6*o + 4. Let v(a) = -a**3 - 8*a**2 + 5*a + 6. Let i(r) = g*u(r) + 2*v(r). Factor i(z).
-2*z*(z - 2)**2
Suppose 0 = 110*s + 851303 - 851523. Factor -24/7 + 2/7*w**3 - 2*w**s + 32/7*w.
2*(w - 3)*(w - 2)**2/7
Let n = 1208933/7 - 172415. Factor -8788/7 - 156/7*m**2 + 4/7*m**3 + n*m.
4*(m - 13)**3/7
Let b(o) = 1. Let q(g) = -g**2 - 8*g - 3. Let l(x) = -2*b(x) - q(x). Let h be l(-14). Factor -9*u - 50*u**2 - 30*u**4 - h*u**3 + 25*u**3 - 5*u**5 - 6*u.
-5*u*(u + 1)**3*(u + 3)
Factor -1135/6*q + 77/2*q**2 - 1/6*q**4 + 275 - 3/2*q**3.
-(q - 5)**2*(q - 3)*(q + 22)/6
Let o be 10/(-4) - 5691/14. Let n = o + 3683/9. Find a, given that -4/9*a + n*a**2 + 0 + 2/9*a**3 = 0.
-2, 0, 1
Let t(r) be the second derivative of -r**4/6 + 4*r**3 + 85*r**2 + 3350*r. What is x in t(x) = 0?
-5, 17
Let l(o) = 5*o**3 - o**2 - 2*o. Let c be l(3). Factor 225*s**3 + c + 84*s - 685*s**2 + 83*s - 266*s + 89*s.
5*(s - 3)*(5*s + 2)*(9*s - 4)
Let m(d) be the second derivative of d**5/20 - 7*d**4/12 + 3*d**2 + 5*d. Let f be m(7). Let 1 + 1 - 5 - 5*b**2 - f*b + 2*b**2 = 0. Calculate b.
-1
Let g(l) be the first derivative of -2*l**3/15 + 13*l**2/5 - 24*l/5 + 531. Factor g(u).
-2*(u - 12)*(u - 1)/5
Let f(w) = -w - 6. Let r be f(6). Let q be 4 + ((-18)/12)/((-9)/r). Factor 6*n**4 + 0*n**q + 2 + 4*n - 10*n**2 - 2 - 8*n**3.
2*n*(n - 2)*(n + 1)*(3*n - 1)
Let k(g) = 156*g**3 - 1239*g**2 - 306*g + 6. Let b(o) = 24*o**3 + o**2 + o + 1. Let c(a) = -6*b(a) + k(a). Factor c(n).
3*n*(n - 104)*(4*n + 1)
Let x(r) be the first derivative of 3*r**5/5 + 6*r**4 + 4*r**3 - 72*r**2 - 2768. Factor x(p).
3*p*(p - 2)*(p + 4)*(p + 6)
Let i(j) be the first derivative of -2*j**3/3 + 18*j**2 - 64*j - 510. Suppose i(v) = 0. What is v?
2, 16
Let w be 22/8*(0 + 2) + -4. Suppose 2*r = 2*i + 2, 5*r = 3*i - 120 + 127. Suppose 4*t**r - 23/2*t - w = 0. Calculate t.
-1/8, 3
Let r(i) be the third derivative of 1313*i**5/30 + i**4/6 + 3*i**2 + 2574*i. Factor r(x).
2*x*(1313*x + 2)
Let c be (-7)/13*4914464/(-6608). Factor c*p - 536/13*p**2 + 14/13*p**3 - 1444/13.
2*(p - 19)**2*(7*p - 2)/13
Let u(l) = -l + 93. Let z be u(-2). Let f = -6 + 8. Solve -z*x - 7*x**2 - 30 + 66*x**2 - 24*x**f = 0.
-2/7, 3
Suppose 810 = 261*u - 251*u. Let q be u/270*(-168)/(-9). Factor q*y - 32/5 + 4/5*y**2.
4*(y - 1)*(y + 8)/5
Suppose -60*c = 3*c - 126. Let 0 + 1/3*d**c - 2*d = 0. Calculate d.
0, 6
Let t be 27/((-2970)/2222) + 21. Factor 4/5*j**4 - 1/5*j**5 + 0*j**2 + 0 - t*j**3 + 0*j.
-j**3*(j - 2)**2/5
Let a = -3952 + 3977. Let v(s) be the first derivative of -147*s**2 - a - 1/2*s**4 + 686*s + 14*s**3. Factor v(g).
-2*(g - 7)**3
Suppose 0 = -1356*x + 1345*x + 22. Let h(m) be the second derivative of 3/80*m**5 - 3/8*m**x - 25*m + 0 - 3/16*m**4 + 3/8*m**3. Factor h(f).
3*(f - 1)**3/4
Let d = -784011/7 + 112011. Factor 130/7*n - 2/7*n**3 + d + 62/7*n**2.
-2*(n - 33)*(n + 1)**2/7
Suppose -60 = -p - 60. Let l be (120/(-45))/((-4)/6). Factor 0*d + p + 0*d**2 + 0*d**3 + 2/7*d**l + 2/7*d**5.
2*d**4*(d + 1)/7
Let m(c) = 11*c**3 + 6*c**2 + 11*c + 16. Let j(k) = -9*k**3 - 5*k**2 - 8*k - 12. Let t(n) = 5*j(n) + 4*m(n). Factor t(y).
-(y - 2)*(y + 1)*(y + 2)
Let n(x) = -x**3 - 2*x**2 - x - 8. Let b be n(-4). Let w be (-3)/2*(-120)/(-27)*-3. Factor b*h**4 - 50 + w*h + 109 - 51 - 36*h**2 - 20*h**3.
4*(h - 1)**2*(h + 1)*(7*h + 2)
Suppose 212*h - 578 - 330 + 272 = 0. Factor 2/13 - 2/13*q**2 + 2/13*q**h - 2/13*q.
2*(q - 1)**2*(q + 1)/13
What is g in 5594*g - 2343*g + 6389*g - 11616200 + 157*g**2 - 318*g**2 + 159*g**2 = 0?
2410
Let w = 220760 - 220758. Factor 0*j - 2/11*j**3 + 0 - 2/11*j**w.
-2*j**2*(j + 1)/11
Suppose -14/3*l**4 + 410/9*l**2 - 88*l - 968/9 + 190/9*l**3 + 2/9*l**5 = 0. Calculate l.
-2, -1, 2, 11
Find t such that 5/2*t**4 - 8 + 1/2*t**5 + 11*t + 11/2*t**2 - 23/2*t**3 = 0.
-8, -1, 1, 2
Suppose -2*f + 6*f + 3*c = 72, -2*c = 4*f - 72. Let j be (-1 + 11)/((-5)/((-15)/2)). Factor j*x**4 - f*x**4 + 4*x**3 - 15*x**2 + x**3 + 18*x**4 - 5*x.
5*x*(x - 1)*(x + 1)*(3*x + 1)
Let l be (-2 + 5)*(-22)/(-22). Let b(u) be the first derivative of -3/4*u**4 + 3/2*u**2 - 9*u + l*u**3 + 12. Factor b(n).
-3*(n - 3)*(n - 1)*(n + 1)
Let w(q) = -18*q**3 - 165*q**2 + 666*q - 618. Let c(x) = x**3 + x**2 - 2*x - 2. Let d(z) = -15*c(z) - w(z). Solve d(o) = 0 for o.
-54, 2
Suppose 0 = -3*w - 11 + 38. Solve 111*p**4 - 12*p**3 + 111*p**4 - 225*p**4 + 24 + 42*p + w*p**2 = 0 for p.
-4, -1, 2
Let g(s) be the first derivative of s**3/7 - 147*s**2/2 + 1026*s/7 - 1706. Find i, given that g(i) = 0.
1, 342
Suppose 3*q + a = 848, 1380 = 5*q - a - 4*a. Suppose 0 = 6*b - 5*b - q. Factor -4*t**3 + 281 + 4*t**2 - b + 8*t.
-4*t*(t - 2)*(t + 1)
Let i(h) be the third derivative of -h**5/15 + 17*h**4/3 - 62*h**3 + 962*h**2 + 2*h. What is n in i(n) = 0?
3, 31
Let v(s) be the second derivative of -s**7/294 + 13*s**6/210 + 33*s**5/140 - 37*s**4/84 - 58*s**3/21 - 30*s**2/7 - 2772*s. Find w such that v(w) = 0.
-2, -1, 2, 15
Let x = 130 - 84. Let x*m + 2*m**2 - 91*m + 45*m = 0. What is m?
0
Let r(s) be the third derivative of -s**5/140 + 2*s**4/7 - 55*s**3/14 + 236*s**2 + 2. Factor r(x).
-3*(x - 11)*(x - 5)/7
Suppose -23*c = -19*c - 4. Let z(o) = 0 + 0*o**2 - 1 + 4*o**2 - 3*o**2 + o. Let p(t) = 5*t**3 + 10*t**2 + 5*t - 5. Let d(u) = c*p(u) - 5*z(u). Factor d(g).
5*g**2*(g + 1)
Suppose -1172 + 1388 = 108*z. Suppose 0 + 2/5*r**z + 18/5*r = 0. Calculate r.
-9, 0
Suppose 1627*z = -1136*z + 5526. Suppose 2/5*w**3 + 0*w + 2/5*w**4 - 12/5*w**z + 0 = 0. Calculate w.
-3, 0, 2
Let r = 487 - 496. Let k be (-2*(-1)/(-4))/(6/r). Determine y so that -3/4 + 3/4*y - 3/2*y**3 + 3/2*y**2 - k*y**4 + 3/4*y**5 = 0.
-1, 1
Let c = 60387/2 - 30191. Factor c*r**3 + 0 - 3*r**2 + 1/2*r.
r*(r - 1)*(5*r - 1)/2
Suppose 0 = -h - 5, 18 = 2*i - 2*h + 2. Suppose -i*q - 3 = -15. What is y in 0*y**4 - y**4 - 6*y**2 - 2*y**q + 9*y**2 = 0?
-1, 0, 1
Let g be (-3988)/(-24) - (-3 - 76/(-24)). Determine n, given that 5 + n**2 - 5 - 20 - 147*n + g*n = 0.
-20, 1
Let f(w) = 2*w**5 - 140*w**4 - 992*w**3 - 2692*w**2 - 3024*w - 1218. Let j(p) = p**4 - 18*p**3 - 2*p**2 + 1. Let c(l) = -f(l) - 2*j(l). Solve c(t) = 0.
-2, -1, 76
Factor -2/9*o**2 - 960*o - 1036800.
-2*(o + 2160)**2/9
Let d be 2/(-3) - (-102)/(-1512)*-3. Let r = 29/28 - d. Factor -15/2*o - 9/2*o**3 - r - 21/2*o**2.
-3*(o + 1)**2*(3*o + 1)/2
Let m(t) be the third derivative of -t**7/5460 + 17*t**6/2340 + 29*t**3/6 + 51*t**2. Let s(r) be the first derivative of m(r). Find h such that s(h) = 0.
0, 17
Find i such that -241*i**5 - 16*i**2 + 242*i**5 + 38*i**4 - 16*i**3 - 37*i**4 = 0.
-4, -1, 0, 4
Let y(h) = -27 + 59 - 2*h - 24. Let q be y(7). Let j(w) = 3*w**2 + 11*w + 8. Let b(t) = 2*t**2 + 6*t + 4. Let n(d) = q*j(d) + 11*b(d). Factor n(x).
4*(x - 1)*(x + 1)
Let v be (-400)/112 + (-4)/(-7). Let h be 96/14 - v/21. Suppose h*r**3 - 12*r**2 + 10 + 3*r**3 - r**4 - 8*r + 6 - r**4 = 0. Calculate r.
-1, 2
Let c be ((-1677)/297 - ((-24)/(-66))/(-4))*-3. Determine z so that -c*z**3 + 2*z**4 + 142/3*z**2 + 12 - 50*z = 0.
1/3, 2, 3
Let k be ((-1782)/(-24))/9 + (-2)/8. Factor -u - 3*u**3 - k*u + 5981*u**2 - 5993*u**2.
-3*u*(u + 1)*(u + 3)
Factor 53802*k**2 + 128*k**4 - 26832*k**2 - 26838*k**2 + 2*k**5 - 262*k**3.
2*k**2*(k - 1)**2*(k + 66)
Find a such that 408/5*a - 2/5*a**3 - 416/5 - 96/5*a**2 = 0.
-52, 2
Determine i, given that 4625 + 4610 - 14*i**2 + 0*i**3 - 9205 + i**3 - 17*i = 0.
-2, 1, 15
Let b(o) be the third derivative of -1/5*o**5 + 0 - 9/2*o**3 + 21/16*o**4 + 68*o**2 + 0*o + 1/80*o**6. Factor b(d).
3*(d - 3)**2*(d - 2)/2
Let m = 901 + -911. Let a be 11 - 20 - m - (-1)/2. Factor 9/4*h + 3/4*h**2 + a.
3*(h + 1)*(h + 2)/4
Determine v so that 0 + 1808*v**2 + 452/7*v**4 - 12993/7*v**3 - 448*v - 4/7*v**5 = 0.
0, 1/2, 56
Suppose 603*j - 1946*j + 2686 = 0. Factor -2/3*k**3 + 20/3*k + j*k**2 + 0.
-2*k*(k - 5)*(k + 2)/3
Suppose -p - 3*q = -11, -2*q + 28 = 4*p + 2*q. Let l = -130 + 151. Factor -10*n**p + 4*n**4 + l*n**5 + 0*n**3 - 9*n**5 + 2*n**3.
2*n**3*(n + 1)**2
Factor 0 + 26/7*n**2 + 4/7*n**3 + 12/7*n.
2*n*(n + 6)*(2*n + 1)/7
Let -946/9*k**2 - 242/9*k**3 - 1174/9*k - 2/9*k**4 - 52 = 0. What is k?
-117, -2, -1
Let j(w) = -w**3 + 16*w**2 + 42*w - 14. Let k be j(17). Let z = k - 2031/5. Determine g so that z*g**2 - 8/5*g**3 - 32/5*g + 16/5 + 1/5*g**4 = 0.
2
Let x(k) = 7*k**2 + 2*k - 4. Let t(i) = -43*i