*4.
(n - 1)**2*(n + 2)*(4*n + 1)/6
Let f(j) = 25*j**3 - 740*j**2 - 1975*j + 2810. Let o(w) = -2*w**3 + 57*w**2 + 152*w - 216. Let g(k) = -3*f(k) - 40*o(k). Let g(a) = 0. Calculate a.
-3, 1, 14
Let s(z) = -24*z**2 + 181*z - 42. Let i(a) = -70*a**2 + 544*a - 128. Let c(g) = 5*i(g) - 14*s(g). Factor c(h).
-2*(h - 13)*(7*h - 2)
Let u = -8663 + 8663. Factor -2/23*b**5 - 2/23*b**3 + 4/23*b**4 + 0*b**2 + u + 0*b.
-2*b**3*(b - 1)**2/23
Let z(x) be the second derivative of x**5/180 - x**4/18 + 4*x**3/27 - 33*x. Solve z(f) = 0 for f.
0, 2, 4
Let b be ((-10)/(-3))/(14/21). Suppose 4*j + 3*r = b, 2*j - 4*r = -r + 25. What is u in 9*u + j*u - 2*u - 19*u**2 + 3 + 4*u**2 = 0?
-1/5, 1
Let o(b) = -151*b - 9211. Let g be o(-61). Factor g*i**3 + 4/9*i**4 + 2/9*i**5 - 2/9*i + 0 - 4/9*i**2.
2*i*(i - 1)*(i + 1)**3/9
Let a(t) = 0*t - t**2 + 13 + 3*t - 2*t + 8*t. Let c be a(10). Factor -35*k**2 + k + 33*k**2 - 2*k**3 + c*k**3.
k*(k - 1)**2
Let a(z) be the third derivative of -z**8/42 - 11*z**7/105 + z**6/20 + z**2 + 10*z. Let a(u) = 0. What is u?
-3, 0, 1/4
Suppose 2*r = 3*y, r + y = -y. Factor -4/9*t + 2/9*t**2 + r.
2*t*(t - 2)/9
Let b(f) be the second derivative of -f**8/840 + f**7/210 + f**6/60 + 10*f**3/3 - 9*f. Let z(q) be the second derivative of b(q). Let z(n) = 0. Calculate n.
-1, 0, 3
Determine d so that -21 + 43/2*d - 1/2*d**2 = 0.
1, 42
Let s(v) = -1. Suppose 0 = w + x + x + 2, -19 = 5*w + x. Let y(p) = 9*p**3 - 33*p**2 + 15*p + 5. Let k(g) = w*s(g) + y(g). Factor k(l).
3*(l - 3)*(l - 1)*(3*l + 1)
Let o(a) be the first derivative of 12 + 0*a + 35/2*a**2 - 5/3*a**3. Factor o(s).
-5*s*(s - 7)
Suppose 2*d**2 + 0*d - 13/3*d**4 + 0 - 37/3*d**3 = 0. What is d?
-3, 0, 2/13
Suppose 4*r = 4*m - 264, -5*r - 5*m - 338 - 12 = 0. Let b be -3 + (-1)/(20/r). Determine u so that 0 - 2/5*u**3 + b*u**4 + 0*u + 0*u**2 = 0.
0, 1
Let c = -308 - -308. Let i(p) be the second derivative of c + 9/10*p**2 - 1/10*p**3 - 3/20*p**4 + p + 3/100*p**5. Suppose i(w) = 0. Calculate w.
-1, 1, 3
Suppose 0 = 2*y + 3*l, 0 = 2*y + 4*l - 3*l - 4. Let s(u) = 5*u + 2. Let d be s(0). Factor -1/5*x**4 + 1/5*x**y - 1/5*x + 0 + 1/5*x**d.
-x*(x - 1)**2*(x + 1)/5
Let m(f) be the second derivative of f**4/24 + 11*f**3/12 + 9*f**2/2 + 3*f - 3. Let m(a) = 0. What is a?
-9, -2
Factor -234*w**2 + 239*w**2 + 3*w + 7*w + 10*w.
5*w*(w + 4)
Let n(k) be the first derivative of -k**4/26 - 124*k**3/39 - 236*k**2/13 - 464*k/13 + 483. Factor n(h).
-2*(h + 2)**2*(h + 58)/13
Suppose 57/4*r**2 - 6*r - 21/4*r**3 - 3 = 0. What is r?
-2/7, 1, 2
Let s(h) be the first derivative of h**4/4 - 3*h**3 + 5*h**2/2 + 24*h + 8. Let c be s(8). Determine o, given that -1/3*o + c - 1/3*o**2 = 0.
-1, 0
Let l(v) = 6*v + 45. Let x be l(13). Factor -125*m**5 + 2*m + 4*m**3 + x*m**5 - 4*m.
-2*m*(m - 1)**2*(m + 1)**2
Suppose 3*b - 6 = -3. Let v = 4 - b. Let -v*k**2 - k**2 - 2*k + 3*k**2 + 1 - 2 = 0. Calculate k.
-1
Let z(l) = -2*l + 25. Let m be z(11). Let s(r) be the first derivative of 2/3*r**m + 2*r + 2*r**2 + 2. Determine k, given that s(k) = 0.
-1
Let f(z) be the second derivative of -2/15*z**6 + 0 - z**2 + z**4 + 13*z - 1/20*z**5 - 5/6*z**3. Factor f(p).
-(p - 1)**2*(p + 2)*(4*p + 1)
Let x(u) be the first derivative of 2/25*u**5 + 7/5*u**2 + 4/5*u + 1/2*u**4 + 6/5*u**3 + 11. Factor x(v).
2*(v + 1)**3*(v + 2)/5
Let l(c) be the second derivative of -c**4/4 - 11*c**3/2 + 39*c**2 + 138*c. Determine a so that l(a) = 0.
-13, 2
Let 30568*a - 9804*a**2 - 6216*a**3 + 98*a**4 + 4833*a + 3390 + 106580*a**2 + 4802 + 21431*a = 0. Calculate a.
-2/7, 32
Let z be (-2)/40*(-440)/15 + (-20)/30. Determine s so that 24/5*s**2 + 48/5*s + z*s**3 + 32/5 = 0.
-2
Determine f, given that -9928*f + 9790*f - 144*f**3 + 279*f**2 - 3*f**4 + 6*f**4 = 0.
0, 1, 46
Let n(j) = j - 3. Let b be n(5). Suppose a - 5*a + 3*x + 13 = 0, b*x + 14 = 4*a. Factor -a*c + 5*c**2 + 6*c + 2*c**3 - 4*c**3 + 4*c**4 - 9*c**4.
-c*(c - 1)*(c + 1)*(5*c + 2)
Let w(m) be the second derivative of m**6/120 - m**5/40 - m**4/4 + m**3/6 - 6*m. Let r(b) be the second derivative of w(b). Factor r(x).
3*(x - 2)*(x + 1)
Let k = 52 - 49. Suppose k*o + 2*o = 0. Factor 1/2*i + o - i**2.
-i*(2*i - 1)/2
Let t(p) be the second derivative of -p**5/5 + 2*p**4 + 8*p**3/3 - 48*p**2 + 12*p + 1. Factor t(u).
-4*(u - 6)*(u - 2)*(u + 2)
Let b(m) be the first derivative of 242*m**3/21 - 44*m**2 + 56*m + 301. Factor b(n).
2*(11*n - 14)**2/7
Let p(y) = -y**3 + 29*y**2 + 32*y - 56. Let l be p(30). Let x(t) be the first derivative of 0*t + 1/30*t**3 - 6 + 0*t**2 - 1/40*t**l. Factor x(a).
-a**2*(a - 1)/10
Let k(y) = -4*y**3 - 120*y**2 - 232*y - 114. Let c(s) = 9*s**3 + 241*s**2 + 465*s + 228. Let w(l) = 4*c(l) + 10*k(l). Factor w(n).
-4*(n + 1)**2*(n + 57)
Let i be 2 + (5 - 3) + -2. Determine w so that -w**i + w**3 + w**2 - 2*w + w**2 = 0.
-2, 0, 1
Factor -3/4*s**4 - 12*s**2 + 0 + 6*s**3 + 0*s.
-3*s**2*(s - 4)**2/4
Let p(u) = 4*u**2 - 44*u. Let m be p(11). Let -3/2*n**3 + 0 + 3/2*n**2 + 3/8*n**4 + m*n = 0. What is n?
0, 2
Suppose 0 = 4*x - 2*x - 4*j - 178, 0 = 3*j - 6. Suppose 18 + x = 3*n. Factor 0*w + n*w**4 - 2*w**5 - 35*w**4 + 0*w.
-2*w**4*(w - 1)
Let c(r) be the first derivative of 4*r**3/3 - 18*r**2 + 32*r + 85. Suppose c(w) = 0. What is w?
1, 8
Let r be -4 + 1 + 1 + (-41)/(-21). Let f = 2/7 - r. Determine w, given that -w**2 + 0 - 2/3*w - f*w**3 = 0.
-2, -1, 0
Let v(x) be the third derivative of -x**7/420 + x**6/120 + x**5/120 - x**4/24 + 3*x**2 + 4*x. Suppose v(g) = 0. Calculate g.
-1, 0, 1, 2
Factor 10*r - 2*r**3 - 97*r**2 - 90*r**2 - r**4 + 8*r**3 - 3 + 175*r**2.
-(r - 3)*(r - 1)**3
Let t(l) be the first derivative of -l**7/2100 - l**6/300 - l**5/150 + 20*l**3/3 - 14. Let c(r) be the third derivative of t(r). Suppose c(o) = 0. Calculate o.
-2, -1, 0
Suppose 0 = -55*d + 162 + 58. Determine f, given that 0*f + 0 - 1/3*f**d + 2/3*f**3 - 1/3*f**2 = 0.
0, 1
Let d(v) be the third derivative of 0*v**3 + 1/8*v**6 + 5/24*v**4 + 0 + 18*v**2 + 1/63*v**7 + 5/18*v**5 + 0*v. Let d(w) = 0. Calculate w.
-3, -1, -1/2, 0
Let d = 120 - -11. Factor 15*p**2 + 5 - d*p + 282*p - 131*p.
5*(p + 1)*(3*p + 1)
Let f(t) = -t**2 - 5*t + 26. Let d be f(-8). What is y in -69 - 10*y**3 + 5*y**5 - 41*y**d - 10*y**2 + 10*y**4 + 11*y**2 - 35*y + 59 = 0?
-1, 2
Let s = 19831/3 + -6610. Factor 4*v - 8/3 - v**3 - 2/3*v**2 + s*v**4.
(v - 2)**2*(v - 1)*(v + 2)/3
Let g be -75 + (28/(-35))/(4/10). Let h = 79 + g. What is p in 3/2 + 3*p**h - 9/2*p**4 - 3*p**3 + 9/2*p - 3/2*p**5 = 0?
-1, 1
Let 2/3*i**2 + 8/9*i - 8/9*i**3 + 2/9*i**4 - 8/9 = 0. What is i?
-1, 1, 2
Solve 334*j - 22*j**2 - 44 + 4 - 48 + 28 = 0.
2/11, 15
Determine b so that 1 - 2/3*b - 1/3*b**2 = 0.
-3, 1
Let m(v) be the third derivative of -v**6/72 - 31*v**5/360 - v**4/48 - 26*v**2 + v. What is x in m(x) = 0?
-3, -1/10, 0
Let y(d) be the second derivative of 8*d + 0*d**3 - 4*d**2 + 1/10*d**5 + 0 + 1/2*d**4. Factor y(z).
2*(z - 1)*(z + 2)**2
Find u such that 604 + 4*u**3 + 2112*u + 1036 - 188*u**2 + 664 = 0.
-1, 24
Let d(b) be the third derivative of -b**7/420 + b**6/40 + 2*b**2 - 37. Solve d(s) = 0 for s.
0, 6
Let j = -6 + 6. Suppose j = -0*q - 5*q + 10. Factor -7*b**2 + 3 + 3*b**q - 1 - 10*b + 12*b**2.
2*(b - 1)*(4*b - 1)
Let r = 22 + -20. Factor -5 + 3*j + j + 289*j**2 - 293*j**r + 29.
-4*(j - 3)*(j + 2)
Let m = 65 - 107. Let f = -40 - m. Solve 18/5 + 12/5*x + 2/5*x**f = 0.
-3
Solve 4/5*w**5 - 26/5*w**2 + 77/5*w**3 + 107/5*w**4 + 0*w + 0 = 0 for w.
-26, -1, 0, 1/4
Let m(u) be the second derivative of -81*u**5/10 + 98*u**4/3 - 76*u**3/3 + 8*u**2 + 21*u. Let y(k) = -k**2. Let d(c) = -m(c) + 4*y(c). Factor d(z).
2*(z - 2)*(9*z - 2)**2
Let y(g) be the third derivative of 0*g + 1/180*g**6 - 1/270*g**5 + 0 + 1/1512*g**8 + 0*g**3 + 7*g**2 - 1/315*g**7 + 0*g**4. Determine f so that y(f) = 0.
0, 1
Let y(d) be the second derivative of -d**6/80 + 3*d**5/40 - 3*d**4/16 + d**3/4 - 3*d**2/16 + 420*d. Factor y(s).
-3*(s - 1)**4/8
Let v be (-2 + 4 + (0 - -2))/3. What is j in 0 - 1/3*j**5 - 1/3*j - 2*j**3 - 4/3*j**4 - v*j**2 = 0?
-1, 0
Suppose -2/3*t**3 - 4/3*t**2 + 4/3 + 2/3*t = 0. Calculate t.
-2, -1, 1
Suppose -8 = 4*p - 20. Suppose -4*f**3 + 1 - 4 + 2 + p*f + 0*f = 0. What is f?
-1, 1/2
Let s(h) = 2*h**3 - 115*h**2 + 594*h + 723. Let q(b) = -25*b**3 + 1380*b**2 - 7130*b - 8675. Let v(k) = -3*q(k) - 