2)
Let s(t) be the second derivative of 1/12*t**6 + 25*t - 25/24*t**4 + 0 + 0*t**2 + 1/8*t**5 + 5/4*t**3. Factor s(m).
5*m*(m - 1)**2*(m + 3)/2
Let r(h) be the third derivative of 1/300*h**6 + 1/75*h**5 - 15*h**2 + 0 + 0*h + 0*h**3 + 1/60*h**4. Factor r(v).
2*v*(v + 1)**2/5
Let f(a) be the first derivative of a**3/5 + 21*a**2/10 + 23. Let f(n) = 0. What is n?
-7, 0
Let a be 1 + 3 + -3 + 4 + -1. Solve a*h**3 + 1 + 53*h**2 + 3 + 12*h - 41*h**2 = 0 for h.
-1
Let i(x) be the second derivative of 0 - 1/22*x**5 + 7/66*x**4 - 2/33*x**3 - 4*x + 0*x**2. Factor i(q).
-2*q*(q - 1)*(5*q - 2)/11
Let o(a) be the second derivative of -5*a**4/12 - 15*a**3/2 - 20*a**2 - 2*a - 58. Factor o(q).
-5*(q + 1)*(q + 8)
Let b(c) = -8*c**2 + 984*c - 60520. Let j(p) = 10*p**2 - 984*p + 60522. Let i(d) = -3*b(d) - 2*j(d). Factor i(z).
4*(z - 123)**2
Suppose -6/5*k**5 - 108/5*k**2 + 54/5*k + 0 - 52/5*k**4 - 144/5*k**3 = 0. Calculate k.
-3, 0, 1/3
Let v(m) be the third derivative of -m**8/840 - m**7/525 - 8*m**2 + 8*m. Solve v(p) = 0 for p.
-1, 0
Find h such that h**2 - 3/2*h**3 - 1/2*h**4 + 6*h + 4 = 0.
-2, -1, 2
Suppose -5 = 5*w - 5*f, f + 2 = -5*w + 21. Suppose 5*n**w - 2*n**5 - 2*n**5 + 13 - 4*n**4 + 5*n**2 - n - 14 = 0. Calculate n.
-1, -1/2, 1/2, 1
Let d = 0 + 17. Suppose -s = 4*b - 10, -5*b + 2*s + d + 2 = 0. Find l such that -1/2*l**5 + 0 - 3/2*l**b - 2*l**4 + 2*l + 2*l**2 = 0.
-2, -1, 0, 1
Let l(f) = -f**3 - 2*f**2 - 3*f - 4. Let j be l(-4). Let p be j/15 + 1*-2. Suppose p*s**5 + 20/9*s**4 + 8/3*s**3 + 2/9*s + 0 + 4/3*s**2 = 0. Calculate s.
-1, -1/3, 0
Let y(b) = 6*b**5 - 20*b**4 - 17*b**3 + 12*b**2. Let r(p) = 2*p**5 + p**3. Let i(m) = r(m) + y(m). Let i(j) = 0. What is j?
-1, 0, 1/2, 3
Let n(d) = -4*d + 3. Let u(k) = k - 1. Let o(h) = 2*n(h) + 7*u(h). Suppose 0 = 2*r + 2. Let j(g) = -2*g**2 + 2. Let z(p) = r*j(p) - 4*o(p). Solve z(b) = 0.
-1
Let a(x) be the third derivative of 0*x**3 + 0*x - 13/20*x**5 - 35*x**2 - 1/4*x**4 + 7/64*x**8 + 11/40*x**7 - 33/80*x**6 + 0. Find v such that a(v) = 0.
-2, -2/7, 0, 1
Let v(b) be the first derivative of 2*b**3 - 183*b**2/2 - 525*b - 22. Let j(y) = y**2 - 26*y - 75. Let a(d) = -27*j(d) + 4*v(d). Find i such that a(i) = 0.
-5
Suppose -p - 29 = -5*p + 3*m, 0 = -3*p - 5*m. Suppose 0 = z - 9 + p. Determine g so that -16/3*g**3 + 0 - 8/3*g - 4/3*g**z - 20/3*g**2 = 0.
-2, -1, 0
Let t be 1680/392 + ((-4)/14 - 0). Suppose 10*w + 28 = 15*w - 2*d, w - 20 = t*d. Determine y, given that 0 + y**3 + 2/3*y - 1/6*y**w - 3/2*y**2 = 0.
0, 1, 4
Let n(x) be the first derivative of -x**6/60 + x**5/15 + x**4/192 - x**3/24 + 5*x**2/2 - 1. Let k(w) be the second derivative of n(w). Solve k(f) = 0 for f.
-1/4, 1/4, 2
Let q(f) = -7*f**2 + 47*f - 8. Let t(x) = x**2 - 2*x - 2. Let c(d) = -4*q(d) + 4*t(d). Factor c(k).
4*(k - 6)*(8*k - 1)
Let v(z) be the third derivative of z**7/560 - z**6/20 + 5*z**5/32 + 21*z**4/32 + 51*z**2 + 3. Factor v(m).
3*m*(m - 14)*(m - 3)*(m + 1)/8
Let p(l) = -l**2 - 3*l + 4. Suppose -t = -3*t + 4*h + 14, 3*t = -h + 14. Let k(j) = 8*j - 7 + 4*j**2 - 10 + t. Let d(m) = 3*k(m) + 10*p(m). Factor d(o).
2*(o - 2)*(o - 1)
Factor -1/4*k**2 - 20*k + 0.
-k*(k + 80)/4
Find i, given that 2*i**2 - 2*i + 32*i + 0*i**2 - 7*i**2 = 0.
0, 6
Let u be (-239)/(-2) + (-2)/20*-5. Let w = 361/3 - u. Suppose w*y + 0 - 1/3*y**2 = 0. What is y?
0, 1
Suppose -2 = -2*l + 2*m, 2*l + 2*m - m - 11 = 0. Determine c, given that -2*c**3 + 5*c**l + 3*c**3 - 5*c**2 + 10*c - 11*c**3 = 0.
-1, 0, 1, 2
Suppose -105*b = -107*b + 6. Factor 6/5*x**b + 0 - 1/5*x**4 - 12/5*x**2 + 8/5*x.
-x*(x - 2)**3/5
Let p(b) be the third derivative of -1/12*b**5 + 0 + 10*b**2 + 0*b - 1/2*b**3 - 1/120*b**6 - 7/24*b**4. Solve p(l) = 0.
-3, -1
Let i(q) = 5*q**3 + 72*q**2 + 234*q + 314. Let j(m) = -70*m**3 - 1010*m**2 - 3275*m - 4395. Let l(n) = 85*i(n) + 6*j(n). Suppose l(v) = 0. What is v?
-4
Let u(j) = 5*j**3 - 212*j**2 + 2606*j - 6003. Let z(a) = 5*a**3 - 211*a**2 + 2608*a - 6004. Let g(h) = 4*u(h) - 3*z(h). Find k such that g(k) = 0.
3, 20
Let l(q) = -4*q + 13. Let n be l(6). Let p = n - -14. Factor 9*u**4 + 2*u**2 - 2*u + 8*u**p - 2*u**3 - 4*u**3 - 11*u**2.
u*(u - 1)*(u + 1)*(9*u + 2)
Let v = 375 + -373. Let u(m) be the first derivative of 1/11*m**v + 0*m + 1/22*m**4 - 6 + 4/33*m**3. What is x in u(x) = 0?
-1, 0
Let y = -11 - -14. Let m(v) be the second derivative of 1/12*v**4 + 1/2*v**2 + 1/3*v**y + 0 + v. Find o, given that m(o) = 0.
-1
Let k(o) = o**3 + 5*o**2 + o. Let t be k(-4). Let m be 3/(-18) - 2*(-3)/t. Factor 1/3 + 0*a - m*a**2.
-(a - 1)*(a + 1)/3
Let s = -547/2 - -277. Let y(m) be the second derivative of 9/20*m**5 + 3*m**2 + 1/2*m**4 - s*m**3 + 4*m + 0. What is p in y(p) = 0?
-2, 1/3, 1
Let l(v) be the first derivative of 4*v**3/3 + 28*v**2 - 60*v - 61. Determine c so that l(c) = 0.
-15, 1
Let a(r) be the second derivative of -r**6/10 + 69*r**5/20 - 81*r**4/4 + 97*r**3/2 - 57*r**2 - 3*r + 51. Solve a(l) = 0.
1, 2, 19
Factor -80 + 3*g**2 + 106 + 148 - 93*g.
3*(g - 29)*(g - 2)
Let o(m) be the first derivative of 2*m**6/3 + 12*m**5/5 - 5*m**4 - 4*m**3 + 8*m**2 + 78. What is w in o(w) = 0?
-4, -1, 0, 1
Let r(n) be the third derivative of n**6/120 - 7*n**5/60 + n**4/3 - n**3/6 - 6*n**2. Let s be r(6). Suppose -14 - 2*f**2 + 7 - s - 3*f + 15*f = 0. What is f?
3
Factor -250*n**3 - 3906250/3*n + 0 - 2/3*n**4 - 31250*n**2.
-2*n*(n + 125)**3/3
Let -27 - 3/4*y**3 + 81/4*y + 15/2*y**2 = 0. What is y?
-3, 1, 12
Let s = 119 - 104. Factor -119*t**4 - s + 6*t - 20*t**3 + 124*t**4 + 14*t + 10*t**2.
5*(t - 3)*(t - 1)**2*(t + 1)
Let i(d) be the first derivative of 3*d**4/4 + d**3 - 86. What is x in i(x) = 0?
-1, 0
Suppose -6*l = 17 - 53. Suppose -2*v - l = -5*v. Factor -1 + 1/2*o + 1/2*o**v.
(o - 1)*(o + 2)/2
Let f be (-2745)/(-325) - 3/((-78)/4). Let t = f - 281/35. Factor t + 2/7*x - 2/7*x**2.
-2*(x - 2)*(x + 1)/7
Let k(t) = -21*t**4 - 12*t**2 + 18*t - 21. Let d = 4 - 2. Suppose 4*h - d*h = 2. Let l(p) = p**4 + p**2 - p + 1. Let w(u) = h*k(u) + 18*l(u). Factor w(c).
-3*(c - 1)**2*(c + 1)**2
Let h(f) be the third derivative of 0 - 15*f**2 - 13/600*f**5 - 3/20*f**3 - 1/10*f**4 + 0*f - 1/600*f**6. What is m in h(m) = 0?
-3, -1/2
Let i be 24/88*6/9. Solve 6/11*p**4 - 14/11*p**2 + 0*p + 8/11 + i*p**5 - 2/11*p**3 = 0 for p.
-2, -1, 1
Suppose 42 = -93*y + 87*y. Let i be y*(-6)/84*6. Factor -3/2 + 3/2*f**2 + 1/2*f - 1/2*f**i.
-(f - 3)*(f - 1)*(f + 1)/2
Let k(f) be the first derivative of f**4/24 + f**3/3 - 5*f**2/4 + 4*f/3 - 22. Let k(l) = 0. Calculate l.
-8, 1
Let l(w) = -4*w**2 - 87*w + 26. Let a be l(-22). Factor 0 - 4/7*p**a + 4/7*p**3 - 4/7*p + 4/7*p**2.
-4*p*(p - 1)**2*(p + 1)/7
Let y be ((-3)/(-6))/(2*(-2)/40). Let v be (y - 1)*2*(-3)/9. Factor -2/7*u**v - 6/7*u**3 + 0 - 6/7*u**2 - 2/7*u.
-2*u*(u + 1)**3/7
Suppose -4*a + 22 = 2*y, 3*y = 2842*a - 2837*a. Solve -1/4*p**4 + 1/4*p**5 + 0*p - 3/4*p**2 - 5/4*p**a + 0 = 0.
-1, 0, 3
Let a(s) be the first derivative of -2/33*s**3 + 16/11*s**2 - 5 - 128/11*s. Factor a(x).
-2*(x - 8)**2/11
Suppose -2*c - 5*j - 18 = -c, 0 = -2*c + 2*j. Let s be c + 3 + -1 - 4/(-3). What is g in 0*g**2 - 1/3*g**3 - 1/6 + s*g + 1/6*g**4 = 0?
-1, 1
Let q be 20/16*(-800)/(-500). Factor -3/2*l**q + 0 + 3/2*l.
-3*l*(l - 1)/2
Let d(x) be the second derivative of -3*x**7/14 - 43*x**6/10 - 663*x**5/20 - 489*x**4/4 - 220*x**3 - 150*x**2 + 113*x. Find k such that d(k) = 0.
-5, -2, -1/3
Let h(c) be the third derivative of 0*c**5 + 0*c**3 - 4*c**2 - 1/72*c**4 + 1/360*c**6 + 0*c + 0. Factor h(t).
t*(t - 1)*(t + 1)/3
Solve -1/4*h**2 - 2*h - 15/4 = 0.
-5, -3
Let 0 - i + 5/4*i**5 + 4*i**4 + 3/4*i**3 - 5*i**2 = 0. Calculate i.
-2, -1/5, 0, 1
Find b such that -4/3*b - 2/3 + 0*b**2 + 2/3*b**4 + 4/3*b**3 = 0.
-1, 1
Factor -4/7*z**2 - 1936/7 - 176/7*z.
-4*(z + 22)**2/7
Let j(q) be the third derivative of -q**5/15 - 73*q**4/3 - 10658*q**3/3 + 21*q**2 + 6*q. Find w such that j(w) = 0.
-73
Let l be (-3)/51 - (-16)/272. Let o(c) be the third derivative of l + 10*c**2 - 1/30*c**5 - 1/4*c**3 + 0*c - 7/48*c**4. Factor o(m).
-(m + 1)*(4*m + 3)/2
Let h(k) = -1772*k - 2. Let x be h(-1). Let c be x/150 + (-1)/(-5). Find j such that 765/7*j**3 - 138/7*j**2 - c*j - 675/7*j**4 + 24/7 = 0.
-1/3, 2/5, 2/3
Let k(u) be the second derivative of -u**7/2520 + u**6/120 - 3*u**5/40 + 3*u**4/2 + 28*u. Let i(