**2.
2*(n - 1)**2*(n + 1)**2/7
Let f(k) be the second derivative of 3*k**5/100 - 151*k**4/20 + 299*k**3/10 - 447*k**2/10 - 1000*k. Find z such that f(z) = 0.
1, 149
Let l(f) = 15*f. Let q be l(1). Let i = 43 - q. Factor 7*b - 4*b**2 + i + b - 28.
-4*b*(b - 2)
Factor 85*t**2 - 55*t - 1077 + 2161 - 1114.
5*(t - 1)*(17*t + 6)
Let t = -77607 - -1397635/18. Let h = t - 314/9. Suppose 3/2*w**2 + h*w + 3 = 0. What is w?
-2, -1
Let w(l) = -l**2 - 10*l - 16. Let t be w(-7). Let -58*j**2 + 59*j**3 - 14*j**4 - 12*j + 8*j**5 + 72 - 7*j**t - 48*j = 0. Calculate j.
-1, 1, 2, 6
Let h(d) be the second derivative of 0*d**2 + 4/3*d**3 + 4 - 3/10*d**5 - 4*d + 0*d**4 + 1/15*d**6. Let h(y) = 0. Calculate y.
-1, 0, 2
Let w(t) = 4137*t**2 + 8407*t - 22. Let k(b) = 20684*b**2 + 42080*b - 112. Let q(z) = 3*k(z) - 16*w(z). Suppose q(m) = 0. Calculate m.
-2, 2/1035
Let d(p) be the third derivative of -2*p**7/35 - 19*p**6/60 - p**5/10 + 2*p**4 + 4*p**3/3 - 8197*p**2. What is l in d(l) = 0?
-2, -1/6, 1
Let n(y) be the third derivative of 0*y + 1/210*y**5 - 8*y**2 + 3/7*y**3 + 1/14*y**4 + 3. Factor n(w).
2*(w + 3)**2/7
Let f(a) = -a**2 + 8*a - 9. Let p(d) = -4*d + 12*d**2 - 19*d + 12*d**2 - 21*d**2 + 27. Let i(w) = -14*f(w) - 4*p(w). Factor i(n).
2*(n - 9)*(n - 1)
Suppose -176/13*w - 2/13*w**5 - 314/13*w**2 - 102/13*w**3 + 34/13*w**4 + 0 = 0. What is w?
-1, 0, 8, 11
Suppose 0 = -2*x - 8, -2*t + 4*x + 2208 = 2*t. Let g = 551 - t. Determine l, given that 0*l + 1/4*l**g + 0 + 1/2*l**4 + 0*l**2 + 1/4*l**5 = 0.
-1, 0
Suppose 0*g + 5*g = 10. Let u = 293 + -875/3. Determine q, given that -49/3*q**g - 343/6*q**3 + u + 14/3*q = 0.
-2/7, 2/7
Let g(a) be the first derivative of -a**3/9 - 1567*a**2/6 - 8687. Factor g(v).
-v*(v + 1567)/3
Suppose 42 - 92 = -10*m. Factor -45*k**4 + 2*k**m + 80*k**3 + 64*k**2 - k**5 + 62*k**4.
k**2*(k + 1)*(k + 8)**2
Suppose -6*y = -4*y - 128. Suppose 0 = -5*d + d + y. Factor 2*k**5 - d*k**4 + 4*k**5 - 2*k**5 + 5*k**3 + 7*k**3.
4*k**3*(k - 3)*(k - 1)
Let p(n) be the third derivative of -n**8/1008 - 4*n**7/105 - 5*n**6/9 - 23*n**5/6 - 111*n**4/8 - 27*n**3 + 13*n**2 + 16. Solve p(q) = 0 for q.
-9, -3, -2, -1
Let z(c) be the third derivative of -2000/9*c**3 + 0 + 1/720*c**6 + 25/3*c**4 - 68*c**2 + 0*c - 1/6*c**5. What is d in z(d) = 0?
20
Let -63*j**3 + 60*j**3 + 71*j**2 + 75*j**2 + 82*j**2 = 0. What is j?
0, 76
Let b(z) be the second derivative of z**6/60 - 3*z**5/10 - 77*z**4/24 - 11*z**3 - 17*z**2 - 1383*z + 2. Factor b(c).
(c - 17)*(c + 1)*(c + 2)**2/2
Solve 54/5 - 27/5*i + 3/5*i**2 = 0.
3, 6
Let z(a) be the second derivative of -37*a**5/50 - 99*a**4/5 - 160*a**3 - 128*a**2/5 - 500*a + 4. Suppose z(i) = 0. What is i?
-8, -2/37
Factor 7*g + 9*g - 5*g + 16*g - 5*g**2 + 6*g**2.
g*(g + 27)
Let u(d) = 8*d**3 + 4879*d**2 + 2634139*d + 475021263. Let h(m) = m**3 + 2*m**2 + 2*m. Let o(t) = 5*h(t) - u(t). Factor o(f).
-3*(f + 541)**3
Suppose 0 = 3*m - 1461 - 2661. Suppose -1378*u**2 - 222*u**4 + 18*u**5 - 494*u + 902*u**3 + 32 + m*u - 232 = 0. Calculate u.
2/3, 1, 5
Let t = 71507/11 - 643541/99. Factor 0*o - 2/9*o**2 + 4/9*o**3 + 0 - t*o**4.
-2*o**2*(o - 1)**2/9
Let g(r) be the second derivative of 5*r**7/42 - 2411*r**6/6 + 545412*r**5 - 1098990130*r**4/3 + 334886664280*r**3/3 - 985024944120*r**2 - 3795*r. Factor g(h).
5*(h - 602)**4*(h - 3)
Let y be (-29 - (-15 - (-555)/(-40)))/((-3)/8). Factor -5/3*h**2 + 8/3 - y*h**3 - 2/3*h.
-(h - 1)*(h + 2)*(h + 4)/3
Let h(q) be the third derivative of 0 + 5/12*q**4 - 1/30*q**5 + 2*q**3 + 8*q**2 + 0*q. Factor h(p).
-2*(p - 6)*(p + 1)
Suppose 0 = 25*v - 23*v - 110. Let 5536*n**3 + v*n + 132 + 62*n + 24*n**2 + 3*n - 5539*n**3 - 3*n**2 = 0. Calculate n.
-2, 11
Let a(w) be the first derivative of w**2/2 + 29*w + 306. Let y be a(-29). Determine u, given that y*u + 0 + 1/4*u**4 + 0*u**3 - 1/4*u**2 = 0.
-1, 0, 1
Let d = -501 + 652. Let t = d - 752/5. Factor 4/5*z**3 - t*z + 0*z**4 - 1/5*z**5 + 2/5 - 2/5*z**2.
-(z - 1)**3*(z + 1)*(z + 2)/5
Factor 72*q**2 - 3/2*q**3 - 657/2*q + 258.
-3*(q - 43)*(q - 4)*(q - 1)/2
Let k(z) be the first derivative of -5*z**3/6 + 12725*z**2/2 - 32385125*z/2 - 3093. Determine b, given that k(b) = 0.
2545
Suppose 5*p + 2*f - 38 = 0, -p = 3*p + f - 28. Let n(w) be the first derivative of 2/3*w**6 - p*w**2 + 4*w + 8/3*w**3 + 2*w**4 - 7 - 12/5*w**5. Factor n(l).
4*(l - 1)**4*(l + 1)
Let a(d) be the second derivative of d**4/12 - 3599*d**3/3 + 12952801*d**2/2 + 2864*d + 2. Factor a(p).
(p - 3599)**2
Let u(s) be the second derivative of s**4/4 - 149*s**3 - 897*s**2/2 - 9427*s. Factor u(q).
3*(q - 299)*(q + 1)
Factor -18*y**2 + 372*y + 6*y**2 - 16*y**2 + 40*y**2 + 732 - 9*y**2.
3*(y + 2)*(y + 122)
Let v be (8/12)/((-55)/(-33)). Let b(z) be the third derivative of -26*z**2 + 0 + 1/90*z**6 - v*z**5 + 0*z - 48*z**3 + 6*z**4. Determine u, given that b(u) = 0.
6
Let u(w) be the third derivative of w**8/80640 - w**7/1440 + 49*w**6/2880 + 9*w**5/5 - w**2 - 83. Let g(f) be the third derivative of u(f). Factor g(s).
(s - 7)**2/4
Suppose -120*i + 3 = -119*i. Find p such that -73022*p**i + 2*p**5 + 73022*p**3 - 16*p**4 = 0.
0, 8
Let w(l) be the third derivative of l**7/1785 + l**6/60 + 38*l**5/255 + 5*l**4/17 + 2503*l**2. Let w(k) = 0. Calculate k.
-10, -6, -1, 0
Let m(y) be the second derivative of -5*y**4/12 + 1705*y**3/6 - 850*y**2 + 17*y - 6. Suppose m(c) = 0. Calculate c.
1, 340
Let n = -188/61 - -1062/305. Let z(i) be the first derivative of 1/20*i**4 - 28 + 1/2*i**2 + n*i + 4/15*i**3. Factor z(t).
(t + 1)**2*(t + 2)/5
Let s(r) = -20*r**4 + 342*r**3 - 1176*r**2 + 1004*r + 144. Let f(i) = i**4 + 2*i**3 + i**2 - i. Let t(m) = 4*f(m) + s(m). Solve t(a) = 0.
-1/8, 2, 18
Let i(c) be the third derivative of c**6/40 - 5*c**5/4 - 93*c**4/4 - 9*c**2 + c + 59. Factor i(d).
3*d*(d - 31)*(d + 6)
Let w(d) be the third derivative of -d**7/350 + 379*d**6/200 + 4*d**2 + 14. Solve w(v) = 0.
0, 379
Let z(d) be the second derivative of -21*d + 2/17*d**3 + 1/510*d**5 + 7/204*d**4 + 0 - 11*d**2. Let b(c) be the first derivative of z(c). Solve b(o) = 0 for o.
-6, -1
Suppose -2*y - 16 = 5*t, -4*y - 7*t = -5*t + 16. Let m be ((-64)/(-48))/(y/(-9)). Factor -10/9*i**3 + 2/9*i**m + 0 - 8/9*i + 16/9*i**2.
2*i*(i - 2)**2*(i - 1)/9
Let f(g) be the first derivative of 15/8*g**2 + 0*g + 50 + 1/8*g**3. Factor f(m).
3*m*(m + 10)/8
Let o(t) be the second derivative of t**5/4 + 400*t**4/3 + 3185*t**3/6 + 795*t**2 + 985*t. Suppose o(g) = 0. Calculate g.
-318, -1
Let t(x) be the first derivative of 1527/4*x**4 - 201/10*x**5 + 3675/2*x + 1733*x**3 + 10815/4*x**2 + 1/4*x**6 - 26. Suppose t(n) = 0. Calculate n.
-1, 35
Let f(t) = t - 7. Let h be f(9). Suppose 4*j - 24 = -w - 3*w, 24 = h*w + 5*j. Factor -7*z**3 - 2*z + z**2 + 5*z - z**2 + 4*z**w.
-z*(z - 1)*(7*z + 3)
Factor 10 - 1/6*l**3 - 79/6*l + 10/3*l**2.
-(l - 15)*(l - 4)*(l - 1)/6
Let u(v) = -66*v**3 + 20*v**2 + v - 15. Let s(z) = -26*z**3 + 10*z**2 - 8. Let g(w) = 5*s(w) - 2*u(w). Factor g(x).
2*(x - 1)*(x + 1)*(x + 5)
Suppose -2*p + 45 = 13*p. Solve 4*t**p - 7*t**3 - 28*t**2 - 12*t + 67*t**2 - 6*t**3 = 0 for t.
0, 1/3, 4
Find h such that 85 - 39/2*h + 1/2*h**2 = 0.
5, 34
Let f(i) be the first derivative of 2*i**6/3 - 56*i**5/5 - 86*i**4 - 656*i**3/3 - 262*i**2 - 152*i + 1002. Factor f(g).
4*(g - 19)*(g + 1)**3*(g + 2)
Suppose 0 + 3/7*a**5 + 549/7*a**3 + 0*a + 153/7*a**4 - 705/7*a**2 = 0. What is a?
-47, -5, 0, 1
Solve 0*r**4 + 160 - 43*r**2 - 30*r**3 - 276*r - 114*r - 5*r**4 + 338*r**2 - 30*r**3 = 0.
-16, 1, 2
Let v(a) be the third derivative of -a**6/840 - a**5/60 + 13*a**4/28 + 2*a**2 + 1366. Suppose v(d) = 0. What is d?
-13, 0, 6
Factor 632/5*j - 206/5*j**2 - 424/5 - 2/5*j**3.
-2*(j - 2)*(j - 1)*(j + 106)/5
Let w(f) be the first derivative of 9*f**4/28 + 2*f**3 - 69*f**2/14 + 18*f/7 + 652. Solve w(j) = 0.
-6, 1/3, 1
Let 1/2*y**2 + 182 - 41/2*y = 0. What is y?
13, 28
Let q = 17731 - 443243/25. Let x(u) be the first derivative of -33 + 0*u**2 - 4/5*u**3 + 17/10*u**4 - 7/15*u**6 + q*u**5 + 0*u. Suppose x(p) = 0. Calculate p.
-1, 0, 2/7, 3
Let c(a) = 284*a + 858. Let x be c(-3). Let o(z) be the second derivative of 1/200*z**5 - 1/60*z**3 + 0 - 1/40*z**4 + 1/100*z**x + 0*z**2 + 3*z. Factor o(n).
n*(n - 1)*(n + 1)*(3*n + 1)/10
Let j(f) = 0*f**2 - 17*f + 17*f + 6 + f**2. Let h be j(0). Find d such th