2. Let g(m) = -2*m**3 - 3*m**2 + 8*m - 7. Let r(k) = 4*g(k) + 4*y(k). Factor r(t).
-4*(t - 1)**2*(t + 5)
Let o be 8*9/6*6/8. Let -13*i**2 + 27*i**2 - i**4 - 10*i**2 + 6*i**3 - o*i**4 = 0. Calculate i.
-2/5, 0, 1
Let a(d) = -d**4 - 5*d**2 + 3*d - 3. Let j(x) = -38*x**2 + 4 - 5*x - 4 + 5 - x**3 + 47*x**2 + 2*x**4. Let i(p) = -5*a(p) - 3*j(p). Factor i(y).
-y**2*(y - 2)*(y - 1)
Let t = -3511/4 - -878. Factor -t*a**3 + 0*a**2 + 1/2 + 3/4*a.
-(a - 2)*(a + 1)**2/4
Let d(h) be the third derivative of h**6/360 - 2*h**5/45 + 5*h**4/18 - 8*h**3/9 + 16*h**2. Factor d(g).
(g - 4)*(g - 2)**2/3
Let n = -11338 - -11340. Determine u, given that 40*u + 5/2*u**3 - 20*u**n + 0 = 0.
0, 4
Let q(g) be the third derivative of g**7/525 - g**6/300 - g**5/75 - 11*g**2 - 5*g. Factor q(t).
2*t**2*(t - 2)*(t + 1)/5
Solve 64/19*a**4 - 18/19*a**3 + 78/19*a**5 - 4/19*a**2 + 0 + 0*a = 0 for a.
-1, -2/13, 0, 1/3
Factor 9/2*j**2 + 27/2 + 27/2*j + 1/2*j**3.
(j + 3)**3/2
Suppose 2*y - 7*x = -4*x + 25, -2*y + 4 = 4*x. Let f be (-6)/(-9)*36/y. What is j in -1/2*j**f + 1/2 - 1/2*j**2 + 1/2*j = 0?
-1, 1
Solve 4*x**3 + 3*x**4 + 4 + 41*x**2 - 11*x**4 - 22*x - 2*x**3 - 17*x**2 = 0 for x.
-2, 1/4, 1
Let f be (1/3)/(2/(-30)). Let k be f/15 - (-13)/3. Factor 0*x**3 + 2*x + 0*x**3 + 4 - 2*x**3 + 2*x**k - 6*x**2.
2*(x - 2)*(x - 1)*(x + 1)**2
Let f be (-1)/((-3)/(4 + -7)) - 34/(-10). Solve f*g**4 + 8/5*g**3 - 12/5*g**2 - 8/5*g + 0 = 0 for g.
-1, -2/3, 0, 1
Factor -3/5*p + 3/5*p**2 - 3/5 + 3/5*p**3.
3*(p - 1)*(p + 1)**2/5
Suppose 0 = 79*t + 41*t. What is g in 2/19*g**5 + t*g**2 + 0*g**4 + 0 + 2/19*g - 4/19*g**3 = 0?
-1, 0, 1
Let z be 1 - (4 + -8)/2. Factor -8*u**2 - 7 + u**3 + 16*u + 10 - z.
u*(u - 4)**2
Suppose -4*t - 4*z + 12 = 0, 0 = z - 0*z - 1. Factor -21 + 10 + 5*r**3 + 10*r**t + 1 - 5*r.
5*(r - 1)*(r + 1)*(r + 2)
Let q(y) be the first derivative of -y**4/2 - 2*y**3 + y**2 + 6*y - 159. Determine n so that q(n) = 0.
-3, -1, 1
Let d(g) = g - 15. Let t be d(0). Let w = t + 27. Let 8*q - w*q**3 - 6*q**2 - 2*q - 3 + 6*q + 9*q**4 = 0. What is q?
-1, 1/3, 1
Suppose 4*n - 180 = 56. Suppose 5*h - x = 8, h = 6*x - 4*x - 2. Factor n*w**h + 12*w**2 + w**2 + 24*w + 2.
2*(6*w + 1)**2
Let z(b) = -b**4 - b**3 + b + 2. Let i(w) = -w**5 + 26*w**4 - 168*w**3 - 420*w**2 - 223*w + 4. Let p(h) = -i(h) + 2*z(h). Factor p(k).
k*(k - 15)**2*(k + 1)**2
Suppose -4*t - 2*u + 4*u + 18 = 0, -5*u - 17 = 4*t. Factor 14/9*y + 10/9*y**t + 4/9.
2*(y + 1)*(5*y + 2)/9
Suppose -17*q + 32 = -9*q. Factor 2 + 2*x**4 - 6*x**2 + 726*x + 2*x**2 - q*x**3 - 724*x + 2*x**5.
2*(x - 1)**2*(x + 1)**3
Let g(a) = 5*a**5 - 10*a**4 + 40*a**3 - 38*a**2 + 15*a. Let f(t) = 3*t**5 - 9*t**4 + 39*t**3 - 39*t**2 + 15*t. Let x(q) = -4*f(q) + 3*g(q). Factor x(s).
3*s*(s - 1)**3*(s + 5)
Let g(a) = -a**3 - 3*a**2 + 2. Let f be g(-3). Suppose 2*v = 4*d - 5 + 1, 5*v = f*d - 10. Factor d + 1/3*l**2 + 4/3*l**3 - l**4 - 2/3*l.
-l*(l - 1)**2*(3*l + 2)/3
Let -169/4 - 1/4*b**2 + 13/2*b = 0. Calculate b.
13
Let t be -11 - 22*(-8)/16. Factor 1/5*o**2 - 1/5 + t*o.
(o - 1)*(o + 1)/5
Let o be ((-36)/(-30) + -1)/(9/45*5). Find g, given that 7/5 + o*g**2 - 8/5*g = 0.
1, 7
Let o(s) be the second derivative of -s**7/2100 - 3*s**6/100 - 81*s**5/100 - 5*s**4/6 - s**3/3 - 4*s. Let x(a) be the third derivative of o(a). Factor x(k).
-6*(k + 9)**2/5
Factor 111*y**3 + 71*y**3 - 17*y**3 + 320*y + 10*y**4 + 720*y**2.
5*y*(y + 8)**2*(2*y + 1)
Let p(y) = 3*y**2 + 41*y + 59. Let q be p(-25). Let s = q - 15447/17. Solve -2/17*j**2 - 2/17*j**4 - s*j**3 + 4/17 + 6/17*j = 0 for j.
-2, -1, 1
Factor 38*q**2 + 41*q**2 + 584*q - 83*q**2 - 21316.
-4*(q - 73)**2
Let o(x) be the first derivative of x**4/4 - 7*x**3/3 - 4*x**2 + 348. Let o(m) = 0. What is m?
-1, 0, 8
Let m(h) be the third derivative of h**8/1848 - 13*h**7/1155 + 47*h**6/660 - 23*h**5/330 - 4*h**4/11 + 12*h**3/11 + h**2 + 30*h. Find y such that m(y) = 0.
-1, 1, 6
Let u(d) = -3*d**3 - 43*d**2 - 116*d - 120. Let b(a) = -3*a**3 - 44*a**2 - 115*a - 123. Let m(l) = -4*b(l) + 5*u(l). Let m(o) = 0. What is o?
-9, -2
Suppose -7*x + 34 = -1. What is s in 16 - x - 6 - 6 + s**2 = 0?
-1, 1
Let b(j) be the first derivative of 2*j**3/3 + 6*j**2 + 10*j + 148. Factor b(n).
2*(n + 1)*(n + 5)
Let -52/5*m - 119/5*m**3 - 4/5 - 167/5*m**2 = 0. What is m?
-1, -2/7, -2/17
Let l = 272/5 + -54. Let z = 109 + -109. Factor 4/5*s**4 + z*s**3 + 0 - l*s**5 + 2/5*s - 4/5*s**2.
-2*s*(s - 1)**3*(s + 1)/5
Suppose -3*t - 3*a = -21, 0 = 2*t - 3*t - 5*a + 19. Suppose -t*w + 5*w = -d + 4, -2*w = -d - 8. Find s such that -2 + 1/2*s**w + 2*s**3 + 3/2*s**2 - 2*s = 0.
-2, -1, 1
Let v = -33 - -13. Let c be (-2)/((v - -18)/(8/2)). Find f such that -24*f**2 - 1/4*f**4 + 64*f + c*f**3 - 64 = 0.
4
Let l be 1 + 58/(-182)*-11 - -1. Let k = l + -66/13. Factor 2/7*z**5 + 4/7*z**2 - 2/7*z**3 - k*z**4 + 0*z - 1/7.
(z - 1)**3*(z + 1)*(2*z + 1)/7
Let o(b) be the second derivative of -32/3*b**3 - 1/15*b**5 + 0 - 4/3*b**4 + 5*b - 4*b**2. Let l(z) be the first derivative of o(z). Let l(d) = 0. What is d?
-4
Determine p so that 2 + 21/2*p + 53/4*p**2 - 7/4*p**4 + 3*p**3 = 0.
-1, -2/7, 4
Let z(t) be the third derivative of 0 + 0*t - 1/540*t**5 - 8*t**2 + 1/108*t**4 - 1/54*t**3. Determine q so that z(q) = 0.
1
Let k(l) = -10*l**2 - 3*l - 3. Let w be k(-3). Let t be (0 + -1)*w/28. Solve 1/2*h**t + 1/2*h + h**2 + 0 = 0.
-1, 0
Let t(q) be the first derivative of q**7/70 + 13*q**6/40 + 12*q**5/5 + 9*q**4/2 - 27*q**2/2 + 28. Let i(m) be the second derivative of t(m). Factor i(b).
3*b*(b + 1)*(b + 6)**2
Let f(r) be the second derivative of r**4/3 + 12*r**3 + 162*r**2 + 2*r - 29. Factor f(u).
4*(u + 9)**2
Let j be 5/1 + (-1 - 0). Suppose 2*x = 3*t - x - 15, -j*t - 5*x = -56. Solve -3 + 0*a**2 + t*a - 3 - 3*a**2 = 0.
1, 2
Let 3378 - 6762 - 24*c - 28*c**2 + 3384 - 4*c**3 = 0. Calculate c.
-6, -1, 0
Let d(w) be the second derivative of w**6/80 - 9*w**5/160 - w**4/8 - 48*w. Let d(n) = 0. Calculate n.
-1, 0, 4
Factor 21/4*k - 3/8*k**2 - 99/8.
-3*(k - 11)*(k - 3)/8
Let o = 1493/20 + -362/5. Factor 37/4*x + 15*x**2 + o*x**3 + 3/2.
(x + 6)*(3*x + 1)**2/4
Let b be (1 + (-78)/70)/((-48)/56). Let w(p) be the first derivative of 5 + 0*p**2 - 1/10*p**4 + 0*p + b*p**3. Find a, given that w(a) = 0.
0, 1
Let q(t) = t**2 - 141*t + 683. Let v be q(5). Factor 1/3*i**2 + v*i + 8/3.
(i + 1)*(i + 8)/3
Let t(d) be the second derivative of -3*d**5/40 - d**4/6 + 5*d**3/12 + d**2/2 + 2*d + 3. Factor t(b).
-(b - 1)*(b + 2)*(3*b + 1)/2
Suppose 15*d + 21*d = 3*d + 165. Determine f so that 1/2 + 4*f**4 + f**3 + 5/4*f - 9/4*f**d - 9/2*f**2 = 0.
-1, -2/9, 1
Let g(c) be the first derivative of 1/6*c**4 + 1/9*c**3 + 0*c**2 - 4*c - 2 + 1/45*c**6 + 1/10*c**5. Let w(b) be the first derivative of g(b). Factor w(t).
2*t*(t + 1)**3/3
Solve 0*r + 0 + 2/5*r**3 + 4/5*r**2 = 0 for r.
-2, 0
Let x(m) = -58*m**2 - 119*m - 4. Let s be x(-2). Factor -2/13*q**3 + 0*q**s + 8/13*q + 0.
-2*q*(q - 2)*(q + 2)/13
Suppose s + 12 = 2*v - 7*v, -s + 3*v = -12. Suppose s*w - 12 + 3 = 0. Factor 14/17*h + 2/17*h**w + 6/17 + 10/17*h**2.
2*(h + 1)**2*(h + 3)/17
Let g be 1 + (-14)/10 + 64/10. Let t be (108/14)/g - 1. Factor 4/7*a**5 - 3/7*a**3 + 4/7*a**4 + 0 + 1/7*a - t*a**2.
a*(a + 1)**2*(2*a - 1)**2/7
Factor 3*v**2 + 356*v + 12135 + 3707 - 4*v**2 + 3*v**2.
2*(v + 89)**2
Let c(w) be the third derivative of -w**7/630 + w**6/360 + 7*w**5/180 - w**4/72 - w**3/3 + 39*w**2 - 2*w. What is h in c(h) = 0?
-2, -1, 1, 3
Let x(o) be the first derivative of o**5/60 + o**4/3 + 7*o**3/6 - 7*o**2 - 3*o + 15. Let p(b) be the second derivative of x(b). Suppose p(r) = 0. Calculate r.
-7, -1
Let l(d) = -9*d**2 - 240*d - 5043. Let p(s) = 8*s**2 + 241*s + 5043. Let w(r) = 5*l(r) + 6*p(r). Solve w(y) = 0.
-41
Let j = -26657 - -26659. Solve 73/2*h**j + 21/2*h + 1 + 42*h**3 = 0 for h.
-1/3, -2/7, -1/4
Suppose j - p = 2, 4*j + 28*p = 33*p + 7. Let t(x) be the first derivative of -27*x - 3/2*x**4 - 36*x**2 - 13*x**j - 2. What is k in t(k) = 0?
-3, -1/2
Let k(m) = m**3 + 6. Let g be k(0). Suppose -2*p = -4*p + g. Solve 39*w**2 + 0*w**3 + 6*w**4 - 37*w**2 - 2*w**5 - 6*w**p = 0 for w.
0, 1
Let r(p) be the second derivative of -2*p**6/45 - p**5/20 - 49*p. Find z such that r(z) = 0.
-3/4, 0
Let f(k) be the first derivative of -k**7/14 + k**6/15 + k**5/3 + 2*k**4/9 + 13*k - 3. Let t(