**2.
-n*(n - 1)**2*(n + 1)/2
Suppose -12 = 11*d - 14*d. Let q = -15/4 + d. Factor 0*k + 1/4*k**5 + 1/4*k**2 + 0 - 1/4*k**4 - q*k**3.
k**2*(k - 1)**2*(k + 1)/4
Factor 0 - 4/5*u - 2/5*u**2.
-2*u*(u + 2)/5
Suppose 77*d**2 - 73*d**2 - 9*d**3 + 2*d + 3*d**3 = 0. Calculate d.
-1/3, 0, 1
Suppose -3 = 2*c + 1. Let x be (20/200)/(c/(-8)). Factor -4/5*j**3 - x*j**2 - 2/5*j**4 + 0*j + 0.
-2*j**2*(j + 1)**2/5
Factor -6/7*z - 2/7*z**2 + 0.
-2*z*(z + 3)/7
Find z such that 0*z**2 + 2*z**2 - 7*z**2 + 3*z**3 - 7*z**2 = 0.
0, 4
Let y(b) = 2*b**3 + 6*b - 2. Let m(h) = -3 - 2*h + 2*h**3 - h**2 + 1 + 8*h. Let a(i) = -6*m(i) + 5*y(i). Factor a(k).
-2*(k - 1)**3
Let z(g) be the first derivative of g**4/4 + 2*g**3/3 - g**2/2 - 2*g + 1. Factor z(a).
(a - 1)*(a + 1)*(a + 2)
Let q(t) = -6*t**3 - 3*t**2 + 10*t + 6. Let y(b) = -2 - b**3 - 9*b + 4*b**3 - 3 + 2*b**3 + 3*b**2. Let r(m) = -6*q(m) - 7*y(m). Factor r(d).
(d - 1)**3
Suppose 9*p + 3*p = 36. Let -12/7*g**p - 2/7 - 2/7*g**2 + 8/7*g = 0. What is g?
-1, 1/3, 1/2
Solve 4/3*l + 0*l**4 + 0*l**2 + 4/3*l**5 + 0 - 8/3*l**3 = 0.
-1, 0, 1
Factor 1017 - 6*t - 1017 + 9*t**2 - 3*t**3.
-3*t*(t - 2)*(t - 1)
Let q(n) be the second derivative of -n**4/8 + 3*n**3 - 33*n**2/4 - 71*n. Find m such that q(m) = 0.
1, 11
Let m = 4 - 0. Suppose -s**5 - s + 2*s**2 - 1 + 2*s**3 + 0*s**4 + 0*s**3 + s**4 - 2*s**m = 0. What is s?
-1, 1
Let d(u) = 2*u**2 - 3*u - 3. Let s(b) = b**2 - b - 1. Let f(m) = -d(m) + 3*s(m). Factor f(p).
p**2
Suppose 0 = 2*d - d - 5. Suppose 2*u - d*u + 3 = 0, -4*a - 4*u = -20. Factor 2/11*r - 2/11*r**2 - 2/11*r**3 + 0 + 2/11*r**a.
2*r*(r - 1)**2*(r + 1)/11
Solve 4/3*d**3 + 0*d - 16/3 + 4*d**2 = 0.
-2, 1
Let f = -11 + 19. Let v(y) be the third derivative of -1/105*y**7 - 1/60*y**6 - 3*y**2 + 1/30*y**5 + 0*y**4 + 1/168*y**f + 0*y + 0 + 0*y**3. Factor v(c).
2*c**2*(c - 1)**2*(c + 1)
Let n(z) be the first derivative of z**7/126 + z**6/45 + z**5/60 - z + 3. Let l(x) be the first derivative of n(x). What is y in l(y) = 0?
-1, 0
Let h(q) be the second derivative of -q**2 - 3*q + 0*q**3 + 1/6*q**4 + 0. Factor h(j).
2*(j - 1)*(j + 1)
Let j = -10 + 15. Let t(l) be the third derivative of 1/210*l**7 - 1/24*l**4 - l**2 + 0*l - 1/40*l**6 + 1/20*l**j + 0 + 0*l**3. Let t(o) = 0. Calculate o.
0, 1
Let f(j) be the second derivative of j**9/13608 + j**8/7560 - j**7/3780 - j**6/1620 - 5*j**3/6 - 4*j. Let i(r) be the second derivative of f(r). Factor i(z).
2*z**2*(z - 1)*(z + 1)**2/9
Let i(g) = 2*g**2 + g + 2. Let f(q) = -5*q**2 - 2*q - 6. Let s(m) = -4*f(m) - 11*i(m). Factor s(d).
-(d + 2)*(2*d - 1)
Let o(f) be the third derivative of -1/48*f**8 - 7/24*f**4 + 1/105*f**7 + 0*f + 1/3*f**3 - 1/15*f**5 + 7/60*f**6 + 0 - f**2. Solve o(i) = 0.
-1, 2/7, 1
Suppose -4*x - 1 = -9. Let u be 1*2 + (4 + -7)/(-3). Factor 0*b**u + 0 + 0*b + 2/3*b**4 - 2/3*b**x.
2*b**2*(b - 1)*(b + 1)/3
Let k be (13 - -2)/(-4 - -5). Suppose 0 = -4*w + 5*r + k, -5*w - 8 = 4*r + 4. Let -1/5*z**2 + 1/5 + w*z = 0. What is z?
-1, 1
Let t(y) = 4*y**4 - 5*y**3 - 10*y**2 + 24*y - 11. Let s(o) = o**4 + o**3 - o**2 + 1. Let a(x) = s(x) - t(x). Factor a(i).
-3*(i - 2)*(i - 1)**2*(i + 2)
Let w(c) be the first derivative of 4*c**3/21 - 8*c**2/7 + 16*c/7 - 3. Factor w(n).
4*(n - 2)**2/7
Suppose -2/3*w - 8/3*w**2 - 2*w**3 + 0 = 0. What is w?
-1, -1/3, 0
Let b = -1 - -4/3. Factor -2/3*o**2 - 5/3*o**3 + 0*o - 4/3*o**4 + 0 - b*o**5.
-o**2*(o + 1)**2*(o + 2)/3
Factor 3 - 3*m**3 + 14*m**2 - 4*m**2 - m**2 - 9*m.
-3*(m - 1)**3
Let l(f) be the first derivative of f**3/6 + f**2/4 - 10. Factor l(t).
t*(t + 1)/2
Let c(h) be the second derivative of h**8/10080 + h**7/1890 + h**6/1080 - h**4/4 + 4*h. Let r(z) be the third derivative of c(z). Factor r(b).
2*b*(b + 1)**2/3
Let b = 7633/4780 + 3/956. Factor -b + 2/5*n**3 + 6/5*n**2 + 0*n.
2*(n - 1)*(n + 2)**2/5
Let s(d) = d**3 + 2*d**2 - 61*d + 22. Let h be s(-9). Determine b, given that 0 - 2*b**3 + 2/3*b**5 - 2/3*b**2 + 4/3*b + 2/3*b**h = 0.
-2, -1, 0, 1
Let w = 483 + -3379/7. Factor 4/7 + 8/7*h**2 + 10/7*h + w*h**3.
2*(h + 1)**2*(h + 2)/7
Factor -5/9 - 2/3*u - 1/9*u**2.
-(u + 1)*(u + 5)/9
Let u = 6767 + -19865/3. Let y = 147 - u. Factor x + y*x**2 - 2/3.
(x + 1)*(5*x - 2)/3
Let y be 88 - (2 + 0/(-2)). Suppose y*g**4 + 20*g + 24*g**5 - 21*g**2 + 62*g**2 + 116*g**3 + 31*g**2 + 2 = 0. What is g?
-1, -1/3, -1/4
Let i = -39 - -41. Let h be (-6)/(-9) + 2/(-21). Factor -h*r**i + 0 + 2/7*r**3 + 2/7*r.
2*r*(r - 1)**2/7
Let l be (0 + 0)*1/(-2). Suppose 21*z - 18*z = 0. Factor 2/5*b**2 + l + z*b - 6/5*b**3.
-2*b**2*(3*b - 1)/5
Suppose t - 4 = -t. Suppose 0*y - 4*y - 12 - 10*y + 9*y**2 + t*y = 0. What is y?
-2/3, 2
Let a(b) be the second derivative of -b**6/150 - b**5/20 - 3*b**4/20 - 7*b**3/30 - b**2/5 - 12*b. Suppose a(r) = 0. Calculate r.
-2, -1
Let y(g) be the first derivative of g**4/22 - 16*g**3/33 + 16*g**2/11 + 15. Let y(p) = 0. Calculate p.
0, 4
Let l(r) = r**3 - 7*r**2 + 7*r - 6. Let b be l(6). Factor -4*t**2 + 2*t**4 + b*t**2 + 2*t**2 + 0*t**4.
2*t**2*(t - 1)*(t + 1)
Let j(d) = 2*d**3 - 3*d**2 + 3. Let i(x) = x**3 - x**2 + x + 1. Let y(k) = -3*i(k) + 3*j(k). Factor y(l).
3*(l - 2)*(l - 1)*(l + 1)
Let m(s) be the second derivative of 1/10*s**6 + 0 - 6/5*s**5 - 12*s**3 + 11/2*s**4 + 27/2*s**2 + 5*s. Determine y, given that m(y) = 0.
1, 3
Let i(l) = l**2 - l - 2. Let u(y) = 2*y**2 - 2*y - 4. Let n(j) = -3*j**3 - 4*j**3 + 3*j**3 - j**2. Let o be n(-1). Let t(r) = o*u(r) - 7*i(r). Factor t(d).
-(d - 2)*(d + 1)
Let w be (-4)/6 + (-10)/(-15). Suppose x = -w + 2. Solve 0*o + 0 - 2/3*o**x = 0 for o.
0
Let m(z) be the third derivative of 0 - 2*z**2 + 2/315*z**7 + 1/90*z**5 + 0*z + 1/72*z**6 + 0*z**4 + 0*z**3 + 1/1008*z**8. Factor m(f).
f**2*(f + 1)**2*(f + 2)/3
Let f(l) = l - 2. Let u be f(4). Factor 0 - 1/4*j**u - 1/4*j.
-j*(j + 1)/4
Let b(o) = 5*o**2 - 4*o + 4. Let n be b(1). Let x(s) be the third derivative of 0*s + 1/42*s**n + 4*s**2 - 4/21*s**3 + 0 + 2/21*s**4. Let x(k) = 0. Calculate k.
-2, 2/5
Let k = 157/3420 - 5/171. Let y(d) be the third derivative of 0*d**3 + 0 - 4/105*d**7 - 2*d**2 + k*d**6 - 1/12*d**4 + 0*d + 2/15*d**5. Factor y(a).
-2*a*(a - 1)*(a + 1)*(4*a - 1)
Let n(q) be the first derivative of 4*q**3/15 - 4*q/5 - 4. Factor n(z).
4*(z - 1)*(z + 1)/5
Suppose 3*x - 5*x - 8 = 0, -x = 3*p - 29. Let q(m) = -9*m**2 - 9*m - 4. Let i(g) = -5*g**2 - 5*g - 2. Let n(r) = p*i(r) - 6*q(r). Solve n(d) = 0 for d.
-2, 1
Factor 3/4*k**4 + 1/4*k**2 + 0 - 3/4*k**3 + 0*k - 1/4*k**5.
-k**2*(k - 1)**3/4
Let j(a) = -3*a - 9. Let d be j(-4). Let f(l) be the first derivative of 1/2*l**4 + 0*l + 1/3*l**2 + 2/3*l**d + 2/15*l**5 + 1. Suppose f(t) = 0. Calculate t.
-1, 0
Let n(q) be the first derivative of 1/10*q**2 + 9 + 0*q - 1/15*q**3. Find d, given that n(d) = 0.
0, 1
Let j be 3 + 7/(-3) - 14/(-6). Let l(m) be the third derivative of 1/70*m**7 + 3*m**2 + 0*m**j + 0*m + 0*m**4 + 0*m**6 + 0 - 1/20*m**5. Factor l(p).
3*p**2*(p - 1)*(p + 1)
Suppose 0 = -4*w + 8*w - 8. Determine r, given that 37/2*r**2 + 9/2*r**4 + 15*r**3 + w + 10*r = 0.
-1, -2/3
Let p(s) = -s. Let r be p(-3). Let k be (0 + -2)*(-1)/r. Factor 0 + 0*c**3 + 0*c + 2/3*c**5 + 0*c**2 - k*c**4.
2*c**4*(c - 1)/3
Let i(u) be the third derivative of u**8/1680 - u**7/840 - u**6/360 + u**5/120 + 2*u**3/3 + 4*u**2. Let a(b) be the first derivative of i(b). Factor a(x).
x*(x - 1)**2*(x + 1)
Let y(i) be the second derivative of 0*i**2 + 1/15*i**6 + 5/6*i**4 - 2/3*i**3 - 2/5*i**5 + 0 - 2*i. Factor y(q).
2*q*(q - 2)*(q - 1)**2
Let n be 194/(-54)*(-12)/(-197). Let o = 2/591 - n. Suppose o*r + 2/9*r**2 + 0 = 0. Calculate r.
-1, 0
Let u(s) be the second derivative of -s**5/4 - 5*s**4/12 + 34*s. Factor u(t).
-5*t**2*(t + 1)
Suppose 5*h - 10 - 15 = 0. Determine d, given that -4*d**4 + 3*d**h - 4*d**2 - 4*d**5 + 0*d**2 - d - 6*d**3 = 0.
-1, 0
Factor 2*w - 4 - 1/4*w**2.
-(w - 4)**2/4
Let t(f) be the third derivative of -f**6/600 - 11*f**5/300 - f**4/5 + 6*f**3/5 + 20*f**2. Factor t(g).
-(g - 1)*(g + 6)**2/5
Solve 6/17*o**3 + 0 - 4/17*o - 2/17*o**4 + 2/17*o**2 - 2/17*o**5 = 0.
-2, -1, 0, 1
Let x(l) be the second derivative of l**7/12 + l**6/5 - 11*l**5/40 - l**4/2 + l**3/3 - 6*l. Let x(c) = 0. What is c?
-2, -1, 0, 2/7, 1
Let o be -47 + 47 + (1 - 1). Suppose 0*d**2 - 1/6*d**3 + 0*d**4 + 1/6*d**5 + o + 0*d = 0. What is d?
-