**2*(c - 2)*(3*c + 2)
Let k(b) = 2*b**2 + 11*b + 18. Let q be k(-3). Factor 4/5*n**5 + 0 + 6/5*n**4 + 0*n + 0*n**2 + 2/5*n**q.
2*n**3*(n + 1)*(2*n + 1)/5
Suppose 5*t = -4 + 19. Let o be t/(-9)*3 + 1. Determine m, given that 1/4*m**3 + 1/2*m**4 + o - 1/4*m - 1/2*m**2 = 0.
-1, -1/2, 0, 1
Solve -4*i + 3*i**2 - i**5 + 3*i**5 + 5*i**3 - 3*i**5 + 0*i**4 - 3*i**4 = 0.
-4, -1, 0, 1
Let a = -157/12 + 55/4. Factor 7/3*x**3 - 16/3*x**2 + 11/3*x - a.
(x - 1)**2*(7*x - 2)/3
Let l = 101 - 1009/10. Let w(q) be the second derivative of 0*q**3 + l*q**5 + 0*q**4 + 0 + 1/6*q**6 + 1/14*q**7 + 0*q**2 - q. Factor w(o).
o**3*(o + 1)*(3*o + 2)
Factor -2/11*t**5 - 6/11*t**4 + 2/11 + 4/11*t**2 - 4/11*t**3 + 6/11*t.
-2*(t - 1)*(t + 1)**4/11
Solve 0 + 219/4*p**4 - 3/4*p**2 - 3/2*p + 105/4*p**5 + 117/4*p**3 = 0 for p.
-1, -2/7, 0, 1/5
Let d(k) be the third derivative of 0 - 4/15*k**5 + 2*k**2 + 0*k + 1/12*k**4 + 1/12*k**6 + 2/3*k**3. Factor d(m).
2*(m - 1)**2*(5*m + 2)
Let p(t) = t + 10. Let s be p(-8). Factor 3*d**2 - 3*d**3 - 4*d**4 - d**2 - d**s.
-d**2*(d + 1)*(4*d - 1)
Let r(v) be the first derivative of v**3/3 - 3*v**2/2 + 2*v + 11. Suppose r(a) = 0. What is a?
1, 2
Suppose -2*h + 3*k = 6 + 6, 5*h = -4*k - 7. Let m be (3 + -2)*0/h. Factor -d**2 + 1/2*d - 1/2*d**5 + 0 + m*d**3 + d**4.
-d*(d - 1)**3*(d + 1)/2
Let p(r) = r**3 + 8*r**2 + 4. Let t be p(-8). Suppose h = -2*h. Factor -2/3*d**t - 2/9*d**5 + h*d + 0 - 2/3*d**3 - 2/9*d**2.
-2*d**2*(d + 1)**3/9
Let v be (-1 - -1)/(1 + -3). Let q(r) be the first derivative of 0*r**2 + 1/9*r**3 + 0*r - 3 - 1/15*r**5 + v*r**4. Factor q(t).
-t**2*(t - 1)*(t + 1)/3
Let x(g) be the third derivative of 1/24*g**4 + 0*g - 1/6*g**3 + 1/30*g**5 + 1/336*g**8 + 0 - 1/210*g**7 - g**2 - 1/60*g**6. Find s, given that x(s) = 0.
-1, 1
Let k(w) be the first derivative of -w**4 - 24. Factor k(b).
-4*b**3
Let u(l) = l**2 + 6*l - 7. Let b be u(-7). Factor b*z + 2/5*z**5 - 2/5*z**3 - 2/5*z**2 + 0 + 2/5*z**4.
2*z**2*(z - 1)*(z + 1)**2/5
Let m(p) be the first derivative of -6*p**5/5 + 21*p**4/20 + 3*p**3/5 + 65. Factor m(c).
-3*c**2*(c - 1)*(10*c + 3)/5
Let k(i) be the first derivative of 1/15*i**3 - 3*i - 1/50*i**5 + 1 + 1/5*i**2 - 1/30*i**4. Let f(q) be the first derivative of k(q). Factor f(y).
-2*(y - 1)*(y + 1)**2/5
Let j be (1/(-1) + -2)/(2 - 3). Let -6/5 + 24/5*t**2 + 3*t**j + 3/5*t = 0. What is t?
-1, 2/5
Let n = -57 + 62. Let s(o) be the third derivative of -1/480*o**6 + 0*o**3 + 1/840*o**7 + 0 + 0*o**n + 3*o**2 + 0*o**4 + 0*o. Factor s(g).
g**3*(g - 1)/4
Factor 1/5*x + 1/5*x**2 - 6/5.
(x - 2)*(x + 3)/5
Let z(c) = 2*c**2 - 9*c - 7. Let i(y) = y + 7. Let m(x) = 2*x + 13. Let j(n) = 11*i(n) - 6*m(n). Let s(t) = -14*j(t) + 2*z(t). Factor s(a).
4*a*(a - 1)
Let q(b) = 5*b**4 - 4*b**3 - b**2 + 7*b + 7. Let h(p) = -2*p**4 + 2*p**3 - 3*p - 3. Let y(i) = 14*h(i) + 6*q(i). Factor y(s).
2*s**2*(s - 1)*(s + 3)
Let n(v) be the second derivative of v**7/98 - 3*v**6/70 + 9*v**5/140 - v**4/28 + 3*v. Find u such that n(u) = 0.
0, 1
Let w(c) be the third derivative of -1/15*c**5 + 0 - 8*c**2 - 2/105*c**7 + 1/2*c**4 + 4/3*c**3 - 1/10*c**6 + 0*c. Factor w(p).
-4*(p - 1)*(p + 1)**2*(p + 2)
Find a, given that -4*a - 30*a**2 + 200*a**5 - 187*a**3 - 16*a**2 - 8*a**2 - 270*a**4 - 45*a**3 = 0.
-1/4, -1/5, 0, 2
Suppose -4*k + 24 = -k. Factor -25*l**2 - k - 10*l - 2 + 9.
-(5*l + 1)**2
Let s(v) be the third derivative of v**5/12 + 17*v**4/24 + v**3 - 18*v**2. Let s(g) = 0. Calculate g.
-3, -2/5
Let m(x) be the second derivative of x**5/100 + 7*x**4/60 + x**3/2 + 9*x**2/10 - 10*x. Suppose m(c) = 0. Calculate c.
-3, -1
Let c(p) be the third derivative of -1/330*p**5 + 1/132*p**4 + 0*p - 3*p**2 + 0 + 1/1155*p**7 - 1/660*p**6 + 0*p**3. Factor c(f).
2*f*(f - 1)**2*(f + 1)/11
Let y(j) be the third derivative of 7*j**8/80 - 11*j**7/50 - 17*j**6/200 + 73*j**5/100 - 4*j**4/5 + 2*j**3/5 - 3*j**2. Let y(t) = 0. What is t?
-1, 2/7, 1
Suppose 3*v + 10 = 10. Let u(g) be the second derivative of v*g**3 - 3*g - 1/75*g**6 + 0*g**2 + 0*g**5 + 0 + 1/30*g**4. Factor u(j).
-2*j**2*(j - 1)*(j + 1)/5
Let q(z) = -z**2 + 5*z + 7. Let n be q(6). Let h be (5 - n)/((-4)/(-2)). Determine x so that 0 + 0*x**h + 0*x + 8/11*x**4 - 2/11*x**3 = 0.
0, 1/4
Let i(t) = -t - 4. Let w be i(-5). Let x be w/4 - (-7)/(-28). Factor -1/3*v + 0*v**2 + 1/3*v**3 + x.
v*(v - 1)*(v + 1)/3
Let r(d) = d**2 + d + 2. Suppose 5*p = 4*p. Let l be r(p). Factor -j**4 - j + l*j**3 + j**4 - j**5.
-j*(j - 1)**2*(j + 1)**2
Let t = 609 - 607. Determine s so that -9*s**t - 3/2 - 3/2*s**4 + 6*s**3 + 6*s = 0.
1
Let k = -37/19 - -206/57. Factor -k*v**3 + 4/3*v + 0 - 8/3*v**2.
-v*(v + 2)*(5*v - 2)/3
Suppose -13 - 7 = -5*p. Let r(y) = 3*y**2 - y + 1. Let s be r(1). Find w such that 0*w + 0 + 0*w**2 - 1/2*w**p - 1/2*w**s = 0.
-1, 0
Let a = -39 - -43. Suppose a*s - 20 = -s. Factor 9/5*h**s - 6/5*h**3 + 0*h + 0 - 3/5*h**2.
3*h**2*(h - 1)*(3*h + 1)/5
Let m(i) = 4*i. Let j(z) = z**2 - 4*z. Let r(l) = -6*j(l) - 5*m(l). Factor r(v).
-2*v*(3*v - 2)
Let w be 0/(-2) - 166/(-126). Let q = 1/63 + w. Factor 2/3*n + 4/3*n**2 + 0*n**3 - 2/3*n**5 - q*n**4 + 0.
-2*n*(n - 1)*(n + 1)**3/3
Let a(k) be the first derivative of -k**7/945 - k**6/540 - 7*k**2/2 + 1. Let w(d) be the second derivative of a(d). Determine q, given that w(q) = 0.
-1, 0
Suppose 2*u = -3*g + 5, -4*u - 15 = -g + 10. Let 3*b**2 + 0*b**2 - 4*b**2 + b**4 - 3*b**3 + 2*b**3 + b**g = 0. What is b?
-1, 0, 1
Factor 8*f**3 - 20*f**2 - 1 + 17/2*f.
(f - 2)*(4*f - 1)**2/2
Suppose 0 = 3*w + 36 - 0. Let g be ((-24)/(-16))/((-9)/w). Factor -24/5*a + 18/5*a**g + 8/5.
2*(3*a - 2)**2/5
Let -1/2*g**2 - g**3 + 0 + 1/2*g**4 + g = 0. Calculate g.
-1, 0, 1, 2
Factor 40/3*u + 100/3 + 4/3*u**2.
4*(u + 5)**2/3
Let g(s) be the third derivative of s**6/96 - s**5/80 - s**4/8 - s**3/6 + 16*s**2. Factor g(b).
(b - 2)*(b + 1)*(5*b + 2)/4
Factor 4*o**4 + 3*o**3 + 0*o**3 + 4*o**3 - 3*o**3.
4*o**3*(o + 1)
Let f = 18 + -16. Let -f*l**2 + 4 - 5*l - 6*l**2 + l = 0. Calculate l.
-1, 1/2
Let t(v) = -v - 6. Let l be t(-8). Factor -4*u + 2 - 4 + u**2 - 1 - l*u**2.
-(u + 1)*(u + 3)
Let t = 8 - 4. Let u be (-50)/(-18) + 12/54*1. Determine k so that -2/3*k**t - 1/3*k**5 + 1/3*k + 0 + 2/3*k**2 + 0*k**u = 0.
-1, 0, 1
Let x(c) be the third derivative of -c**6/660 + c**5/330 + c**4/66 - 5*c**2. Suppose x(j) = 0. What is j?
-1, 0, 2
Let g(n) = n**3 - n - 1. Let k be g(2). Suppose f = -0*f - k*c - 10, -3 = -3*f - 4*c. Factor f*a**4 + 4*a**4 + a**5 + a**2 + 3*a**3 - 6*a**4.
a**2*(a + 1)**3
Let u be 1/8 + 104/(-832). Factor u*j + 3/7*j**5 + 0 + 1/7*j**2 - 5/7*j**4 + 1/7*j**3.
j**2*(j - 1)**2*(3*j + 1)/7
Let p be (-35 - -38) + (-6)/2 + 0. Find x, given that 1/4*x**2 - 1/2*x + p = 0.
0, 2
Let p(i) be the third derivative of -2*i**7/105 - 7*i**6/60 - 3*i**5/10 - 5*i**4/12 - i**3/3 + 14*i**2. Solve p(n) = 0.
-1, -1/2
Let l(d) = -d**3 - 5*d**2 + 4*d - 8. Let o be l(-6). Let x = -15/11 + 67/33. Factor 2/3*g**5 - x*g**o + 2/3*g**2 + 0*g - 2/3*g**3 + 0.
2*g**2*(g - 1)**2*(g + 1)/3
Factor -3/4*a**2 + 3/4*a + 3/4 - 3/4*a**3.
-3*(a - 1)*(a + 1)**2/4
Let t be (3/(-9)*0)/(-1). Let j = t + 4. Factor 4*k**j - 3*k**3 - 2 - 7*k**2 + 3 + 3*k + k**2 + k**2.
(k - 1)**2*(k + 1)*(4*k + 1)
Solve -1/8*m**2 + 1/2*m - 3/8 = 0.
1, 3
Let u(j) be the third derivative of -1/60*j**4 + j**2 + 0*j - 1/150*j**5 + 0 + 0*j**3. Factor u(y).
-2*y*(y + 1)/5
Suppose p - 5 = -2*h, -7 = -p - 2*h - 2*h. Factor -8/3*f**2 - 2*f**p - 8/9*f + 0.
-2*f*(3*f + 2)**2/9
Let r(k) = k**2 - 12*k - 26. Let o be r(-2). What is x in -1/3*x + 0*x**o - 1/6*x**4 + 1/3*x**3 + 1/6 = 0?
-1, 1
Let s(b) be the second derivative of -b**4/24 - 3*b. Solve s(l) = 0.
0
Let s be (-2)/(-2) + (-16)/48. Factor 2/3*t**2 + 0 - s*t.
2*t*(t - 1)/3
Let d(s) be the first derivative of 1/2*s**2 + 1/60*s**5 - 1/48*s**6 + 5/48*s**4 + 0*s - 2 - 1/6*s**3. Let h(j) be the second derivative of d(j). Factor h(x).
-(x - 1)*(x + 1)*(5*x - 2)/2
Factor 0 - 3*f**3 - 1/4*f**5 + 3/2*f**4 + 5/2*f**2 - 3/4*f.
-f*(f - 3)*(f - 1)**3/4
Factor -1/3*p**2 + 0 + 1/3*p - 1/3*p**3 + 1/3*p**4.
p*(p - 1)**2*(p + 1)/3
Let j = -8 - -17. Let r be 11/j - (2 + -1). Find f such that 0 - r*f**2 + 2/9*f = 0.
0, 1
Suppose 3*n = -4*y, 5*n + 3*y + 1 = 3*n. Determine d, given that 2/7*d**n + 2/7*d - 2/7*d**3 + 0 - 2/7*d**2 = 0.
-1, 0, 1
Factor 1/2*t**4 +