6. Let n(y) be the second derivative of 0*y**3 - 1/180*y**6 + 0*y**2 - 1/252*y**7 + 0*y**4 + 0*y**5 + i - 4*y. Factor n(g).
-g**4*(g + 1)/6
Let r(u) = u**2 - 66*u - 174. Let w(h) = 0*h**2 - 393 - 395*h + 5*h**2 - 652. Let j(d) = -35*r(d) + 6*w(d). Let j(s) = 0. What is s?
-6
Suppose x = -x + 3*h + 37, -5*x + 80 = -5*h. Let j = x + -9. Factor -146*m**j + 216*m + 78 + 434*m**2 + 128*m**3 - 24.
2*(4*m + 3)**3
Let n(d) be the third derivative of 169/270*d**6 + 0*d - 6*d**2 - 11/27*d**4 + 0 - 4/27*d**3 - 13/54*d**5. Factor n(g).
2*(2*g - 1)*(13*g + 2)**2/9
Let y(n) be the first derivative of -2*n**5/15 + n**4/9 + 32*n**3/27 + 14*n**2/9 + 2*n/3 + 306. Let y(j) = 0. What is j?
-1, -1/3, 3
Factor 3/2*l**4 - 45/2 - 15*l**2 + 6*l**3 - 42*l.
3*(l - 3)*(l + 1)**2*(l + 5)/2
Suppose 8*z - 1675*z**5 + 1674*z**5 - 12*z**2 - 9*z**4 + 2*z**3 + 12*z**4 = 0. What is z?
-2, 0, 1, 2
Suppose v - 5 = -6*x + 2*x, 3*x + 3 = -3*v. Let f(i) be the second derivative of 0*i**3 + 0 + 0*i**x + 1/50*i**5 - 6*i - 1/15*i**4. Factor f(l).
2*l**2*(l - 2)/5
Let k(a) be the third derivative of -3*a**7/175 + 43*a**6/300 - 31*a**5/75 + a**4/3 + 8*a**3/15 - a**2 + 131. Let k(o) = 0. What is o?
-2/9, 1, 2
Let u(d) be the third derivative of -d**8/6720 - d**7/840 - d**6/240 - 2*d**5/15 + 7*d**2. Let a(k) be the third derivative of u(k). Factor a(c).
-3*(c + 1)**2
Let s(t) be the third derivative of 1/672*t**8 - 1/126*t**7 + 0*t - 2*t**2 + 0*t**5 + 1/18*t**3 + 1/72*t**6 - 3 - 5/144*t**4. Factor s(a).
(a - 1)**4*(3*a + 2)/6
Let k(r) be the second derivative of r**4/66 + 16*r**3/33 + 63*r - 2. Factor k(n).
2*n*(n + 16)/11
Let s = 6558 + -6556. Factor 0 - 2/7*p + 2/7*p**s.
2*p*(p - 1)/7
Let l(y) = 17*y - 100. Let g be l(-25). Let i be 70/g - (-4)/30. Determine s so that -2/15*s**2 + 2/15*s**3 + i + 0*s = 0.
0, 1
Factor -235/6*w**3 + 16/3*w - 1/6*w**2 - 2/3 - 121/6*w**5 - 319/6*w**4.
-(w + 1)**3*(11*w - 2)**2/6
Let s(h) = -30*h**2 - 8*h - 8. Let b(l) = -19*l**2 - 6*l - 5. Let n(j) = 8*b(j) - 5*s(j). Factor n(r).
-2*r*(r + 4)
Let m(c) be the third derivative of -c**5/15 - c**4/3 + 10*c**3 - 3*c**2 + 24. Suppose m(s) = 0. Calculate s.
-5, 3
Find x such that -2/19*x**5 + 64/19*x**2 + 24/19 - 8/19*x**4 + 12/19*x**3 + 70/19*x = 0.
-4, -1, 3
Let v = -2/49 + 53/98. Let p(n) = -n**2 - 3*n - 2. Let u be p(-2). Factor v*s + 1/4*s**2 + u.
s*(s + 2)/4
Let g = -92 + 99. Suppose 2*s - 3*s - g = -2*f, -f + 2 = -2*s. Factor -4/7*d**3 + 2/7*d**f + 4/7*d + 0*d**2 - 2/7.
2*(d - 1)**3*(d + 1)/7
Let f(u) be the third derivative of u**6/480 - 3*u**5/40 + 9*u**4/8 - 5*u**3/3 + 17*u**2. Let n(c) be the first derivative of f(c). Factor n(q).
3*(q - 6)**2/4
Suppose -359 = -r + 117. Let b = 3348/7 - r. Solve -b*p - 32/7 - 2/7*p**2 = 0 for p.
-4
Let n(g) be the third derivative of g**5/450 + g**4/18 + g**3/5 - 280*g**2. Factor n(z).
2*(z + 1)*(z + 9)/15
Let m = -13100/7 + 13106/7. Suppose -2/21*a**4 - 58/21*a**2 - 26/7*a - 12/7 - m*a**3 = 0. What is a?
-3, -2, -1
Suppose -3*m = -5*p + 5, -3*m + 2*p - 2 = -7*m. Let q(w) be the third derivative of 8*w**2 - 1/40*w**4 + 0*w + 0 - 1/75*w**5 - 1/600*w**6 + m*w**3. Factor q(o).
-o*(o + 1)*(o + 3)/5
Factor -14*h**3 + 10*h**2 + 27*h**3 - 18*h**3 + 15*h.
-5*h*(h - 3)*(h + 1)
Let f be ((-86)/(-12900))/((-8)/(-10)). Let o(s) be the second derivative of f*s**5 + 0*s**2 + 0 - s + 0*s**4 - 1/36*s**3. Factor o(h).
h*(h - 1)*(h + 1)/6
Let t be 56/42*(-12)/24 - (-22)/24. Solve 1/2*d**3 + 0 - 1/4*d**2 - t*d**4 + 0*d = 0 for d.
0, 1
Let l(k) be the second derivative of 1/70*k**6 - 33/70*k**5 - 35*k**3 + 0 + 147/2*k**2 + 6*k**4 + 27*k. Factor l(p).
3*(p - 7)**3*(p - 1)/7
Suppose 45*c = 39*c. Let f(b) be the third derivative of 1/12*b**3 + 9*b**2 + 0*b + c - 1/120*b**5 + 1/240*b**6 - 1/48*b**4. What is n in f(n) = 0?
-1, 1
Let y(n) be the third derivative of n**8/3360 - n**7/1260 - n**4/6 + 27*n**2. Let j(t) be the second derivative of y(t). Factor j(p).
2*p**2*(p - 1)
Let r(v) be the third derivative of v**7/420 - v**5/20 - v**4/6 - 4*v**3/3 - 7*v**2. Let m(k) be the first derivative of r(k). Let m(q) = 0. What is q?
-1, 2
Suppose 148*v = 143*v + 45, 4*v = -5*f + 46. Let 2/3*t**4 + 14/3*t + 10/3*t**3 + 6*t**f + 4/3 = 0. What is t?
-2, -1
Suppose 13*t + 8*t - 2*t = -18*t. Factor 0*s + 3*s**4 + 0*s**2 + 0 + 3/2*s**5 + t*s**3.
3*s**4*(s + 2)/2
Let x be (3 - 4)/(-5) + (-57)/(-15). Factor 2*f**2 - 35*f**4 + 0*f**2 + 34*f**x - 1.
-(f - 1)**2*(f + 1)**2
Let q(o) be the second derivative of -o**5/20 - 3*o**4/8 - o**3 + 8*o**2 + 14*o. Let m(i) be the first derivative of q(i). Find r such that m(r) = 0.
-2, -1
Let o(r) = r**3 + 20*r**2 + 18*r. Let i be o(-19). Let a = 21 - i. Factor 0*j + 2/3*j**4 + 0*j**a + 2/3*j**3 + 0.
2*j**3*(j + 1)/3
Let u(j) be the third derivative of -3*j**2 + 0*j**3 - 7/180*j**6 + 0 + 0*j + 1/9*j**4 + 2/15*j**5. Factor u(n).
-2*n*(n - 2)*(7*n + 2)/3
Let f(d) = d. Let b be f(7). Suppose 2*q + 3*a = 6*q + b, 2*a - 2 = 4*q. Let 1/4*t - 1/4*t**q + 3/2 = 0. What is t?
-2, 3
Let r(w) be the second derivative of 7*w**6/135 + 2*w**5/45 - 49*w**4/54 + 14*w**3/27 + 8*w**2/3 + 14*w - 15. Find c, given that r(c) = 0.
-3, -4/7, 1, 2
Let s(o) be the second derivative of 11*o**4/4 - 35*o**3/2 + 9*o**2 + 3*o - 1. Factor s(m).
3*(m - 3)*(11*m - 2)
Let r(a) = a**2 + a. Let x be r(0). Suppose -5*y + 6 + 4 = x. Solve y*z**3 + 3*z**4 + z**3 - 5*z**5 - z**3 = 0 for z.
-2/5, 0, 1
Let i(v) = 13*v**2 + v. Let g be i(-1). Let d(q) = -q**3 + 12*q**2 - q + 16. Let c be d(g). Suppose 3*m + 3*m - c*m**2 + 2*m = 0. What is m?
0, 2
Suppose 0*a = -a + 3. Suppose 3*x - h = -4*h + 18, 3*x - 2*h = a. Factor t - x*t**2 - 3*t**2 + 4*t**2 - 3*t.
-2*t*(t + 1)
Let i(d) = d**3 + 39*d**2 + 33*d - 187. Let s be i(-38). Factor 1/2*t**4 - 4 + s*t**2 - 5/2*t**3 + 2*t.
(t - 2)**3*(t + 1)/2
Let l be (3 + -1)/((-2)/(-68)). Suppose w + l = 5*w. Solve 4*t - t + 14*t**3 - w*t**3 = 0.
-1, 0, 1
Let 22/9*h - 2/9*h**5 - 4/3*h**4 + 4/3 - 20/9*h**3 + 0*h**2 = 0. Calculate h.
-3, -2, -1, 1
Let f be 1*((3 - 2) + 3/(-3)). Let s(n) be the third derivative of f - 1/3*n**4 + 0*n + 0*n**3 + 6*n**2 + 2/5*n**5 - 1/12*n**6. Factor s(a).
-2*a*(a - 2)*(5*a - 2)
Let b(o) be the third derivative of -o**6/540 + 2*o**5/45 + o**4/4 - 18*o**3 - 125*o**2. Factor b(j).
-2*(j - 9)**2*(j + 6)/9
Suppose -2 = -2*i, -b + 3*i = 4*b - 447. Let m = -88 + b. Let 0 + 1/6*n**m + 0*n = 0. What is n?
0
Let u = -8650 - -173147/20. Let c(q) be the second derivative of 0*q**2 + 2*q**3 + 7*q**4 + 0 + 5*q + u*q**5. Factor c(b).
3*b*(7*b + 2)**2
Let d(c) = -29*c + 667. Let h be d(23). Determine l, given that 1/2*l**5 - 1/2*l - l**2 + h + 0*l**3 + l**4 = 0.
-1, 0, 1
Let b(a) = -7*a**2 + 32*a - 40. Let y(x) be the second derivative of -x**4/12 + x**3/6 + 12*x. Let s(f) = b(f) - 2*y(f). What is c in s(c) = 0?
2, 4
Let a(r) = 8*r - 37. Let s be a(5). Solve 5*p**3 - 15*p**s - 4*p**4 + 0*p**3 + 14*p**2 = 0.
-7/2, 0, 1
Let b(q) be the third derivative of q**8/672 - q**7/420 - q**6/15 + 2*q**5/15 - 6*q**2 + 8. Factor b(h).
h**2*(h - 4)*(h - 1)*(h + 4)/2
Let w = 4/49130635 + -56588667037/20192690985. Let f = -1/411 - w. Determine m so that f*m - 4/5 - 2*m**2 = 0.
2/5, 1
Let v(y) = -8*y**3 + 6*y**2 - 4*y - 6. Let b(u) = 9*u**3 - 9*u**2 + 3*u + 7. Let z(o) = -6*b(o) - 7*v(o). Factor z(a).
2*a*(a + 1)*(a + 5)
Let y(n) be the third derivative of -n**7/210 + n**6/40 - 92*n**2. Factor y(w).
-w**3*(w - 3)
Let s(c) be the first derivative of c**6/120 + c**5/10 - 5*c**4/8 + 16*c**3/3 - 15. Let r(h) be the third derivative of s(h). Factor r(a).
3*(a - 1)*(a + 5)
Let y(x) = -x**2 - 1. Let w(p) be the third derivative of -p**5/12 - 2*p**3/3 + 16*p**2. Let a(k) = w(k) - 4*y(k). Determine n so that a(n) = 0.
0
Suppose 42*z**4 + 3*z**4 - 192*z**2 + 57*z + 89*z**3 + 148*z**3 - 21*z = 0. What is z?
-6, 0, 1/3, 2/5
Let r = -6536/5 + 45757/35. What is d in 16/7 - d**2 - 8/7*d - r*d**3 = 0?
-4, 1
Factor -2/3*c**4 + 1/3*c**5 + 4/3*c**2 + 13/3*c + 2 - 2*c**3.
(c - 3)*(c - 2)*(c + 1)**3/3
Let a(l) = -10*l**3 + 7*l**2 + 10*l - 1. Let v(h) = h**2 + 1. Let g = -6 + 0. Let j(n) = -n - 11. Let c be j(-13). Let r(z) = c*a(z) + g*v(z). Factor r(w).
-4*(w - 1)*(w + 1)*(5*w - 2)
Let a be (10/(-4) - 0)*2 - 2093/(-322). Factor -a*c + 0 + c**2 + 1/2*c**3.
c*(c - 1)*(c + 3)/2
Let r = 14988 + -29967/2. Factor -