e (-6)/(-3)*(-990)/(-748). Let k = l + -133/153. Factor 16/9*s**3 - 4/9*s**4 + 0 - k*s + 4/9*s**2.
-4*s*(s - 4)*(s - 1)*(s + 1)/9
Let u(b) be the third derivative of -19*b**5/30 + 7*b**4/6 + 5*b**3/3 + 303*b**2 - 2. Factor u(g).
-2*(g - 1)*(19*g + 5)
Let q(t) be the second derivative of 0*t**2 - 3/40*t**5 - 3/8*t**4 + 4*t + 11 - 1/2*t**3. Factor q(x).
-3*x*(x + 1)*(x + 2)/2
Let k(w) be the third derivative of -w**7/210 - 109*w**6/60 - 647*w**5/60 - 215*w**4/12 + 2827*w**2. Factor k(p).
-p*(p + 1)*(p + 2)*(p + 215)
Let c be (-68 + 17)/((-2)/(-20)). Let z = -507 - c. Factor -8/5*p - 4/5*p**4 + 0 - 4*p**2 - 16/5*p**z.
-4*p*(p + 1)**2*(p + 2)/5
Let p(m) be the second derivative of -80*m + 1/24*m**4 + 0 + 7/2*m**2 - 5/4*m**3. Find y such that p(y) = 0.
1, 14
Let r(g) be the third derivative of -g**6/780 - g**5/78 - g**4/52 + 3*g**3/13 - 361*g**2 + 2. Factor r(y).
-2*(y - 1)*(y + 3)**2/13
Suppose -2*i - 3*x = 54, 3*i - 29 = -2*x - 120. Let g be (-6)/(8/(-3) - (-11)/i). Factor 6/13*k + 8/13 - 2/13*k**g.
-2*(k - 4)*(k + 1)/13
Suppose 3*s - 4*s + 22 = 4*m, -2*s = 4*m - 24. Solve 12*b**3 - 8*b**4 + 282*b**5 + 3*b**s + 29*b**2 + 16*b - 286*b**5 = 0.
-2, -1, 0, 2
Let u(q) = q**3 - 13*q**2 - 31*q + 20. Let c be u(15). Factor 265 - 265 + c*y**2 + 18*y + 32*y.
5*y*(y + 10)
Let z(n) be the first derivative of 4/7*n**2 - 1/42*n**4 + 4 + 8*n + 0*n**3. Let p(q) be the first derivative of z(q). Suppose p(f) = 0. Calculate f.
-2, 2
Let h be ((-8)/16)/((-1)/(-8)) - (206886/(-261))/58. Factor 8/3 - 11/3*i**3 + h*i**2 - 26/3*i - 1/3*i**4 + 1/3*i**5.
(i - 2)*(i - 1)**3*(i + 4)/3
Factor -736/3*w + 0 - 28/3*w**3 + 2584/3*w**2.
-4*w*(w - 92)*(7*w - 2)/3
Let f(u) be the first derivative of -15*u**4/4 - 57*u**3 + 264*u**2 - 252*u + 3820. Factor f(t).
-3*(t - 2)*(t + 14)*(5*t - 3)
Let o(y) be the third derivative of -5*y**8/336 + 5*y**7/42 + 3*y**6/8 - 53*y**5/12 - 5*y**4/3 + 40*y**3 + 12*y**2 + 8. Determine v, given that o(v) = 0.
-3, -1, 1, 4
Let m(i) = 8*i**2 - 9. Suppose -5*s - 4*k = -35, 2*s + 0*k + 9 = 3*k. Let x be m(s). What is a in 30*a**3 - x*a**3 + 38*a**3 + 5*a**4 - 5*a - 5*a**2 = 0?
-1, 0, 1
Let g(r) be the third derivative of r**6/40 - 17*r**5/20 - 14*r**4 + 1078*r**3 - 148*r**2. Suppose g(l) = 0. What is l?
-11, 14
Let c(p) be the first derivative of -2*p**5/85 + 6*p**4/17 - 30*p**3/17 + 54*p**2/17 - 5018. What is y in c(y) = 0?
0, 3, 6
Factor 3/11*s**4 - 84/11*s + 0 - 124/11*s**2 + 5/11*s**3.
s*(s - 6)*(s + 7)*(3*s + 2)/11
Suppose 5*n + 2*u = 370, 0 = -4*n + 4*u + 184 + 112. Suppose -4*o + 84 = 2*g - 0*g, 3*o - n = 4*g. Factor -31*k**2 + 22*k**2 - 19*k - o - 8 - 32*k.
-3*(k + 5)*(3*k + 2)
Let t(a) be the first derivative of 0*a - 29 - 1/600*a**6 - 1/60*a**4 - 18*a**2 + 0*a**3 - 1/100*a**5. Let j(g) be the second derivative of t(g). Factor j(p).
-p*(p + 1)*(p + 2)/5
Suppose 81*t - 319 + 169 = 174. Let h(l) be the first derivative of -3*l**3 - 6 + 3/2*l**2 + 6*l - 3/4*l**t + 3/5*l**5. Factor h(q).
3*(q - 2)*(q - 1)*(q + 1)**2
What is t in -2691 + 5394 + 3*t**2 - 22*t - 2696 = 0?
1/3, 7
Let w(c) be the second derivative of c + 0*c**2 - 29 + 0*c**3 + 0*c**5 + 1/12*c**4 - 1/120*c**6. Factor w(t).
-t**2*(t - 2)*(t + 2)/4
Let n = -64 + 60. Let v be (n - -1) + 0 + 5. Factor -728*b + 2*b**5 + 727*b - 2*b**4 + v*b**2 - b**5.
b*(b - 1)**3*(b + 1)
Let h be -16*1 - (73059/(-923) - -63). Factor 2/13*f**3 - h*f**2 - 2/13*f + 2/13.
2*(f - 1)**2*(f + 1)/13
Let v(x) be the first derivative of 4/9*x + 1/3*x**2 - 1/6*x**4 - 2/27*x**3 - 2/45*x**5 + 35. Solve v(y) = 0 for y.
-2, -1, 1
Suppose -10*p + 1111 - 301 = 0. Let c = -79 + p. Let 55*v**2 - 6*v**4 + 20*v**3 + v**4 - 80*v**c + 10*v = 0. Calculate v.
0, 1, 2
Determine d so that -2/7*d**3 - 217728*d + 36578304 + 432*d**2 = 0.
504
Let t = -48 + 56. Let b(w) = w - 6. Let a be b(t). Find q, given that 82*q**2 - 164*q**2 + 87*q**a - 60*q**3 + 5*q = 0.
-1/4, 0, 1/3
Let u(s) = 128*s**2 - 11825*s + 4380800. Let f(a) = 68*a**2 - 5912*a + 2190400. Let d(g) = -15*f(g) + 8*u(g). Factor d(q).
4*(q - 740)**2
Let c be 0/(12/4)*((-2142)/42)/51. Factor 0*q**2 + 20/3*q**3 + 0*q + c + 2/3*q**5 + 22/3*q**4.
2*q**3*(q + 1)*(q + 10)/3
Suppose 3*g + 17 = j, -j - g + 1 = 4. Factor -3*r - 7*r**3 + 2*r**4 + 3*r - r**3 + 2*r**j + 12*r.
2*r*(r - 3)*(r - 2)*(r + 1)
Let i(g) be the third derivative of g**7/210 - g**6/20 + 2*g**5/15 + g**4/4 - 3*g**3/2 - g**2 - 1207*g. Solve i(q) = 0 for q.
-1, 1, 3
Let f(a) = 13*a - 49. Let i be f(4). Factor -124*h - 18*h**2 + 15*h**i - 3*h**4 + 124*h.
-3*h**2*(h - 3)*(h - 2)
Determine x, given that -13105*x**3 + 722676637*x - 11445030*x**2 + 3338138120 + 187218060*x - 5*x**4 - 4236574677*x = 0.
-874, 1
Let a be (1/(-4*2))/(-25 - -27 - 3). Let l(w) be the second derivative of 0 + 11*w - a*w**4 - 1/40*w**5 + 3/4*w**3 - 5/4*w**2. Solve l(r) = 0 for r.
-5, 1
Suppose 0 = r - 3, 3*v - 18 = -4*r - 0*r. Suppose 46*l - 60*l + 56 = 0. Factor 0 - 13/5*h**3 - 1/5*h**5 + 6/5*h**l + 12/5*h**v - 4/5*h.
-h*(h - 2)**2*(h - 1)**2/5
Let p(i) be the first derivative of i**7/42 - i**6/6 + i**5/4 + 5*i**4/6 - 10*i**3/3 - 30*i**2 + 16. Let a(n) be the second derivative of p(n). Factor a(v).
5*(v - 2)**2*(v - 1)*(v + 1)
Suppose 467*n = -136 + 1070. Let l(q) be the first derivative of 4*q - 53/5*q**n + 6 - 22/15*q**3. Let l(s) = 0. What is s?
-5, 2/11
Suppose 0*s - 2*p = 3*s + 15, 0 = -3*s - 3*p - 15. Let t(d) = -5*d**2 - 7*d + 10. Let x(b) = -b**2. Let a(l) = s*t(l) + 30*x(l). What is k in a(k) = 0?
2, 5
Factor 2/11*t**3 + 312/11*t - 304/11 - 84/11*t**2.
2*(t - 38)*(t - 2)**2/11
Let o be (3 - (-16)/(-6))/(3/(-45)). Let v be (4/o)/(4/(-30)). What is x in 6*x**2 - 3*x + 2*x**5 - v*x**4 + 13*x**5 - 12*x**5 = 0?
-1, 0, 1
Let k(i) be the third derivative of -1/165*i**5 + 0*i**3 - 1 + 0*i + 0*i**4 + 1/660*i**6 - 7*i**2. Let k(b) = 0. What is b?
0, 2
Suppose -834*r = 8306 - 8306. Factor r - 3/7*t**4 - 3/7*t**3 + 48/7*t**2 + 48/7*t.
-3*t*(t - 4)*(t + 1)*(t + 4)/7
Suppose -18 = -5*x + 3*x. Let v be (-16)/4*(1 - x)/2. Factor 3*q**2 - 7*q**2 - v*q + 4*q.
-4*q*(q + 3)
Let o(s) be the third derivative of 3*s**8/70 - 109*s**7/175 + 69*s**6/25 - 26*s**5/25 - 72*s**4/5 - 64*s**3/5 + 1666*s**2. Determine l, given that o(l) = 0.
-2/3, -1/4, 2, 4
Factor -3/5*o**2 - 3/5*o**3 + 1/5*o**4 - 6/5 + 11/5*o.
(o - 3)*(o - 1)**2*(o + 2)/5
Let h(u) = 47*u**3 + 11*u**2 - 9*u - 1. Let y be h(1). Suppose g**3 + y*g - 2*g**2 + 13*g**2 - 68*g + 9*g**2 + 4*g**3 - 80 = 0. Calculate g.
-4, -2, 2
Let r(l) = -3*l**5 - 2*l**2 + 2*l + 2. Suppose 15 = -f - 4*d - 0*d, 3*d + 11 = -f. Let p(z) = z**5 + z**2 - z - 1. Let j(w) = f*r(w) + 2*p(w). Factor j(t).
-t**5
Let t(c) = 17*c**2 - 7*c - 7. Let k be t(-1). Let i be (k/(-510)*-18)/((-2)/(-54)). Factor i*a - 81/5 + 3/5*a**3 - 27/5*a**2.
3*(a - 3)**3/5
Let q(k) be the third derivative of 5*k**8/336 - 2*k**7/21 - 37*k**6/24 + 58*k**5/3 - 70*k**4 - 6793*k**2. Factor q(h).
5*h*(h - 4)**2*(h - 3)*(h + 7)
Let g = -158 + 160. Solve -36 - 45*p**g - 115*p + 5*p**4 + 15*p**3 + 5 - 29 = 0 for p.
-4, -1, 3
Let m = 368 - 364. Solve -1912*i - 7*i**2 + i**2 + m + 4*i**4 - 2*i**2 + 6*i**3 + 1906*i = 0 for i.
-2, -1, 1/2, 1
Let i(w) be the first derivative of -w**6/3 + 52*w**5/5 - 123*w**4/2 - 772*w**3/3 + 124*w**2 + 720*w + 6059. Find b, given that i(b) = 0.
-2, -1, 1, 10, 18
Let c(h) = -6*h**2 + 62*h + 8. Let i(a) = 4*a**2 - 59*a - 9. Let d(z) = -5*c(z) - 6*i(z). Factor d(o).
2*(o + 7)*(3*o + 1)
Let c(r) be the second derivative of 0*r**2 - 19*r + 0*r**3 - 3 - 4/45*r**4 + 1/105*r**7 + 2/15*r**5 - 14/225*r**6. Factor c(a).
2*a**2*(a - 2)**2*(3*a - 2)/15
Suppose 0 = -5*j + w + 14, 0 = 5*j - j + 2*w - 14. Let o be (1/45*(-495)/(-110))/(2/4). Solve -12/5*z**2 + o*z**j + 9*z - 10 = 0.
2, 5
Let u(t) be the third derivative of -t**7/315 - 133*t**6/90 - 16873*t**5/90 + 9044*t**4/3 - 18496*t**3 - 1925*t**2. Factor u(s).
-2*(s - 3)**2*(s + 136)**2/3
Let o(y) = y**2 - 6*y - 34. Let h be o(10). Find x, given that 0*x**2 - 72*x + 2*x**2 - h*x**2 + 7*x**2 + 68 + x**2 = 0.
1, 17
Let b be (-6)/(-105)*20/4*14. Factor 12*f**b - 12*f + f**3 + 4*f**3 + 97*f**2 - 113*f**2 - 9*f**4.
f*(f - 2)*(f + 3)*(3*f + 2)
Suppose 3580*r - 3337*r = 0. What is l in 26/5*l**3 - 4/5*l**2 + 0 + r*l = 0?
0, 2/13
Let q be 180/((-24)/(-4)) + -5. Factor 7*r**2 - 2*r**3 - q*r**2 + 24*r**2 - 4*