6. Let d be t(8). Let n(k) = -10*k**2 + 2*k - 1. Let r(w) = w**2. Let y = 23 - 41. Let u(l) = d*n(l) + y*r(l). Factor u(i).
2*(i - 1)**2
Let z(q) be the second derivative of -q**4/18 + 121*q**3/27 - 40*q**2/9 - 402*q. Find i, given that z(i) = 0.
1/3, 40
Let u be (1 - (-3 + 4))*1. Let b(f) be the third derivative of u*f + f**2 - 1/210*f**5 - 1/21*f**3 + 0 - 1/42*f**4. Factor b(p).
-2*(p + 1)**2/7
Let p(d) be the second derivative of d**7/1260 + d**6/108 + 7*d**5/180 + d**4/12 + 2*d**3/3 + 17*d. Let l(h) be the second derivative of p(h). Factor l(x).
2*(x + 1)**2*(x + 3)/3
Let 60*j**2 + 35*j - 138*j**2 + 73*j**2 - 35*j**3 + 5*j**4 = 0. Calculate j.
-1, 0, 1, 7
Let j(k) = k**2 - 11*k - 10. Let y be j(12). Suppose y*z - 12 + 8 = 0. Suppose 1/3*w**3 - 8/3 - 2*w**z + 4*w = 0. Calculate w.
2
Factor 7*d - 4*d**2 + 1/3*d**3 - 10/3.
(d - 10)*(d - 1)**2/3
Let a = 12766/329 + 392/47. Let u = 48 - a. Factor u*b + 2/7*b**2 + 4/7.
2*(b + 1)*(b + 2)/7
Find d, given that -5*d**3 - 15 + 25*d + 8*d**2 - 15 + 2*d**2 = 0.
-2, 1, 3
Suppose 27*j - 2549*j**4 - 3*j + 274*j**2 + 698*j**3 + 72*j**5 + 2069*j**4 = 0. Calculate j.
-1/6, 0, 3, 4
Let h = 282 - 280. What is c in -1/3*c**h - 16/3 + 8/3*c = 0?
4
Suppose 7*z - 2*z - 20 = 0. Let n(t) = 2*t**2 - 7*t + 4. Let f be n(z). Factor -6*j**3 + f*j**3 + j**3.
3*j**3
Let i(o) = -3*o**4 - 2*o**3 + 6*o**2 + 2*o - 3. Let a(j) = -13*j**4 - 8*j**3 + 25*j**2 + 8*j - 12. Let d(r) = -4*a(r) + 18*i(r). Let d(f) = 0. What is f?
-3, -1, 1
Suppose -16 + 46 = 10*j. Suppose -2/7*x**j + 0*x - 2/7*x**2 + 0 = 0. Calculate x.
-1, 0
Let b(k) = 3*k**2 + 19*k - 11. Let q be b(-7). Let m be ((-29)/(-522))/(1/q - 0). Suppose 1/6*g - 1/6*g**3 + m*g**2 - 1/6 = 0. What is g?
-1, 1
Let f(c) be the third derivative of c**8/1680 + c**7/35 + 23*c**6/40 + 94*c**5/15 + 40*c**4 + 768*c**3/5 - 13*c**2 + 4. Factor f(r).
(r + 3)**2*(r + 8)**3/5
Let s be (-16172)/(-130) - ((-16)/10 - -1). Factor -12*n**3 - 6*n**2 + s*n + 24 - 129*n - 34*n**2.
-4*(n + 1)*(n + 3)*(3*n - 2)
Let m(t) be the third derivative of -t**5/60 + 7*t**4/24 - 5*t**3/3 - 20*t**2 + 2. What is l in m(l) = 0?
2, 5
Let z(b) = 93631*b**2 + 2453*b + 1. Let w(m) = -93630*m**2 - 2454*m + 2. Let i(p) = 5*w(p) + 6*z(p). Factor i(y).
4*(153*y + 2)**2
Let p(c) = -7*c**5 - 11*c**4 - 9*c**3 + 10*c**2 - 5*c. Let f(a) = 10*a**5 + 16*a**4 + 13*a**3 - 14*a**2 + 7*a. Let v(z) = -5*f(z) - 7*p(z). Factor v(x).
-x**3*(x + 1)*(x + 2)
Let o = -45 - -35. Let w = o - -10. Factor 0*c + 4/5*c**4 + 2/5*c**5 + 2/5*c**3 + 0 + w*c**2.
2*c**3*(c + 1)**2/5
Let d = -10 + 14. Suppose -g + 7 = d*a, -g + 3 = 8. Let -306*m**3 + 0*m**2 + m**4 + 2*m**2 + 303*m**a = 0. Calculate m.
0, 1, 2
Let n = -14 + 22. Suppose 0 = -2*m + 8 + n. Factor -2*o - 16*o**2 + m*o**2 - 4 + 10*o**2.
2*(o - 2)*(o + 1)
Suppose -33*k**3 - 19*k + 92*k**2 - 80*k - 2*k**4 + 35*k + 7*k**3 = 0. What is k?
-16, 0, 1, 2
Let w(v) = 6*v**3 + 5*v**2 - v - 2. Let c(f) = f**3 - f - 1. Let r(j) = 2*c(j) - w(j). Factor r(g).
-g*(g + 1)*(4*g + 1)
Solve 11 - 45*v**2 + 125*v + 27 + 5 - 13 = 0 for v.
-2/9, 3
Let z(r) be the third derivative of 0*r + 4/3*r**4 + 2/105*r**7 + 0 - 36*r**2 - 1/15*r**5 - 1/6*r**6 - 8/3*r**3 + 1/84*r**8. Factor z(y).
4*(y - 1)**3*(y + 2)**2
Let m(y) be the second derivative of -y**6/10 + 141*y**5/10 - 2209*y**4/4 - 234*y. Determine l so that m(l) = 0.
0, 47
Factor -4/3*k + 0 - 10/9*k**2 + 4/9*k**3 + 2/9*k**4.
2*k*(k - 2)*(k + 1)*(k + 3)/9
Let j(t) be the first derivative of -4*t - 3/4*t**5 - 1/2*t**4 - 5 + 0*t**2 + 0*t**3. Let y(v) be the first derivative of j(v). Factor y(q).
-3*q**2*(5*q + 2)
Let y(q) be the third derivative of 17*q**5/60 - 19*q**4/24 - q**3/3 - 5*q**2. Let u(k) = -k**2 + k + 1. Let x(h) = -20*u(h) - 5*y(h). Factor x(t).
-5*(t - 1)*(13*t - 2)
Let 1/4*p**3 + 13/4*p**2 + 55/4*p + 75/4 = 0. Calculate p.
-5, -3
Factor -15 + 6*d + 8 - d**2 + 31 - 2*d**2.
-3*(d - 4)*(d + 2)
Let t = 2330 + -2325. Let l(c) be the third derivative of -5*c**2 + 0 + 0*c**4 + 0*c**3 + 0*c - 1/60*c**6 + 1/10*c**t. Factor l(n).
-2*n**2*(n - 3)
Let t(c) = 40*c**2 - 130*c - 985. Let k(m) = 5*m**2 - 16*m - 123. Let w(s) = 25*k(s) - 3*t(s). Factor w(h).
5*(h - 6)*(h + 4)
Let d = -583 - -2918/5. Factor 0*h + 0*h**2 + 9/5*h**3 + d*h**5 + 12/5*h**4 + 0.
3*h**3*(h + 1)*(h + 3)/5
Suppose 4*k - 1 - 11 = 0. Factor 4*g**3 + 2*g**3 - 23*g**2 + 17*g**2 - k*g**3.
3*g**2*(g - 2)
Let h be (4/(-4))/1*-2. Solve 8*y**h + 14 - 16*y + 0 - 4*y**2 - 2 = 0.
1, 3
Solve 2365*y + 2681*y - 73*y**2 - 39*y**2 + 2*y**3 - 48778 - 62*y**2 = 0 for y.
29
Let h = -40 + 43. Factor -6*i**2 - 2*i**2 + 14*i**4 + i**4 + 4*i**h - 3*i**4.
4*i**2*(i + 1)*(3*i - 2)
Let m(d) be the second derivative of 28*d + 90*d**3 + 0 - 15/2*d**4 + 1/4*d**5 - 540*d**2. Factor m(t).
5*(t - 6)**3
Suppose -2*o = -2, 329*o - 333*o = -4*f + 8. Let 37/8*s**2 + 9/8*s**4 - 5/2*s - 15/4*s**f + 1/2 = 0. What is s?
2/3, 1
Suppose h + 5*m - 2 = 4*m, -2*h = 4*m - 8. Factor 0*u**2 + h*u**2 - 3 + 3*u**2.
3*(u - 1)*(u + 1)
Suppose -4*y + 87 = -3*z + 18, 2*y - 36 = 2*z. Factor -2 + s**3 - 4 + y*s**2 - 9*s**3 + 2*s**3 - 3*s.
-3*(s - 2)*(s - 1)*(2*s + 1)
Factor -63*k**2 - 164*k**3 - 172*k**3 + 348*k**3 - 153*k + 42.
3*(k - 7)*(k + 2)*(4*k - 1)
Let v = -2 + 5. Let c be (-4 - (-33)/v)*7. Factor -90*o**3 - 12*o**4 - 64*o**2 + 174*o**4 + c*o - 57*o.
2*o*(o - 1)*(9*o + 2)**2
Let w(q) be the third derivative of 1/180*q**5 + 0*q + 2/9*q**3 - 1/18*q**4 - 7*q**2 + 0. Let w(a) = 0. Calculate a.
2
Let -18*w**3 + 65*w**4 - 12*w**3 + 2*w**5 - 27*w**3 + 3*w**5 - 13*w**3 = 0. What is w?
-14, 0, 1
Let g(p) be the first derivative of 10 + 2/7*p**2 + 3/7*p + 1/21*p**3. Factor g(h).
(h + 1)*(h + 3)/7
Let w be 8 + 6/135*-177. Solve -w*r**2 + 0*r + 0 + 4/15*r**5 + 2/5*r**4 + 0*r**3 = 0 for r.
-1, 0, 1/2
Let n(a) be the first derivative of 2*a**3/39 + 8*a**2/13 + 30*a/13 - 729. Factor n(y).
2*(y + 3)*(y + 5)/13
Let w(n) be the second derivative of 8/21*n**3 + n + 4/7*n**2 + 1/70*n**5 + 5/42*n**4 + 0. Factor w(f).
2*(f + 1)*(f + 2)**2/7
Let x = -169/2 - -85. What is t in -x*t - 1/2*t**2 + 1 = 0?
-2, 1
Let z(x) be the second derivative of -x**5/30 + x**4/2 - 5*x**3/3 + 13*x**2 + 4*x. Let f(n) be the first derivative of z(n). Suppose f(h) = 0. Calculate h.
1, 5
Suppose -4*n + 30 = 2*f, -2*f + 0*n + n = -5. Factor -25*o + 3*o**3 + 6*o**2 - f*o**3 + 13*o**2 + 0*o**3 + 8.
-(o - 8)*(o - 1)*(2*o - 1)
Let b(o) be the third derivative of -o**5/120 - 19*o**4/48 + 5*o**3/3 + 208*o**2 + 2*o. Factor b(s).
-(s - 1)*(s + 20)/2
Factor 22*o + 43/2*o**2 + 9/2*o**3 - 6.
(o + 2)*(o + 3)*(9*o - 2)/2
Let u = -46 - -49. Suppose -u*r**2 - 7 - 47*r + 59*r - 5 = 0. Calculate r.
2
Find x, given that 1935*x + 2*x**4 - 2168*x**3 - 14*x**4 + 2537*x**3 + 675 - 2967*x**2 = 0.
-1/4, 1, 15
Suppose 4*r + 22 = 8*r + 2*j, -7 = -r - j. Let c(f) be the third derivative of 0 + 2/9*f**3 + 0*f - 1/12*f**r + 1/90*f**5 - f**2. Factor c(m).
2*(m - 2)*(m - 1)/3
What is d in 4 + 8/3*d**2 + 2/3*d**3 - 22/3*d = 0?
-6, 1
Suppose p + 16 = -4*a, 11*p = 9*p + 4*a + 28. Let f(x) be the first derivative of 0*x**2 - 4 + 0*x - 3/4*x**p + 1/2*x**3 + 3/10*x**5. Let f(v) = 0. What is v?
0, 1
Let v(d) = -10*d**3 - d**2 + 16*d + 7. Let j(b) = -3*b**3 - b**2 + b - 1. Let a(o) = -3*j(o) + v(o). Factor a(f).
-(f - 5)*(f + 1)*(f + 2)
Let j(l) be the first derivative of l**4/20 + 13*l**3/15 + 24*l**2/5 + 36*l/5 - 98. Factor j(i).
(i + 1)*(i + 6)**2/5
Factor -125 + 10*f - 1/5*f**2.
-(f - 25)**2/5
Let f = -282 - -282. Let d(k) be the third derivative of 0 - 1/300*k**6 + 0*k**4 + 1/150*k**5 + 2*k**2 + f*k + 0*k**3. Solve d(u) = 0 for u.
0, 1
Let v(t) = t + 6. Let i be v(-4). Suppose -1 - 106*c**2 + 93*c**3 + 156*c - 23 - 15*c**4 - 92*c**i = 0. What is c?
1/5, 2
Factor -16/3*g + 4/3 + 16/3*g**2.
4*(2*g - 1)**2/3
Let g = -33481/4 + 8371. What is d in 21/8*d + g - 21/8*d**3 - 3/4*d**2 = 0?
-1, -2/7, 1
Suppose -8*d**5 - 120*d**3 - 104*d**5 - 16*d**2 - 23*d**4 + 51*d**4 - 301*d**4 - 57*d**5 = 0. Calculate d.
-1, -4/13, 0
Suppose 0 = 7*v - 16 + 9. Let w be (5 + -9)/(-12)*v. Find n such that 2/3 - n + w*n**2 = 0.
1, 2
Let q(z) be the first derivative of -16*z**6/3 - 208*z**5/5 - 225*z**4/2 - 380*z**3/3 - 59*z**2 - 12*z + 45. Suppose q(y) = 0. What is y?
-3, -2, -1, -1/4
Let z(r) be the first derivative of 363*r**4/8 - 2343*r**3/2 