8/5600 - g**7/1050 - g**6/450 + g**5/30 + 3*g**2. Let d(q) be the third derivative of z(q). What is c in d(c) = 0?
-2/3
Let x = 20 - 20. Let 1/4*k**4 + 0 - 1/2*k + x*k**3 - 3/4*k**2 = 0. What is k?
-1, 0, 2
Let g = 2/81 - -152/405. Suppose -17*l - 13 + 47 = 0. Determine u, given that g - 1/5*u**l - 1/5*u = 0.
-2, 1
Let t be (1/(-6))/(8/(96/(-30))). Let z(n) be the second derivative of 1/60*n**4 + 0 - t*n**3 + 0*n**2 + 3*n. Suppose z(d) = 0. Calculate d.
0, 2
Suppose -2*m + 17 = -5. Suppose -7*w + m*w - 2*w**2 - 3 + 1 = 0. Calculate w.
1
Let h be (2 - -4)/((-18)/(-12)). Factor -5*g + h*g**4 - 4*g**2 - 77*g**3 + g + 81*g**3.
4*g*(g - 1)*(g + 1)**2
Let n = 11 - 8. Factor 9*i**n - i + 6*i**2 + i + 32*i**5 - 35*i**5.
-3*i**2*(i - 2)*(i + 1)**2
Let m be (-27)/18*(-3)/((-405)/(-24)). Let a(y) be the first derivative of -1 + 0*y + 1/9*y**6 + m*y**5 + 0*y**3 + 0*y**2 + 1/6*y**4. Factor a(l).
2*l**3*(l + 1)**2/3
Let o(s) be the second derivative of s**7/10080 + s**6/2880 - s**4/4 + 3*s. Let i(b) be the third derivative of o(b). Factor i(a).
a*(a + 1)/4
Factor -10 - 4*x**4 - 11 + 21 + 4*x**2.
-4*x**2*(x - 1)*(x + 1)
Let w(n) = -n**3 - n**2 + 4*n + 3. Let c be w(-4). Let t be ((-2)/(-5))/(21/c). Factor 0 + t*k**4 + 2/3*k - 2/3*k**2 - 2/3*k**3.
2*k*(k - 1)**2*(k + 1)/3
Let h(m) = -m + 8. Let j be h(6). Let a be (-12)/(-5)*(-5)/(-2). Suppose -r**j + 3*r**2 + 8*r + 14 - a = 0. What is r?
-2
Let b = 10 - 10. Determine z, given that 2*z - 7*z**2 + b + 0 + 14*z**2 = 0.
-2/7, 0
Suppose 0 = 2*q + 4*b - 32, -q = -b + 2 - 3. Let f(c) be the second derivative of 0*c**3 + c + 1/20*c**5 + 0*c**2 + 0 - 1/60*c**q - 1/24*c**4. Factor f(a).
-a**2*(a - 1)**2/2
Suppose 0 = a - 6*a + 20. Let j = -2 + a. Determine v, given that v**2 - v**2 + v**2 + j - 2*v + 5*v = 0.
-2, -1
Let l(a) = 9*a**3 + 7*a**2 + a - 12. Let b(c) = -5*c**3 - 3*c**2 - c + 6. Let y(v) = 5*b(v) + 3*l(v). Suppose y(h) = 0. What is h?
-3, -1, 1
Let c(f) = -22*f**3 + 12*f**2 + 10*f + 12. Let t(a) = -4*a - 5*a**2 + 3*a**3 + 1 + 4*a**3 + 2*a**3 - 6. Let v(k) = -5*c(k) - 12*t(k). Factor v(x).
2*x*(x - 1)*(x + 1)
Let k be 312/20 + (-2)/(-5). Determine z so that k*z**2 - z**2 - 3*z**3 - 27 - 8*z - z = 0.
-1, 3
Suppose 2*t + 0*t = -5*q + 167, -4*q - 2*t + 132 = 0. Let y = q + -139/4. Factor y*z + 0 + 1/4*z**3 + 1/2*z**2.
z*(z + 1)**2/4
Suppose -20*y + 16*y = 0. Let h be (-25)/20 + (-4)/(-2). Factor h*d**3 + 3/4*d**2 + 0 + y*d.
3*d**2*(d + 1)/4
Let v(q) be the third derivative of -q**5/40 + q**4/4 - q**3 - 7*q**2. Factor v(a).
-3*(a - 2)**2/2
Let w(f) be the second derivative of 0 - 4/3*f**2 + 1/18*f**4 - f + 0*f**3. Let w(o) = 0. Calculate o.
-2, 2
Let g(r) = -4*r**4 + 19*r**3 - 17*r**2 + 11*r - 3. Let c(j) = 12*j**4 - 58*j**3 + 50*j**2 - 34*j + 10. Let w(a) = -3*c(a) - 10*g(a). Factor w(v).
4*v*(v - 2)*(v - 1)**2
Let c(u) be the third derivative of 1/270*u**5 + 0*u - 1/945*u**7 + 0*u**4 + 3*u**2 + 0*u**3 + 1/1512*u**8 - 1/540*u**6 + 0. Determine f, given that c(f) = 0.
-1, 0, 1
Determine s so that 2/19*s**4 - 2/19 + 4/19*s - 4/19*s**3 + 0*s**2 = 0.
-1, 1
Let k = 91 - 91. Solve k*j + 0 + 2/7*j**2 + 2/7*j**3 = 0 for j.
-1, 0
Let k(j) be the second derivative of -1/180*j**5 - 2/9*j**3 + 3/2*j**2 - 1/18*j**4 - 3*j + 0. Let t(b) be the first derivative of k(b). Factor t(d).
-(d + 2)**2/3
Let t(r) be the first derivative of -25*r**6/6 - 12*r**5 - 45*r**4/4 - 10*r**3/3 + 23. Factor t(w).
-5*w**2*(w + 1)**2*(5*w + 2)
Suppose 0 = -0*z - 4*z + 12. Let a be 5*24/20 + (-12)/3. What is y in 0*y + 0 + 4/3*y**z + 0*y**a + 2*y**5 - 14/3*y**4 = 0?
0, 1/3, 2
Let b(m) be the first derivative of 21*m**5/5 - 15*m**4/4 - 9*m**3 + 15*m**2/2 + 6*m - 5. Factor b(k).
3*(k - 1)**2*(k + 1)*(7*k + 2)
Let x(q) be the third derivative of q**8/5880 - q**6/1260 + 5*q**3/6 - q**2. Let i(s) be the first derivative of x(s). Factor i(c).
2*c**2*(c - 1)*(c + 1)/7
Suppose -4*h = -h - 9. Suppose h*n - 2 - 5 = -5*r, 3*n + 3*r - 9 = 0. Determine p so that -p**2 + n*p + 2*p**2 + 3*p**2 - 2*p**2 = 0.
-2, 0
Let m(d) be the first derivative of 0*d + 6 + 2/3*d**3 - d**2. What is y in m(y) = 0?
0, 1
Let f(r) be the second derivative of 5*r**6/6 + 3*r**5/4 - 35*r**4/12 - 5*r**3/2 + 5*r**2 - 7*r. Factor f(x).
5*(x - 1)*(x + 1)**2*(5*x - 2)
Determine i so that -123*i**2 - 12*i**3 + 95*i**2 + 3 + 6 + 7 = 0.
-2, -1, 2/3
Let b = 4820 + -14311/3. Let s = -49 + b. Factor 4/3*o**2 + 0 + s*o**3 + 2/3*o.
2*o*(o + 1)**2/3
Suppose 2*q - 3 = -3*l, 0*l - l = -q - 6. Solve 1 + o**5 - 1/2*o**4 - 1/2*o**2 - 7/2*o**l + 5/2*o = 0.
-1, -1/2, 1, 2
Let p(j) be the third derivative of j**6/660 + 9*j**2. What is i in p(i) = 0?
0
Let w = -5 + 5. Let b(m) be the third derivative of 7/90*m**5 + 11/72*m**4 - 2*m**2 + w + 0*m + 1/9*m**3. Find f, given that b(f) = 0.
-1/2, -2/7
Let r(a) be the second derivative of a**4/18 - 8*a**3/9 + 7*a**2/3 + 29*a. Factor r(u).
2*(u - 7)*(u - 1)/3
Let q(d) be the second derivative of -2/9*d**2 - 2/27*d**4 + 3*d + 0 + 5/27*d**3 + 1/90*d**5. Let q(c) = 0. Calculate c.
1, 2
Solve 64/5 + 2016/5*h**2 + 2052/5*h**4 - 608/5*h - 3024/5*h**3 - 486/5*h**5 = 0 for h.
2/9, 2/3, 2
Let o be (18/(-4) - -4)*0/(-3). Factor 0*z - 4/7*z**3 + o*z**2 + 0 + 2*z**4.
2*z**3*(7*z - 2)/7
Let l(g) be the second derivative of 3*g**5/20 + 21*g**4/4 + 60*g**3 + 150*g**2 + 4*g - 3. Factor l(r).
3*(r + 1)*(r + 10)**2
Suppose -17 = 5*w + 2*o, 0 = -0*o + 4*o + 4. Let z = 5 + w. Suppose 0*p**4 + 3*p**3 - p**4 + p**z - 2*p**5 - p**5 = 0. Calculate p.
-1, -1/3, 0, 1
Let h(r) be the second derivative of r**5/5 + 8*r**4/3 + 14*r**3 + 36*r**2 - 30*r. Solve h(l) = 0.
-3, -2
Suppose -5*u - 3*a = 1 - 9, -2*a - 1 = -3*u. Let i be ((-12)/(-120))/(u/4). Solve i + 0*y - 2/5*y**2 = 0 for y.
-1, 1
Factor -4/3*s**3 - 2/3*s**4 + 0*s - 2/3*s**2 + 0.
-2*s**2*(s + 1)**2/3
Let l(a) = -4*a**3 + a**2 + 3*a + 3. Let y(z) = 7*z**3 - 2*z**2 - 5*z - 5. Let c(x) = -10*l(x) - 6*y(x). Determine w so that c(w) = 0.
0, 1
Let y(l) be the first derivative of -4*l**3/3 - 13. Factor y(v).
-4*v**2
Determine g so that -3*g**2 + 6*g**3 + 5*g - 7*g + 3*g**4 - 4*g + 0*g**4 = 0.
-2, -1, 0, 1
Let f be (-9)/(-18) + 3/(-6). Factor -3/5*w**2 + f - 3/5*w.
-3*w*(w + 1)/5
Determine s so that 0*s**4 + 2/3*s**5 + 0*s**2 - 4/3*s**3 + 2/3*s + 0 = 0.
-1, 0, 1
Let t = -11 - -15. Let j(z) be the third derivative of -z**2 + 0 - 1/210*z**5 + 1/420*z**6 + 0*z - 1/84*z**t + 1/21*z**3. Factor j(p).
2*(p - 1)**2*(p + 1)/7
What is g in 4/13 + 22/13*g**4 + 22/13*g + 46/13*g**2 + 46/13*g**3 + 4/13*g**5 = 0?
-2, -1, -1/2
Let x(k) be the third derivative of k**5/150 - k**4/60 - 2*k**3/15 + 5*k**2. What is d in x(d) = 0?
-1, 2
Let z(u) be the first derivative of 8*u + 28/3*u**3 + 18*u**2 + 1. Factor z(k).
4*(k + 1)*(7*k + 2)
Let x(o) be the first derivative of o**4/4 + 4*o**3 + 18*o**2 + 16. Let x(r) = 0. Calculate r.
-6, 0
Let m(d) be the second derivative of d**6/75 - 8*d. Find x such that m(x) = 0.
0
Let m(j) = 2*j**2 + j - 52. Let w be m(5). Suppose 0 = d - 0*d. Factor 0 + 0*r**2 + d*r - 2/5*r**4 + 2/5*r**w.
-2*r**3*(r - 1)/5
Factor -2/17*q - 4/17 + 2/17*q**2.
2*(q - 2)*(q + 1)/17
Find z, given that 10*z + z**2 - 4 - 2*z**3 - 2*z**4 + 5*z**2 - 8*z = 0.
-2, -1, 1
Let o(q) be the second derivative of -q**7/63 + 4*q**6/45 - q**5/5 + 2*q**4/9 - q**3/9 - 7*q. Solve o(x) = 0.
0, 1
Let k be (-3)/((-3)/(-3)) + 4. Let g be 0 + 0 + 2 + k. Factor -1/2 + 0*o**2 - o + o**g + 1/2*o**4.
(o - 1)*(o + 1)**3/2
Let k(s) = -s**3 + 6*s**2 - 6*s + 6. Let l be k(6). Let t = 33 + l. Let 19/4*h**4 + 2*h**t + 7/4*h**5 + 0*h + 0 - h**2 = 0. What is h?
-2, -1, 0, 2/7
Factor -9/5*o - 6/5 + 0*o**2 + 3/5*o**3.
3*(o - 2)*(o + 1)**2/5
Let y(j) = -j**2 + 6*j + 8. Suppose 21 = -2*k + 5*k. Let g be y(k). Factor 3/2*a + g - 3/2*a**3 - 1/2*a**2 - 1/2*a**4.
-(a - 1)*(a + 1)**2*(a + 2)/2
Let a = -5 - -10. Suppose 0*n = s + 3*n - 8, -a*s + 4*n + 40 = 0. Let -64*f**3 + 135*f**4 - s*f**2 - 32*f**3 + 243*f**5 + 20*f**2 = 0. What is f?
-1, 0, 2/9
Let i(t) = -t**2 + t - 1. Let j(z) = 4*z**2 + 2*z - 2. Let a(n) = 6*i(n) + j(n). Factor a(k).
-2*(k - 2)**2
Suppose 0 = -3*v + 7*v - 5*j - 23, -5*j - 7 = 4*v. Let 2*p**4 + 3 - v*p**3 - 5 + 2 = 0. What is p?
0, 1
Let a(v) be the first derivative of v**4/12 + v**3/9 - v**2/6 - v/3 + 61. Factor a(w).
(w - 1)*(w + 1)**2/3
Let m(d) be the third derivati