 be 0 + 2 + -1 + 47. Let k = 37 + -19. Factor -k*i**5 - n*i**4 - 6*i + 0*i + 2*i + 2*i - 44*i**3 - 16*i**2.
-2*i*(i + 1)**2*(3*i + 1)**2
Let c(y) be the third derivative of y**7/2520 + y**6/1080 - y**3/6 - 3*y**2. Let j(d) be the first derivative of c(d). Factor j(p).
p**2*(p + 1)/3
Suppose -2*k - 4 = 0, 0 = -3*y + 3*k - 5 + 11. Let c(u) be the third derivative of 2*u**2 - 1/12*u**4 - 1/60*u**5 - 1/6*u**3 + 0*u + y. Solve c(t) = 0.
-1
Let x(l) = -10*l**3 - 2*l + 1. Let a be x(1). Let k = a + 18. Factor 3*g**2 - k*g**2 + g**3 + g**2 + 2*g**2.
g**2*(g - 1)
Let q(d) be the third derivative of -2/27*d**3 + 0 - 2/135*d**5 - 3*d**2 + 0*d + 5/108*d**4 + 1/540*d**6. Factor q(m).
2*(m - 2)*(m - 1)**2/9
Let a be (-4)/(-6) + 33/(-9). Let b = 5 + a. Factor -1 + 0 + b*q**2 - 1.
2*(q - 1)*(q + 1)
Let v be ((-4 + 3)/9)/(-1). Let n(j) be the second derivative of 0*j**2 - 2*j - v*j**3 + 1/18*j**4 + 0. Factor n(z).
2*z*(z - 1)/3
Factor -5/2*t**2 + t - 3/2*t**3 + 0.
-t*(t + 2)*(3*t - 1)/2
Let d be ((-62)/(-465))/(2/20). Factor 8/9*f**4 + 2/9*f + d*f**3 + 8/9*f**2 + 0 + 2/9*f**5.
2*f*(f + 1)**4/9
Let p(r) be the third derivative of 0*r - 3*r**2 + 1/144*r**4 - 1/360*r**5 + 1/36*r**3 - 1/720*r**6 + 0. Determine i so that p(i) = 0.
-1, 1
Let n(y) be the third derivative of 2*y**2 + 0*y + 0*y**3 - 1/15*y**5 + 0 - 1/3*y**4. Factor n(v).
-4*v*(v + 2)
Let i(z) be the third derivative of -z**7/1680 + z**6/720 + z**5/120 + z**3/2 - 2*z**2. Let q(a) be the first derivative of i(a). Factor q(s).
-s*(s - 2)*(s + 1)/2
Let j = -25/33 - -12/11. Let p(h) be the first derivative of -3 + 1/5*h**5 + 0*h + 1/2*h**4 + j*h**3 + 0*h**2. Factor p(z).
z**2*(z + 1)**2
Let u(p) be the second derivative of p**4/18 - 16*p**3/9 + 64*p**2/3 - 10*p. Solve u(w) = 0.
8
Let f be (12/15)/(2 + 8/(-5)). Determine z, given that 0*z + 1/2*z**f + 0*z**3 - 1/4*z**4 - 1/4 = 0.
-1, 1
Suppose -8*z + 0*z - z**2 + 2*z - 3 - 6 = 0. Calculate z.
-3
Factor 1/5*p**2 + 12/5*p + 0.
p*(p + 12)/5
Let h(i) be the second derivative of i**4/2 + 4*i**3/3 + i**2 - i. Factor h(k).
2*(k + 1)*(3*k + 1)
Let u(i) be the third derivative of -i**8/1008 + i**7/315 - i**5/90 + i**4/72 + 6*i**2. Factor u(p).
-p*(p - 1)**3*(p + 1)/3
Factor 0 - 2*v**3 + 10/9*v**4 + 14/9*v**2 - 2/9*v**5 - 4/9*v.
-2*v*(v - 2)*(v - 1)**3/9
Solve 0*n**3 + 0 + 0*n - 2/5*n**2 + 2/5*n**4 = 0 for n.
-1, 0, 1
Suppose 4*p + r - 3 = -7, -4 = 5*p + r. Find i, given that -28/3*i**3 + 20/3*i**2 + 4*i**4 + p - 4/3*i = 0.
0, 1/3, 1
Let p = 0 + 7. Suppose 5*t - 2*n = 19, 4*t + 0 - 2 = -5*n. Factor -j**3 + j**4 + 3*j**2 - p*j + 6*j - 2*j**t.
j*(j - 1)**3
Let v be 4/(-5)*(-15)/(-2). Let j = v + 8. Factor -4*g**2 - j*g**3 + g**2 + 0*g**2 - g**2.
-2*g**2*(g + 2)
Let g(h) = 15*h**4 - 63*h**3 + 93*h**2 - 57*h + 10. Let y(u) = 255*u**4 - 1070*u**3 + 1580*u**2 - 970*u + 170. Let w(b) = 35*g(b) - 2*y(b). Factor w(z).
5*(z - 2)*(z - 1)**2*(3*z - 1)
Let a(x) be the first derivative of x**6/42 - 3*x**5/35 + 4*x**3/21 - 6. Solve a(c) = 0.
-1, 0, 2
Let j(w) = 0*w**4 + w**4 + 2*w + 2*w**3 - 4*w. Let a(f) = 1. Let r(h) = -4. Let o(u) = 3*a(u) + r(u). Let t(z) = j(z) + o(z). Suppose t(s) = 0. Calculate s.
-1, 1
Let l(u) be the first derivative of 1/210*u**5 + 0*u**4 - 1/21*u**3 - 1/2*u**2 + 0*u - 1. Let p(x) be the second derivative of l(x). Factor p(r).
2*(r - 1)*(r + 1)/7
Let s(o) = -o + 57. Let u be s(0). Factor 0*q**2 + u*q + 25*q**4 + 36*q**3 + 24*q**2 - 9*q**4 - 53*q.
4*q*(q + 1)**2*(4*q + 1)
Let z be 160 + 0/2 + 0. Let v be (-56)/z + 6/10. Suppose -3/4*r**3 + 0 - 1/4*r**4 + 3/4*r**5 + 0*r + v*r**2 = 0. What is r?
-1, 0, 1/3, 1
Suppose -5*f + 5*c + 45 = -15, -f = -2*c - 17. Suppose f*r - 10 = 2*r. Let 8/3*k**r - 2*k - 2/3 = 0. Calculate k.
-1/4, 1
What is s in -6*s**2 + 14/3*s + 4/3 = 0?
-2/9, 1
Factor 5/4*q**2 + 5/4*q**3 - 5/4*q**5 - 5/4*q**4 + 0*q + 0.
-5*q**2*(q - 1)*(q + 1)**2/4
Let v(i) = -i - 2. Let q be v(-6). Suppose -3*h - 26 = -q*s - h, 0 = 5*h + 25. Suppose 0*t + 0*t**2 + 0 + 1/5*t**3 - 1/5*t**s = 0. Calculate t.
0, 1
Let w(b) be the third derivative of 0*b**4 + 2*b**2 - 1/300*b**6 + 0*b + 1/75*b**5 + 0*b**3 + 0. Solve w(l) = 0 for l.
0, 2
Factor -8/5*n**4 + 16/5 + 4/5*n**5 - 32/5*n**3 - 8/5*n**2 + 28/5*n.
4*(n - 4)*(n - 1)*(n + 1)**3/5
Let r be (-7)/(-2) - 6/4. Factor -13/4*f**r - 1 + 3/2*f**3 - 1/4*f**4 + 3*f.
-(f - 2)**2*(f - 1)**2/4
Let s(p) = 2*p**2 - 6*p + 1. Let v be s(5). Let n = v + -17. Factor 0 - 2/7*z**2 - 4/7*z**3 - 2/7*z**n + 0*z.
-2*z**2*(z + 1)**2/7
Let i(r) be the second derivative of -r**5/20 + r**2/2 + r. Let z(y) = 2*y**3 - 6*y**2 - 12*y - 11. Let b(x) = -6*i(x) - 2*z(x). Find o such that b(o) = 0.
-2
Let z = 7/45 + 29/45. Factor -2/5 - z*o**2 + 6/5*o.
-2*(o - 1)*(2*o - 1)/5
Factor -1/4*c**4 + c**3 - 3/4*c**2 - c + 1.
-(c - 2)**2*(c - 1)*(c + 1)/4
Factor 2*o**2 + 18*o - 2*o**4 - 18*o.
-2*o**2*(o - 1)*(o + 1)
Suppose -2*a = r + 2*r - 9, -5*a = 2*r - 17. Let h be r - (-2 - -2 - 1). Factor 2 + 0*w + 2*w + 2*w**3 - h*w**2 - 4*w.
2*(w - 1)**2*(w + 1)
Find x such that -3*x + 3*x**2 + 1 - 5*x + 2 + 2*x = 0.
1
Let f(q) be the third derivative of 2*q**7/35 + q**6/40 - 7*q**5/20 - q**4/8 + 3*q**3/2 - 6*q**2 - 5*q. Factor f(a).
3*(a - 1)*(a + 1)**2*(4*a - 3)
Let k(v) = -v**3 + 39*v**2 - 59*v + 29. Let n(y) = 5*y**3 - 155*y**2 + 235*y - 115. Let u(q) = -15*k(q) - 4*n(q). Find h, given that u(h) = 0.
1, 5
Let k(d) be the second derivative of 3/8*d**2 - 4*d + 1/8*d**3 + 0 - 1/16*d**4 - 3/80*d**5. Solve k(q) = 0.
-1, 1
Suppose 0 = -4*x + 12 - 4. Let s(q) be the first derivative of 9/16*q**4 + 4/3*q**3 + 5/8*q**2 - x - 1/2*q. Factor s(r).
(r + 1)**2*(9*r - 2)/4
Let b(n) be the second derivative of n**2 + 0 - 3*n + 0*n**4 + 0*n**3 - 1/60*n**6 - 1/105*n**7 + 0*n**5. Let t(d) be the first derivative of b(d). Factor t(q).
-2*q**3*(q + 1)
Let l(v) be the first derivative of v**6/120 + v**5/40 - 2*v**3/3 + 5. Let u(f) be the third derivative of l(f). Suppose u(n) = 0. Calculate n.
-1, 0
Let o be 7 - 7 - (-8)/14. Find m such that 0 - 2/7*m**2 - 2/7*m**4 + 0*m + o*m**3 = 0.
0, 1
Let g(j) be the second derivative of -j**7/17640 + j**6/2520 - j**5/840 - 5*j**4/12 - 3*j. Let f(c) be the third derivative of g(c). Factor f(h).
-(h - 1)**2/7
Suppose u = -3*q + 44, -q + 6*q - 4*u - 62 = 0. Let o be (-14)/q + (-22)/(-10). Suppose -o*r + 3/5 + 3/5*r**2 = 0. Calculate r.
1
Suppose 5*n - 21 = -3*l, 4 = -4*l - n + 5*n. Suppose -3*j - 1 = -4. Factor -3*o**2 - o - o**3 + 6*o**l - 2*o + j.
-(o - 1)**3
Let z(w) be the second derivative of w**6/45 + 7*w**5/15 + 11*w**4/6 - 112*w**3/9 + 64*w**2/3 - 32*w. Suppose z(j) = 0. What is j?
-8, 1
Let d(n) be the second derivative of 0*n**5 + 0*n**3 + 0 - 1/45*n**6 + 1/18*n**4 + 0*n**2 - 3*n. Factor d(i).
-2*i**2*(i - 1)*(i + 1)/3
Suppose 0 = -p + 4*p - 6. Suppose 2/5*y**p + 2/5 - 4/5*y = 0. What is y?
1
Let x(n) = n**2 - 3*n. Let g be x(4). Let o = 4 - g. Factor -4*q - 2 + 0 + o - 2*q**2.
-2*(q + 1)**2
Let r(l) be the third derivative of -l**8/1680 + l**7/280 - l**6/120 + l**5/120 - l**3/6 - l**2. Let z(y) be the first derivative of r(y). Factor z(q).
-q*(q - 1)**3
Factor 20*n**2 + 14*n - 6*n**2 + 6*n**3 + 2 - 4*n.
2*(n + 1)**2*(3*n + 1)
Suppose 5*r = -4*j + 16, 3*r + 0*r = -j + 11. Let 2*p**2 + 5*p**r - 3*p**2 - p**2 - 6*p**5 + 3*p**3 = 0. What is p?
-2/3, 0, 1/2, 1
Let i = -48/31 + 285/124. Let -1/4*c**2 + 0 + i*c = 0. Calculate c.
0, 3
Suppose -5/4*l**2 + 1/2*l - 1/2*l**5 + 0 + 5/4*l**4 + 0*l**3 = 0. What is l?
-1, 0, 1/2, 1, 2
Let n(v) = v**2 + 2*v - 5. Let l be n(-5). Let b be (-4)/l + (-189)/(-35). Find g such that 0 - 1/2*g**b + 0*g + 0*g**2 + 0*g**4 + 1/2*g**3 = 0.
-1, 0, 1
Determine u so that 48/19*u + 288/19 + 2/19*u**2 = 0.
-12
Let v(d) = d**2 - 2*d + 1. Let l be v(5). What is x in 2*x + 10*x**3 + l*x**2 + 0*x + 18*x**5 + 48*x**4 + 34*x**3 = 0?
-1, -1/3, 0
Find b, given that b**4 - b - 3*b**2 - 6*b**3 + 7*b + 2*b**4 = 0.
-1, 0, 1, 2
Let w(u) be the third derivative of u**8/11760 + u**7/2940 + 7*u**3/6 - 8*u**2. Let p(h) be the first derivative of w(h). Factor p(n).
n**3*(n + 2)/7
Let j(c) = -c**2 + 5*c + 1. Let h be j(3). Let l = h + -4. Solve -6*y**l - y**2 + 3*y**4 + 3*y**2 - 5*y**4 + 4*y**5 + 2*y = 0.
-1, -1/2, 0, 1
Let f = -15 + 18. Factor 3*l**2 - 3 + 2 + 1 - f.
3*(l - 1)*(l + 1)
Let r(n) be the second derivative of n**7/14 +