1)/5
Let i(c) be the second derivative of c**6/180 + c**5/90 - c**4/18 - 2*c**2 - 4*c. Let r(m) be the first derivative of i(m). Solve r(w) = 0.
-2, 0, 1
Let f(k) be the second derivative of -9*k**6/5 + 57*k**5/10 - 31*k**4/6 - k**3/3 + 2*k**2 + k. Solve f(u) = 0 for u.
-2/9, 1/3, 1
Let m(n) be the second derivative of -2/21*n**4 + 7*n + 0 - 1/294*n**7 - 1/7*n**2 + 1/105*n**6 + 1/70*n**5 + 1/6*n**3. Factor m(a).
-(a - 1)**4*(a + 2)/7
Suppose -3/7*d**5 - 3/7*d**3 + 0 - 6/7*d**4 + 0*d**2 + 0*d = 0. What is d?
-1, 0
Let g(f) = -2*f - 8. Let h = 23 - 28. Let d be g(h). Factor 0 - 2/3*q + 2/3*q**d.
2*q*(q - 1)/3
Let o be 3 - ((-58)/(-12) + -2). Let i(z) be the second derivative of 0*z**3 + o*z**4 + z + 0*z**2 + 0. Factor i(s).
2*s**2
Suppose 3*n - 19 = -v, -2*v + 23 = 3*v - 3*n. Let w = 15 - v. Solve 31*a**5 + 34*a**4 - 131*a**5 + 24*a**3 - 4*a**4 - w*a**2 = 0.
-1/2, 0, 2/5
Let s = 654 - 654. Let 2/11*c**3 + 0*c - 4/11*c**4 + 0 + 2/11*c**5 + s*c**2 = 0. What is c?
0, 1
Let m(k) be the third derivative of -k**5/15 - k**4/6 + 4*k**3/3 - 2*k**2. Factor m(p).
-4*(p - 1)*(p + 2)
Let o = 3 + -1. Factor 3*t - 2 - 2*t - 5*t + 3*t + t**o.
(t - 2)*(t + 1)
Let k be 146/6 - (-8)/(-24). Suppose 6*r - k = -3*l + 2*r, r +