**3.
5*(m - 2)**2*(m + 1)*(m + 2)
Let l(w) be the first derivative of -w**3/9 - 565*w**2/3 - 319225*w/3 + 1658. Factor l(b).
-(b + 565)**2/3
Let o(k) be the first derivative of 3/5*k**5 + 24*k - 30*k**2 + 18*k**3 + 127 - 21/4*k**4. Factor o(y).
3*(y - 2)**3*(y - 1)
Let a = -13865/3 - -4622. Let h(m) be the second derivative of 0*m**2 - 1/12*m**4 + 0 - a*m**3 + 6*m. Factor h(f).
-f*(f + 2)
Let l be (1725/90)/23*20/(600/18). Factor -l*r**3 + 0 - 3/2*r**4 + 1/2*r**5 + 3/2*r**2 + 0*r.
r**2*(r - 3)*(r - 1)*(r + 1)/2
Factor -133 + 76*c - 164*c - 14*c**3 + 54*c**2 + 76*c + 53.
-2*(c - 2)*(c + 1)*(7*c - 20)
Suppose -48 + 30 = -9*k. Suppose 2*d + 8*d**k - 7*d + 2*d**3 + 3*d + 2 - 10 = 0. What is d?
-4, -1, 1
Let j(d) = -d**2 + 7*d - 2. Let r(x) = 8*x**2 - 51*x + 15. Let z(s) = 5*j(s) + r(s). Factor z(n).
(n - 5)*(3*n - 1)
Suppose 4*a + 0*a + 3*q - 17 = 0, -5*q + 25 = 5*a. Let c be 3/a + 63*(-3)/(-18). Factor -21/2*h**3 + 0 - c*h**4 - 3*h**2 - 9/2*h**5 + 0*h.
-3*h**2*(h + 1)**2*(3*h + 2)/2
Let f(x) be the first derivative of 3*x**4/4 - 416*x**3/3 - 559*x**2/2 - 140*x - 11107. Suppose f(b) = 0. Calculate b.
-1, -1/3, 140
Let j = 2175934/75 - 29012. Let z = -4/75 + j. Factor z*h**2 - 4/5 - 2/5*h.
2*(h - 2)*(h + 1)/5
Let d(b) be the third derivative of b**6/30 - 293*b**5/15 - 592*b**4/3 - 792*b**3 - 770*b**2. Suppose d(r) = 0. What is r?
-2, 297
Let n(g) be the third derivative of -7/6*g**5 + 4*g + 0 + 2*g**4 + 16*g**2 - 4/3*g**3. Factor n(q).
-2*(5*q - 2)*(7*q - 2)
Let c(o) be the first derivative of o**4 + 4*o**3/3 - 108*o**2 - 576*o + 4046. Find p, given that c(p) = 0.
-6, -3, 8
Suppose -41/3 - 4/3*v**3 + 41/3*v**2 + 4/3*v = 0. What is v?
-1, 1, 41/4
Let -282*d - 1104 - 3/2*d**2 = 0. Calculate d.
-184, -4
Let y(g) be the second derivative of 15/2*g**3 - 5/4*g**4 - 6*g**2 + 0 - 2*g + 1/12*g**5. Let k(u) be the first derivative of y(u). Factor k(z).
5*(z - 3)**2
Let v(u) = -u**4 - u**2 + 19*u - 12. Let w(p) = p**4 - p**2 - 16*p + 12. Let t(c) = 4*v(c) + 5*w(c). Solve t(z) = 0 for z.
-2, 1, 3
Let f(m) be the second derivative of m**4/36 + 358*m**3/9 + 64082*m**2/3 + 1228*m. Factor f(k).
(k + 358)**2/3
Let i be ((-11)/60)/(-4*8/80). Let a = i + -17/72. Factor -2/9*q**4 + a*q**2 + 0*q**3 + 0*q + 0.
-2*q**2*(q - 1)*(q + 1)/9
Let r(s) be the first derivative of 1/15*s**3 - 21 - 3/10*s**2 + 2/5*s. Factor r(p).
(p - 2)*(p - 1)/5
Let c(y) be the first derivative of y**3/4 - 243*y**2/8 + 60*y - 3362. Find i, given that c(i) = 0.
1, 80
Let o(s) be the second derivative of -s**5/120 - 319*s**4/72 - 8533*s**3/12 - 8427*s**2/4 + 508*s. Factor o(h).
-(h + 1)*(h + 159)**2/6
Factor 292*o**2 + 1556068/3 + 21316*o + 4/3*o**3.
4*(o + 73)**3/3
Factor 22201/4 + 1/4*k**2 - 149/2*k.
(k - 149)**2/4
Let u(v) be the second derivative of 1/36*v**4 + 4/9*v**3 + 5/2*v**2 + 85*v + 0. Factor u(b).
(b + 3)*(b + 5)/3
Let y(f) = -f + 28. Let l(g) = -19*g**3 + g + 1. Let t be l(-1). Let j be y(t). Suppose -15*r**2 + 6 + j*r + 21 + 62*r**3 - 59*r**3 = 0. Calculate r.
-1, 3
Let a(k) = -22*k - 15. Let s be a(3). Let o = s - -87. Factor 2*x**2 - o*x + x**2 + 6*x - 9*x**3 - 3*x**4 + 9*x.
-3*x*(x - 1)*(x + 1)*(x + 3)
Let n be 183/6 + (-15)/12*-2. Let k(l) = l - 28. Let g be k(n). Factor 0*y**2 - 10/11*y**3 + 0*y - 8/11*y**4 + 0 + 2/11*y**g.
2*y**3*(y - 5)*(y + 1)/11
Let s(b) be the second derivative of b**6/10 + 21*b**5/20 - 41*b**4/4 + 33*b**3/2 - 2*b - 576. Factor s(t).
3*t*(t - 3)*(t - 1)*(t + 11)
Factor 113/3*j**4 + 2/3*j - 224/3*j**3 + 0 + 109/3*j**2.
j*(j - 1)**2*(113*j + 2)/3
Let n(f) be the third derivative of -f**5/240 - 437*f**4/24 - 190969*f**3/6 - 3*f**2 + 156*f. What is q in n(q) = 0?
-874
Factor -13*i**4 + 822*i**3 - 22*i**4 + 3125*i - 21625*i**2 - 2567*i**3.
-5*i*(i + 25)**2*(7*i - 1)
Let l(h) be the second derivative of -h**7/63 + 82*h**6/15 - 242*h**5/5 + 1444*h**4/9 - 640*h**3/3 - 62*h + 17. Factor l(y).
-2*y*(y - 240)*(y - 2)**3/3
Let r(b) be the second derivative of 1/12*b**3 - 1/24*b**4 + 1/2*b**2 + 0 - 26*b. Solve r(a) = 0.
-1, 2
Determine c so that 6*c**2 + 631*c - 5*c**2 - 2*c**2 - 597*c - 93 = 0.
3, 31
Suppose 1250/9*c**2 + 38642/9 + 13900/9*c = 0. What is c?
-139/25
Let s be (140/105)/(40/(-18))*-5. Let r(j) be the first derivative of -14*j**2 - 32*j - 32 + 4/3*j**s. Factor r(g).
4*(g - 8)*(g + 1)
Let k(f) be the second derivative of -f**5/60 + 263*f**4/36 + 398*f**3/9 + 266*f**2/3 - 6485*f. Factor k(n).
-(n - 266)*(n + 1)*(n + 2)/3
Let w = -62 - -143. Let n = w + -80. Let 3*i + 8*i**2 + i**3 + 8*i**2 - 23*i**2 + 10*i**2 + n = 0. What is i?
-1
Let x(l) be the first derivative of 15/14*l**2 + 1/7*l**3 - 3 + 0*l - 60/7*l**4 - 48/35*l**5. Determine m, given that x(m) = 0.
-5, -1/4, 0, 1/4
Suppose p = x - 16, 0 = 4*x - 5*x - 2*p + 7. Let k(l) = 17*l - 219. Let h be k(x). Factor -16/3*t - 16/3*t**h + 4/3*t**3 + 0 + 4/3*t**4.
4*t*(t - 2)*(t + 1)*(t + 2)/3
Let r = -35 + 38. Let g be (-27)/r*3/(-9). Factor -4*z - 3*z**2 + 2*z**2 - z**2 - 5 + g.
-2*(z + 1)**2
Suppose -2*l - 3*f = -871, 12*f = 14*f + 10. Let d = -443 + l. Find q, given that 0 + 8/5*q**2 - 8/5*q**4 + 4/5*q**3 + d*q - 4/5*q**5 = 0.
-2, -1, 0, 1
Suppose 1095*b - 1097*b + 8 = 0. Let r be -6*1*(-3)/9. Factor -h**b - 3*h**3 - 2*h**4 + 3*h**2 + 3*h + 0*h**r.
-3*h*(h - 1)*(h + 1)**2
Let r = 57471/2 + -28735. Determine i so that 162 + 18*i + r*i**2 = 0.
-18
Let b be ((-40)/6)/((-20)/60). Let l(q) = q**4 - q**2 + q. Let i(z) = -16*z**4 - 68*z**3 + 272*z**2 + 304*z. Let f(t) = b*l(t) + i(t). Factor f(v).
4*v*(v - 9)**2*(v + 1)
Let j = -472476 - -4252324/9. Factor 4/3*a**2 + 16/9 - j*a + 2*a**3.
2*(a + 2)*(3*a - 2)**2/9
Let m(h) = 2*h**2 + 53*h + 36. Let l be m(-26). Let y(o) be the first derivative of -8*o + l - 16/3*o**3 + o**4 + 10*o**2. Factor y(k).
4*(k - 2)*(k - 1)**2
Let q be ((-16)/(-12))/(10/15). Suppose -q*a + 0*a = a. Suppose -1/4*x + 0 + 3/4*x**5 + a*x**2 + 3/2*x**3 + 2*x**4 = 0. Calculate x.
-1, 0, 1/3
Let d(u) be the first derivative of u**3/30 + 757*u**2/10 + 1513*u/10 + 5918. Factor d(f).
(f + 1)*(f + 1513)/10
Let o(j) = -j**3 - 34*j**2 - 183*j + 1940. Let p be o(-19). Let -248/3*c + 80/3*c**4 + 604/9*c**2 + 914/9*c**3 + 16 + p*c**5 = 0. Calculate c.
-6, -2, 1/3
Suppose 110 = z + 3*u, z + 4*u = -0*z + 111. Determine c so that -37*c + 69*c - 14*c**3 + 5*c**2 - 60*c - z*c**2 = 0.
-7, -2/7, 0
Let h(i) be the second derivative of -1/270*i**6 + 4/45*i**5 - 6*i - 7/18*i**4 - 13/18*i**2 + 20/27*i**3 + 2. Factor h(l).
-(l - 13)*(l - 1)**3/9
Let p(h) be the first derivative of -10*h**4 - 15*h**2 - 44 + 0*h - 65/3*h**3 - h**5. Factor p(v).
-5*v*(v + 1)**2*(v + 6)
Let d(v) be the third derivative of -85/2*v**3 + 1/12*v**5 + 35/12*v**4 + 79*v**2 + 0 + 0*v. Factor d(q).
5*(q - 3)*(q + 17)
Find u such that 183/5*u + 24/5*u**2 + 156/5 - 3/5*u**3 = 0.
-4, -1, 13
Let j(n) = -n**3 - 11*n**2 - 24*n. Let h(u) = -2*u**2. Let b(s) = 22*h(s) - 2*j(s). Find o, given that b(o) = 0.
0, 3, 8
Let v(t) = 5*t**2 - 51*t + 112. Let x be v(7). Let j(d) be the first derivative of x*d - 1/8*d**2 + 1/6*d**3 - 1/16*d**4 - 8. Factor j(g).
-g*(g - 1)**2/4
Let c be 3/(-9)*(1 + (-1262)/14). Let y be (135/35 - 15) + 14. Factor -c*t - 80/7 - y*t**2.
-4*(t + 10)*(5*t + 2)/7
Let j(l) = -l**2 - 22*l - 29. Let m(y) = 9*y**2 - 15*y - 20. Let i(b) = 2*b**2. Let f(w) = 15*i(w) - 3*m(w). Let q(v) = 4*f(v) + 9*j(v). Factor q(a).
3*(a - 7)*(a + 1)
Let i(a) be the first derivative of -a**6/3 - 54*a**5/5 - 97*a**4/2 - 78*a**3 - 46*a**2 + 2284. What is l in i(l) = 0?
-23, -2, -1, 0
Find s such that 1/6*s**2 + 1253/6 - 209*s = 0.
1, 1253
Factor -12619 + 411 - 163*t**2 - 5735 - 8301 - 366*t**2 - 7452*t.
-(23*t + 162)**2
Factor -3302318 - 992*f**3 + 81672*f**2 + 1166*f**4 - 2204480*f + 1015170 - 1162*f**4.
4*(f - 83)**3*(f + 1)
Let c(z) be the first derivative of 21*z**5/25 - 9*z**4/5 - 6*z**3/5 + 6*z**2 - 27*z/5 + 3680. Solve c(m) = 0 for m.
-9/7, 1
Let x(f) = -45*f + 100. Let c be x(0). Find l such that -112*l + c + 16*l - 92*l**2 + 4*l**4 + 11*l**2 + 96*l**3 - 23*l**2 = 0.
-25, -1, 1
Let q(z) be the first derivative of -3*z - 1/6*z**4 + 11/9*z**3 - 1 - 2*z**2. Factor q(i).
-(i - 3)**2*(2*i + 1)/3
Let z be (5 - (-285)/(-45))*6 + 10. Find u, given that 1/5*u**z + 0 + 9/5*u = 0.
-9, 0
Let x(k) = 4*k**3 + 8*k. Let z(s) = -3*s**3 - 661 - s**2 + 661 - 6*s. Let y(n)