Let u(c) = 82*c**2 - 103*c - 110. Let l(s) = -5*i(s) + 24*u(s). Factor l(x).
3*(x + 1)*(x + 35)
Let v(o) = o**3 + 16*o**2 + 63*o + 89. Let j be v(-11). What is l in j - 2*l + 1/4*l**2 + 3/4*l**3 = 0?
-2, 2/3, 1
Let j(k) = 4*k**3 - 100*k**2 - 8*k + 1149. Let p(l) = 5*l**3 - 100*l**2 - 5*l + 1150. Let b(s) = -10*j(s) + 9*p(s). Factor b(u).
5*(u - 3)*(u + 4)*(u + 19)
Factor -144*w**2 - 130*w**2 - 185*w + 249*w**2 - 70.
-5*(w + 7)*(5*w + 2)
Let q(d) = -d**2 - 14*d - 32. Let t be q(-10). Suppose -2*f + 2040 = t*f. Suppose -f*k**2 - 378*k**3 - 108*k + 30 - 147*k**4 - 42 - 123*k**2 = 0. What is k?
-1, -2/7
Let o(t) = 65*t**3 - 61*t**2 + 65*t + 3. Let c(v) = -23*v**3 - v**2 + v - 1. Let p(f) = -3*c(f) - o(f). Factor p(g).
4*g*(g - 1)*(g + 17)
Let d(u) be the third derivative of -8*u**7/315 + 11*u**6/90 + 14*u**5/15 - 11*u**4/18 - 76*u**3/9 + 3*u**2 - 585. Find z such that d(z) = 0.
-2, -1, 1, 19/4
Suppose 4*w = 3*q + 149, -q = 5*w - 203 + 31. Let a = -8 - -11. Factor -18*z + 2*z**4 + w*z - 4*z**a - 13*z - 2.
2*(z - 1)**3*(z + 1)
Let 2160 + 708*t**2 - 3/2*t**4 - 81/2*t**3 - 2826*t = 0. Calculate t.
-40, 1, 6
Let f(a) be the second derivative of a**5/90 - 2*a**4/9 + 4*a**3/3 - 43*a**2 - 7*a. Let d(r) be the first derivative of f(r). Suppose d(i) = 0. What is i?
2, 6
Let b(u) be the second derivative of 5/3*u**3 + 0 + 211*u + 5/6*u**7 + 0*u**2 - 65/12*u**4 - 23/6*u**6 + 27/4*u**5. Factor b(g).
5*g*(g - 1)**3*(7*g - 2)
Factor 22*d + 5*d**4 - 15*d**2 - 602 + 3*d + 592 - 8*d**3 + 3*d**3.
5*(d - 1)**3*(d + 2)
Suppose 18*f - 11 = 295. Let o(s) = -s**4 - 5*s**2 - 6*s + 6. Let z(u) = -3*u**4 + u**3 - 14*u**2 - 18*u + 17. Let y(a) = f*o(a) - 6*z(a). Factor y(i).
i*(i - 6)*(i - 1)*(i + 1)
Suppose y**3 + 202 + 2*y**3 + 71*y + 95 - 74*y + 3 - 300*y**2 = 0. Calculate y.
-1, 1, 100
Let d(o) = 33*o**2 + 737*o - 888. Let x(a) = 30*a**2 + 741*a - 888. Let r(g) = 3*d(g) - 4*x(g). Solve r(w) = 0.
-37, 8/7
Let g(z) be the first derivative of z**4 + 52*z**3 - 848*z**2 + 1536*z - 9637. Factor g(k).
4*(k - 8)*(k - 1)*(k + 48)
Let m be (-30 + 31)/(10/4 + -2). Suppose -d**3 - d**2 - 6*d**m + 2*d**3 = 0. What is d?
0, 7
Factor 7/3*k**2 - 9 - 7*k + 1/3*k**3.
(k - 3)*(k + 1)*(k + 9)/3
Let w(y) be the second derivative of -y**6/45 - y**5/2 + 4*y**4/3 + 1216*y**3/9 + 1536*y**2 - y - 499. Find b, given that w(b) = 0.
-8, 9
Let p(s) be the second derivative of s**5/5 - 155*s**4/3 + 204*s**3 + 545*s + 1. Solve p(d) = 0.
0, 2, 153
Suppose -4*k - 2084 = 308. Let r = 598 + k. Let r + 1/2*v**3 + v**2 + 0*v = 0. What is v?
-2, 0
Let p(z) be the third derivative of z**8/840 - 47*z**7/525 + 29*z**6/100 + 139*z**5/150 - 44*z**4/15 - 12*z**3 - 225*z**2. Solve p(f) = 0 for f.
-1, 2, 45
Let w(m) be the first derivative of -3*m**5/5 + 915*m**4/4 + 1232*m**3 + 1854*m**2 + 4293. Find n such that w(n) = 0.
-2, 0, 309
Let c be 70/693 + -10 + (-1598)/(-153). Find i, given that c*i**2 + 10/11 + 2/11*i**3 - 18/11*i = 0.
-5, 1
Let h = -22796 + 22801. Factor 8/9 - 1/9*i**h + 38/9*i**2 - 28/9*i - 25/9*i**3 + 8/9*i**4.
-(i - 2)**3*(i - 1)**2/9
Let u(z) = -7*z + 163. Let t be u(23). Factor -2*b**4 - 2*b**3 + 3*b**2 + t*b + 18 + 3*b**2 - 22 + 0*b**3.
-2*(b - 1)**2*(b + 1)*(b + 2)
Let i(h) = 7*h**2 - 12*h - 24. Let n(u) = -8*u**2 + 10*u + 24. Let z be -3*(-10)/9*(-12)/8. Let t(o) = z*n(o) - 6*i(o). Determine d, given that t(d) = 0.
-1, 12
Suppose -5*n = 2*d + 15, d + n + 2*n = -9. Let q be (d - -5 - 1)/(1 - -1). Suppose -l + 3*l + 2*l - 2*l**2 - 4*l**3 - q*l**2 + 4 = 0. Calculate l.
-1, 1
Let o(b) = -b**4 - b**3 + b - 1. Let h(a) = 38*a**4 - 140*a**3 + 84*a**2 + 11*a - 7. Let d(y) = -2*h(y) + 14*o(y). What is w in d(w) = 0?
-2/45, 0, 1, 2
Find h, given that -49/2*h**3 - 3/2*h**4 + 0 - 325/6*h - 415/6*h**2 = 0.
-13, -5/3, 0
Suppose 123*q = 987 + 1473. Let y(c) be the first derivative of 7/6*c**5 + 10/3*c - 5/36*c**6 + 125/18*c**3 - 95/24*c**4 + q - 20/3*c**2. Solve y(i) = 0.
1, 2
Let j(n) be the first derivative of n**6 - 3*n**5/5 - 15*n**4/4 - 2*n**3 - 1276. Determine v, given that j(v) = 0.
-1, -1/2, 0, 2
Let -3/4*q**5 - 62*q - 199/4*q**3 + 11*q**4 + 16 + 171/2*q**2 = 0. Calculate q.
2/3, 1, 4, 8
Factor 0 + 1184/13*s**2 + 1408/13*s + 2/13*s**5 + 360/13*s**3 + 46/13*s**4.
2*s*(s + 4)**3*(s + 11)/13
Suppose -47401 + 43589 = -462*x - 995*x + 69038. Factor -429/2*f**3 + 0 - x*f + 115*f**4 - 230*f**2 - 25/2*f**5.
-f*(f - 5)**2*(5*f + 2)**2/2
Let x(i) be the second derivative of -i**5/100 - 7*i**4/30 - 3*i**3/10 + 113*i**2/2 + 17*i. Let j(q) be the first derivative of x(q). Factor j(v).
-(v + 9)*(3*v + 1)/5
Let a be -5*(-63)/90*(3 + -1). Let c(m) be the first derivative of 0*m + a + m**3 + 1/4*m**4 + m**2. Factor c(q).
q*(q + 1)*(q + 2)
Let i be 12/(-28) - 12/(-28). Let y(f) = 29*f + 29. Let a be y(-1). Suppose a*u - 5*u**2 + 5/2 + i*u**3 + 5/2*u**4 = 0. Calculate u.
-1, 1
Let v = -1522 + 1843. Let q = 325 - v. Factor 5/3*l**3 - 3*l**2 - 1/3*l**q - 2/3 + 7/3*l.
-(l - 2)*(l - 1)**3/3
Let v(m) = 7*m**2 - 16*m + 9. Let j(c) = 4*c**2 + 4*c + 4. Let p be j(-1). Let z(a) = 8*a**2 + 8 + 3*a - 15*a - 4*a. Let f(r) = p*v(r) - 3*z(r). Factor f(s).
4*(s - 3)*(s - 1)
Let q(d) be the first derivative of 166 + 1/16*d**4 - 1/3*d**3 + 1/2*d**2 + 0*d. Solve q(g) = 0 for g.
0, 2
Suppose 5*i = 4*r - 17, 10*r - 13*r - 5*i + 4 = 0. What is k in 10 + k**2 + 20*k**r + 33*k**2 + k**2 + 2*k**4 + 13*k**2 + 44*k + 4 = 0?
-7, -1
Let b(p) be the first derivative of p**6/12 - 247*p**5/10 + 10329*p**4/4 - 101817*p**3 + 2184813*p**2/4 - 1594323*p/2 - 431. Factor b(u).
(u - 81)**3*(u - 3)*(u - 1)/2
Let a be 3 + -15 + ((-3612)/1617)/((-36)/198). Determine m so that 2*m**3 + 18/7*m - a*m**4 - 30/7*m**2 + 0 = 0.
0, 1, 3
Let d be ((-2)/(-8))/((-123)/(-4100)*15). Let t(y) be the second derivative of 26/9*y**3 + 0 - 38*y - d*y**4 - 16/3*y**2. Factor t(c).
-4*(c - 1)*(5*c - 8)/3
Let w = 18649 - 37297/2. Let w*m**2 + 3 + 7/2*m = 0. What is m?
-6, -1
Let a(y) be the first derivative of 3*y**4/4 + 329*y**3 - 1983*y**2/2 + 993*y + 4273. Factor a(c).
3*(c - 1)**2*(c + 331)
Let i(v) be the second derivative of 0 + 0*v**2 + 0*v**3 - 5/4*v**4 - 185*v - 1/4*v**5 + 5/42*v**7 + 1/2*v**6. Suppose i(y) = 0. What is y?
-3, -1, 0, 1
Let f(b) be the third derivative of -1/780*b**6 + 0*b - 129*b**2 + 0*b**4 - 4/195*b**5 + 0*b**3 + 0. Factor f(h).
-2*h**2*(h + 8)/13
Let w(m) be the second derivative of m**4/9 + 396*m**3 + 3562*m**2/3 - 3885*m + 1. Factor w(f).
4*(f + 1)*(f + 1781)/3
Let b(o) be the first derivative of 1331*o**4/18 - 28556*o**3/3 + 459492*o**2 - 9858192*o + 2023. Determine y so that b(y) = 0.
354/11
Let j(g) = -3*g**2 - 40*g + 31. Let l be j(-14). Factor 0*c**2 - 9*c - 8*c - 6*c - 2*c**2 - c + 2*c**l.
2*c*(c - 4)*(c + 3)
Let f(l) = -8*l**3 + 12*l + 6. Let m be f(-1). Factor 54/7 - 87/7*p - 3/7*p**3 + 36/7*p**m.
-3*(p - 9)*(p - 2)*(p - 1)/7
Let z = -211279/4 + 52820. Factor -z*j**4 + 1/4*j**2 - 1/4*j**3 + 1/4*j + 0.
-j*(j - 1)*(j + 1)**2/4
Let p = 151/246 - 14/123. Factor -p*q**3 + 1/2*q**2 + 0 + 1/2*q - 1/2*q**4.
-q*(q - 1)*(q + 1)**2/2
Let f = 73533/220 - 3675/11. Let u(o) be the second derivative of -1 + 2*o**4 - 17/2*o**3 - f*o**5 + 14*o + 15*o**2. Factor u(a).
-3*(a - 5)*(a - 2)*(a - 1)
Let n(p) = -4*p**4 - 6*p**3 + 4*p**2 - 6*p. Let i(q) = 9*q**4 + 13*q**3 - 9*q**2 + 13*q. Let j(x) = -x. Let g be j(13). Let b(h) = g*n(h) - 6*i(h). Factor b(z).
-2*z**2*(z - 1)*(z + 1)
Let t(o) = -9*o - 4. Let w be t(-2). Factor -2*r**3 - w*r**2 + 8*r + 5*r**2 + 3*r**2.
-2*r*(r - 1)*(r + 4)
Let j(c) be the first derivative of -4*c**5/5 - 141*c**4 - 20708*c**3/3 - 29118*c**2 - 38088*c + 1726. Solve j(a) = 0 for a.
-69, -2, -1
Let 10*c**4 - 25*c**2 + 2*c + 6*c + 1945*c**3 - 1955*c**3 + 2*c**5 - 25*c**2 + 40 = 0. Calculate c.
-5, -2, -1, 1, 2
Suppose -19489*j + 19316*j = -346. Factor -17496*f - 2/9*f**4 - 24*f**3 - 118098 - 972*f**j.
-2*(f + 27)**4/9
Let x(o) be the third derivative of 17/30*o**4 + 2 - 1/75*o**5 + 15*o**2 + 0*o + 12/5*o**3. Find g such that x(g) = 0.
-1, 18
Let b(k) = -k**3 - 9*k**2 - 5*k - 32. Let s(d) = -d**3 - 5*d**2 + d - 16. Let t(q) = -3*b(q) + 5*s(q). Determine c so that t(c) = 0.
-2, -1, 4
Let p(n) be the third derivative of n**7/420 + 7*n**6/80 - 3*n**5/8 + 23*n**4/48 - 453*n**2 - 1. Factor p(j).
j*(j - 1)**2*(j + 23)/2
Let s = 120 + -116. Let