**5 + 35*j**4 - 15*j**3 - 15*j**2 + 10*j + 5. Let n(p) = g(p) + 5*i(p). Find u, given that n(u) = 0.
-2/3, 0, 1
Let n(k) be the second derivative of k**4/8 - 21*k**3/2 + 123*k**2/4 - 622*k. Suppose n(c) = 0. Calculate c.
1, 41
Suppose t - 4*t = -5*z + 10, -8 = -4*z. Let o(l) be the second derivative of -1/24*l**3 - l - 9/80*l**5 + 1/8*l**4 + t + 0*l**2 + 1/30*l**6. Factor o(g).
g*(g - 1)**2*(4*g - 1)/4
Let a(m) be the second derivative of -m**6/40 - m**5/10 + 37*m**2/2 + 27*m. Let s(r) be the first derivative of a(r). Factor s(c).
-3*c**2*(c + 2)
Factor 8/9*x**2 - 50/9*x**5 - 16/3*x**3 + 0*x + 10*x**4 + 0.
-2*x**2*(x - 1)*(5*x - 2)**2/9
Let -6*w**4 - 11*w**4 + 30*w**4 - 12*w**4 = 0. Calculate w.
0
Factor 28/5*a**3 + 0*a - 32/5*a**2 - 1/5*a**5 - 4/5*a**4 + 0.
-a**2*(a - 2)**2*(a + 8)/5
Let d(a) be the second derivative of 5*a**4/12 - 55*a**3/6 + 25*a**2 + 173*a. Factor d(u).
5*(u - 10)*(u - 1)
Factor -3 + 8*l**2 + l**2 - 7*l**2 + 0*l**2 - 29.
2*(l - 4)*(l + 4)
Let v(z) = z**2 - 14*z - 2655. Let d be v(-45). Factor 4/11*i**2 - 4/11*i**4 - 2/11*i + 2/11*i**5 + 0*i**3 + d.
2*i*(i - 1)**3*(i + 1)/11
Let o = 2 - 16. Let z(q) = -q**3 - 13*q**2 + 13*q - 8. Let f be z(o). Solve x**2 + 4*x**2 - 12*x**3 + 10*x**4 + f*x**4 - 9*x**2 = 0.
-1/4, 0, 1
Let m(p) = 5*p - 31. Let i be m(7). Factor i*f**2 - f**4 + 51*f - 51*f - 3*f**4.
-4*f**2*(f - 1)*(f + 1)
Let z be (5675/10 - 4) + -3. Let c = 574 - z. Solve c + 9/2*d + 3/2*d**3 - 15/2*d**2 = 0 for d.
-1, 3
Let y(k) be the third derivative of k**7/70 + 3*k**6/40 - k**5/20 - 3*k**4/8 - 111*k**2. Factor y(a).
3*a*(a - 1)*(a + 1)*(a + 3)
Suppose 3*c + 483 = -822. Let y = 3060/7 + c. Factor 3*w**2 - 6/7 - y*w.
3*(w - 1)*(7*w + 2)/7
Let w(x) = x**3 + 19*x**2 + 19*x + 21. Let y be w(-18). Solve -4*a**3 + 2*a**3 + a**2 + a**y = 0.
0, 1
Let y(r) be the second derivative of -r**5/45 + 7*r**4/54 + 4*r**3/27 - 13*r - 4. Factor y(c).
-2*c*(c - 4)*(2*c + 1)/9
Let z(d) be the first derivative of 19*d**3/15 - 23*d**2/10 + 4*d/5 + 9. Factor z(f).
(f - 1)*(19*f - 4)/5
Let v(r) be the second derivative of -4*r**2 + 0 + 8*r - 2/3*r**3 + 1/3*r**4. Solve v(z) = 0 for z.
-1, 2
Let l(d) be the first derivative of 26 - 1/6*d - 1/18*d**3 - 1/6*d**2. Factor l(p).
-(p + 1)**2/6
Let p(c) be the third derivative of c**5/90 - 10*c**4/9 + 400*c**3/9 - 49*c**2. Determine n, given that p(n) = 0.
20
Let l(b) = 3*b - 28. Let f be l(10). Find k such that -2*k**3 - f + 4*k + 8*k**2 - 12*k + 2 = 0.
0, 2
Factor -71/3*x**2 + 0*x + 0 + 1/3*x**3.
x**2*(x - 71)/3
Suppose -2 = 5*j + 2*b - 32, -b + 5 = 0. Let n(d) be the first derivative of -1/4*d**j + 0*d**2 - 3 - 4/5*d**5 - 1/2*d**6 + 0*d + 0*d**3. Factor n(g).
-g**3*(g + 1)*(3*g + 1)
Let o be ((-39)/(-12) + -2)/(1/4). Suppose o*h + 2*a - 6 = 0, -2*h + 0*a - a + 2 = 0. Factor 20/3*m - 2/3 - 145/6*m**h - 175/6*m**4 + 235/6*m**3 + 49/6*m**5.
(m - 1)**3*(7*m - 2)**2/6
Let i(n) be the third derivative of -n**6/720 + n**5/80 - n**4/24 + 5*n**3/6 + 4*n**2. Let l(x) be the first derivative of i(x). Factor l(g).
-(g - 2)*(g - 1)/2
Let i(u) be the third derivative of u**7/3360 + u**6/960 - 13*u**4/24 + 10*u**2. Let l(j) be the second derivative of i(j). Find n, given that l(n) = 0.
-1, 0
Let c(z) be the third derivative of z**5/100 + 3*z**4/2 + 90*z**3 + 41*z**2 - 2. Factor c(n).
3*(n + 30)**2/5
Let y(n) be the first derivative of -4/21*n**3 + 2/7*n**2 + 0*n - 1/7*n**4 - 6 + 4/35*n**5. Let y(b) = 0. What is b?
-1, 0, 1
Let r(w) be the first derivative of w**5/20 + 3*w**4/8 - 2*w**3 + 9*w**2 - 4. Let q(b) be the second derivative of r(b). Factor q(g).
3*(g - 1)*(g + 4)
Let v(x) = -2*x**3 - 14*x**2 - 25*x - 23. Let w be v(-5). Factor -12/7*s + 0 - 9/7*s**w + 3/7*s**3.
3*s*(s - 4)*(s + 1)/7
Factor 34/21 + 32/21*v - 2/21*v**2.
-2*(v - 17)*(v + 1)/21
Let l(s) be the first derivative of 3*s**5/5 - 93*s**4 + 3844*s**3 + 168. Factor l(g).
3*g**2*(g - 62)**2
Suppose -4*o + 9 = -w, 0 = -5*o + 7*o - 2*w. Let c(n) be the first derivative of 0*n + 12/5*n**5 + 4/3*n**o - 3*n**4 - 8 - 2/3*n**6 + 0*n**2. Factor c(f).
-4*f**2*(f - 1)**3
Suppose 6*n - 54 = -36. Let j(m) be the first derivative of -4/7*m + 2 - 2/21*m**n + 3/7*m**2. Find b such that j(b) = 0.
1, 2
Let i = -25408/3 + 8470. Determine r so that i*r - 4/9 - 2/9*r**2 = 0.
1, 2
Let t(i) be the first derivative of i**3/12 + 3*i**2/4 + 2*i + 64. Solve t(v) = 0 for v.
-4, -2
Let w(u) be the second derivative of u**4/28 - 5*u**3/14 - 9*u**2/7 - 77*u. Let w(d) = 0. Calculate d.
-1, 6
Solve -736/9*h + 33856/9 + 4/9*h**2 = 0.
92
Let f(m) be the third derivative of 10*m**2 + 0 + 50/3*m**3 + 1/15*m**5 + 0*m + 5/3*m**4. Solve f(t) = 0.
-5
Suppose -q + 2*q = 3. Suppose -2*u = q*u. Factor -4*f**3 + u*f - 3*f**4 + 3*f**5 - f**3 + 3*f - 3 - f**3 + 6*f**2.
3*(f - 1)**3*(f + 1)**2
Let k(y) be the third derivative of -2/33*y**3 + 5/132*y**4 - 2/165*y**5 - 6*y**2 + 0 + 1/660*y**6 + 0*y. Factor k(w).
2*(w - 2)*(w - 1)**2/11
Let c(r) = -r**2 + r - 1. Suppose -3*g = 4*h - 3 - 4, g + 5*h = 17. Let o(n) = n**3 - n**2 - 2. Let p(m) = g*o(m) + 6*c(m). Factor p(v).
-3*v*(v - 1)*(v + 2)
Let y(j) = -46*j**4 + 108*j**3 - 70*j**2 - 16*j. Let x(k) = 15*k**4 - 36*k**3 + 23*k**2 + 5*k. Let h(i) = 16*x(i) + 5*y(i). Factor h(c).
2*c**2*(c - 3)*(5*c - 3)
Let l(t) be the third derivative of t**7/504 - 7*t**4/12 + 3*t**2. Let i(u) be the second derivative of l(u). Factor i(y).
5*y**2
Let w be (-5)/450*16 - (-2)/(-9). Let b = w + 19/10. Factor 1/2*r**2 - b - r.
(r - 3)*(r + 1)/2
Suppose 17 = -w + 5*x, -13*w = -11*w + 4*x - 22. Factor 2/7*s**w + 4/7*s**2 - 2/7*s - 4/7.
2*(s - 1)*(s + 1)*(s + 2)/7
Let s = -1634/7 + 14776/63. Factor 4/9 + 2/9*t**3 + 8/9*t**2 + s*t.
2*(t + 1)**2*(t + 2)/9
Let d(s) be the first derivative of -4*s**5/5 + s**4 + 8*s**3 + 160. Factor d(c).
-4*c**2*(c - 3)*(c + 2)
Let o(n) be the first derivative of -n**6/4 + 21*n**5/10 - 21*n**4/8 - 19*n**3/2 + 12*n**2 + 30*n + 309. Suppose o(w) = 0. Calculate w.
-1, 2, 5
Let a be ((-12)/(-15))/((-2)/(-10)). Suppose 22*t**4 - 16*t - 67*t**3 - a*t**5 + 2*t**4 + 15*t**3 + 48*t**2 = 0. What is t?
0, 1, 2
Let h = 832 - 832. Let s(u) be the third derivative of 3/14*u**3 + 0*u + h - 4*u**2 + 1/70*u**5 - 1/8*u**4. Factor s(q).
3*(q - 3)*(2*q - 1)/7
Let c be 164/40 - (-4)/(-1). Let p(h) be the second derivative of -3/50*h**5 - c*h**4 - 1/75*h**6 - 1/15*h**3 + 0*h**2 - 2*h + 0. Suppose p(b) = 0. What is b?
-1, 0
Suppose 4*x + 380 = 38*x - 300. Suppose 5*j - 10 = 15. Factor -81/2*r**j + 117/2*r**4 - x*r**3 + 0*r + 0 + 2*r**2.
-r**2*(r - 1)*(9*r - 2)**2/2
Let r(x) be the third derivative of -3/56*x**4 - 1/490*x**7 + 0*x - 1/210*x**5 + 0 + 5/42*x**3 - 4*x**2 - 1/2352*x**8 + 1/84*x**6. Suppose r(h) = 0. What is h?
-5, -1, 1
Suppose 34 = 2*g - 0*g. Factor 71*c**4 + 53*c**3 - 2*c**5 + 6*c**5 - g*c**3 - 47*c**4.
4*c**3*(c + 3)**2
Let k(d) be the first derivative of -d**6/10 - 6*d**5/5 - 15*d**4/4 - 577. Solve k(m) = 0 for m.
-5, 0
Solve -26/7*r**4 + 8/7 + 16/7*r - 34/7*r**3 - 6/7*r**5 - 6/7*r**2 = 0 for r.
-2, -1, 2/3
Let x(r) = r + 15. Let u be x(-6). Factor -4*g + u*g + 11 + 2 - 5*g**2 - 3.
-5*(g - 2)*(g + 1)
Suppose 66 = -x + 3*d, 0 = -0*x - 4*x - 2*d - 250. Let l be (-6)/x - (-4)/12. Factor 0 + 1/7*u**3 + 2/7*u + l*u**2.
u*(u + 1)*(u + 2)/7
Let h(g) = -g**2 + 1. Let z(k) = 2 - 15 + 17*k - 10*k**2 + 3*k + 3. Let n(c) = -6*h(c) + z(c). Factor n(x).
-4*(x - 4)*(x - 1)
Factor -4/7*f**2 + 20/7*f - 4/7*f**3 - 12/7.
-4*(f - 1)**2*(f + 3)/7
Let n(y) = -2*y + 4. Let c be n(10). Let s be 0 + (c/12 - -2). Factor 0 + 2/3*g + s*g**2.
2*g*(g + 1)/3
Determine g so that -5/3*g**4 - g**3 + 0 - 4/3*g + 4*g**2 = 0.
-2, 0, 2/5, 1
Let u(b) = 2*b**3 - 10*b**2 + 10*b + 22. Let a(r) = r**3 - 4*r**2 + 4*r + 9. Let s(v) = 12*a(v) - 5*u(v). Factor s(q).
2*(q - 1)*(q + 1)**2
Let b(f) be the first derivative of -8 + 0*f + f**2 + 5/3*f**3 - 2/5*f**5 + 1/4*f**4. Factor b(q).
-q*(q - 2)*(q + 1)*(2*q + 1)
Suppose 2*a = -5*f + 139, -a + 23 = f - 3*a. Factor -v - 2*v - v + 2*v**2 - 25 + f.
2*(v - 1)**2
Let i(f) be the third derivative of f**9/1512 + f**8/240 + f**7/120 + f**6/180 - 2*f**3/3 - 15*f**2. Let u(b) be the first derivative of i(b). Factor u(p).
p**2*(p + 1)*(p + 2)*(2*p + 1)
Let 42*s**3 - 103*s**3 + 30*s**3 + 34*s**3 + 3*s**4 - 3*s**5 - 3*s**2 = 0. What is s?
-1, 0, 1
Let f(w) be t