+ 1)/7
Let d(z) = -z**2 + 3*z + 2. Let l be d(3). Let n = l + 1. Factor 4*y + 2 - 10*y - 2*y**2 + 4*y + 2*y**n.
2*(y - 1)**2*(y + 1)
What is w in 8/3*w**3 + 20/3*w - 7*w**2 - 13/6 - 1/6*w**4 = 0?
1, 13
Let a(p) be the first derivative of p**7/3360 - p**6/480 + p**5/240 + 2*p**3 - 1. Let c(w) be the third derivative of a(w). Suppose c(o) = 0. What is o?
0, 1, 2
Let j(y) = -y**2 - 10*y - 1. Let s(a) = -10*a**2 - 110*a - 10. Let h(n) = 65*j(n) - 6*s(n). Factor h(b).
-5*(b - 1)**2
Solve 41*c**3 + 4 - 10 + 102*c**2 - 4*c - 181*c**3 = 0 for c.
-1/5, 3/7, 1/2
Let v(l) be the first derivative of l**4/9 - 2*l**3/27 - 13. Factor v(r).
2*r**2*(2*r - 1)/9
Let l be 5/10*(3 + -1). Factor -h**4 + 2 + 3*h - l - 3*h**3 - h**4 + h**2 + 0.
-(h - 1)*(h + 1)**2*(2*h + 1)
Suppose -3*o + 3*k = -3, -11 = -0*o - 3*o - 5*k. Factor -2*y - o*y**2 - 4/7 - 4/7*y**3.
-2*(y + 1)*(y + 2)*(2*y + 1)/7
Let k(r) be the third derivative of -r**8/168 + 4*r**7/105 - r**6/15 - r**5/15 + 5*r**4/12 - 2*r**3/3 + r**2. Factor k(v).
-2*(v - 2)*(v - 1)**3*(v + 1)
Let h be ((405/(-80))/3)/(6/(-8)). Determine b, given that -9/4*b**2 + h*b + 3/4*b**3 - 3/4 = 0.
1
Suppose 6 = 2*p - 0. Solve 1 + 3 - 4 + p*i**2 + 2*i + i**3 = 0 for i.
-2, -1, 0
Let x(b) be the third derivative of -b**7/70 + b**6/40 + b**5/20 - b**4/8 - b**2. Let x(p) = 0. Calculate p.
-1, 0, 1
Find b such that -4/7 - 2/7*b**2 + 9/7*b = 0.
1/2, 4
Factor -44/7*d**4 - 26/7*d - 76/7*d**3 - 4/7 - 64/7*d**2 - 10/7*d**5.
-2*(d + 1)**4*(5*d + 2)/7
Let x = -1631/3 - -549. Let l = -1/2 - -7/6. Factor x*m + 32/3*m**2 + l.
2*(4*m + 1)**2/3
Let r(t) be the third derivative of -t**5/30 - t**4/12 - 22*t**2. Suppose r(s) = 0. Calculate s.
-1, 0
Let n(x) = -x**2 + 8*x + 20. Let m be n(10). Let 6/5*u + 4/5 - 2/5*u**3 + m*u**2 = 0. Calculate u.
-1, 2
Let b(w) = -2*w**3 - 6*w**2 + 4*w + 4. Let m(t) = 10*t**3 + 30*t**2 - 21*t - 19. Let f(r) = 11*b(r) + 2*m(r). Solve f(h) = 0.
-3, -1, 1
Factor 3*t**3 + 4*t**5 - 2*t**5 - 5*t**5.
-3*t**3*(t - 1)*(t + 1)
Suppose -28/5*r**2 - 12/5*r + 0 - 4/5*r**4 - 4*r**3 = 0. What is r?
-3, -1, 0
Let h(q) be the second derivative of -q**5/5 + 2*q**4/3 - 2*q**3/3 - 5*q. Let h(p) = 0. Calculate p.
0, 1
Let b = 3019/924 + -4/231. Let s = b + -3. Factor 0*u**2 - 1/4*u + 0 + s*u**3.
u*(u - 1)*(u + 1)/4
Suppose 4*g + 0*g + 60 = 0. Let l be -3*(6/g)/2. Factor -2/5 - l*a**2 - a.
-(a + 1)*(3*a + 2)/5
Let s = -2/3 - -4/3. Factor -2/3 + 2/3*l - 2/3*l**3 + s*l**2.
-2*(l - 1)**2*(l + 1)/3
Let g(f) be the first derivative of -f**5/4 - 15*f**4/8 - 65*f**3/12 - 15*f**2/2 - 5*f + 20. Factor g(a).
-5*(a + 1)**2*(a + 2)**2/4
Suppose 3*i + r = 28, 0 = -3*i - 3*r - 0*r + 18. Let f = 13 - i. Factor 0 - 14/5*k**3 + 2*k**f + 4/5*k.
-2*k*(k - 1)*(7*k + 2)/5
Factor 9/4*f**4 - 3/4 - 3/4*f**5 - 3/2*f**3 - 3/2*f**2 + 9/4*f.
-3*(f - 1)**4*(f + 1)/4
Let b(h) be the first derivative of -h**5/5 - h**4/2 + 7. Factor b(l).
-l**3*(l + 2)
Let p(j) be the first derivative of -j**7/3 + 4*j**6/5 - 3*j**5/10 - j**4/3 - 2*j - 1. Let z(v) be the first derivative of p(v). Suppose z(d) = 0. What is d?
-2/7, 0, 1
Let q(v) be the third derivative of 0*v**4 + 5*v**2 + 0*v**5 + 0*v**3 - 1/60*v**6 + 0*v + 0 - 1/168*v**8 + 2/105*v**7. Factor q(w).
-2*w**3*(w - 1)**2
Let j(u) = u + 1. Let g(c) = -4*c - 3. Let h(m) = 2*g(m) + 6*j(m). Let r be h(-1). Factor -2/5*o - 6/5*o**r + 0 - 2/5*o**4 - 6/5*o**3.
-2*o*(o + 1)**3/5
Factor 0 - 7/3*b**3 - 26/3*b**2 + 8/3*b.
-b*(b + 4)*(7*b - 2)/3
Factor 18/5 - 6/5*n - 2/5*n**3 - 2*n**2.
-2*(n - 1)*(n + 3)**2/5
Let g(s) be the first derivative of -2/15*s**5 - 2/3*s**2 + 0*s + 2/3*s**3 - 3 + 0*s**4. Factor g(j).
-2*j*(j - 1)**2*(j + 2)/3
Suppose -3 = -3*b + 9. Suppose -2*r - 2*a + b*a = -8, 0 = r - 5*a - 20. Let -1/4*j**3 + r + 1/4*j**2 - 1/4*j**4 + 1/4*j = 0. What is j?
-1, 0, 1
Let l = -18/13 + 116/65. Factor l*c**4 + 18/5*c**2 + 4/5 + 2*c**3 + 14/5*c.
2*(c + 1)**3*(c + 2)/5
What is x in 7/4*x + 3/4 + 1/4*x**3 + 5/4*x**2 = 0?
-3, -1
Suppose 33 - 49 = -4*v. Determine d so that 2*d + 7*d + v*d**2 - d**2 = 0.
-3, 0
Suppose -2*h - 20 = -3*h. Factor -h*y**5 + 4*y**3 + 6*y**4 + 9*y**5 + 13*y**5.
2*y**3*(y + 1)*(y + 2)
Let u = -241 + 497/2. Determine k so that u*k + 6*k**3 - 33/2*k**2 + 3 = 0.
-1/4, 1, 2
Let w be -1*(1 - 20/5). Let 2/7*p**2 + 6/7*p**4 + 6/7*p**w + 2/7*p**5 + 0*p + 0 = 0. Calculate p.
-1, 0
Factor -12*d**2 - d**5 - 10*d**2 + 3*d**3 + 20*d**2.
-d**2*(d - 1)**2*(d + 2)
Let p(c) be the second derivative of c**5/50 + c**4/10 + c**3/5 + c**2/5 + 4*c. Suppose p(w) = 0. What is w?
-1
Let u(g) be the first derivative of -g**3/9 + 7. Suppose u(z) = 0. Calculate z.
0
Let i(p) be the second derivative of -1/240*p**5 + 0*p**3 + 4*p - 3/2*p**2 - 1/48*p**4 + 0. Let j(h) be the first derivative of i(h). Solve j(w) = 0 for w.
-2, 0
Suppose -4*t = 2*p - 4 - 0, 4*p = -2*t + 8. Find s such that 0 + 1/2*s + 1/4*s**p = 0.
-2, 0
Suppose 0 = -d + 4*b - 7, -4*d + 13 = -2*d + b. Factor -3/5*i**4 + 0*i**2 - 3/5*i**d + 0*i + 0*i**3 + 0.
-3*i**4*(i + 1)/5
Let x(a) be the second derivative of a**4/42 - 2*a**3/21 - 3*a**2/7 - 13*a. Factor x(c).
2*(c - 3)*(c + 1)/7
Let c(q) be the third derivative of -q**6/340 + 7*q**5/510 - 5*q**4/204 + q**3/51 - 2*q**2. Factor c(m).
-2*(m - 1)**2*(3*m - 1)/17
Factor -2/9*x**3 - 2/9*x**4 + 2/9*x**2 + 0 + 2/9*x.
-2*x*(x - 1)*(x + 1)**2/9
Let x be (2 - -4)*((-10)/(-4) + -2). Factor 0 - 4/3*q + 10/3*q**2 - 2*q**x.
-2*q*(q - 1)*(3*q - 2)/3
Let n = -85/2 - -43. Let f(u) be the second derivative of -2*u + 0*u**3 + 1/12*u**4 + 0 - n*u**2. Solve f(x) = 0 for x.
-1, 1
Factor 1/3*n + 1/3*n**2 + 0.
n*(n + 1)/3
Let s(u) be the second derivative of u**9/37800 - u**7/6300 + u**4/12 + u. Let l(n) be the third derivative of s(n). Suppose l(t) = 0. What is t?
-1, 0, 1
Let n(c) = c**3. Let p(r) = -22*r**3 + 11*r**2 + 9*r - 3. Let s(g) = -5*n(g) - p(g). Let l(v) = v**3 - v**2 - v + 1. Let j(w) = -3*l(w) + s(w). Factor j(d).
2*d*(d - 1)*(7*d + 3)
Let x(d) be the second derivative of d**8/336 - 2*d**7/105 + d**6/20 - d**5/15 + d**4/24 + 2*d**2 + 2*d. Let u(b) be the first derivative of x(b). Factor u(j).
j*(j - 1)**4
Let s(z) be the first derivative of z**5/30 - z**3/3 + 2*z**2/3 - 3*z - 3. Let q(x) be the first derivative of s(x). Factor q(d).
2*(d - 1)**2*(d + 2)/3
Let m(h) be the third derivative of -h**6/40 + h**5/4 + 40*h**2. Factor m(c).
-3*c**2*(c - 5)
Let t(l) be the first derivative of 2*l**5/75 - l**4/30 - 2*l**3/15 + l**2/15 + 4*l/15 + 4. Suppose t(m) = 0. Calculate m.
-1, 1, 2
Suppose 2/13*j**2 - 4/13*j - 6/13 = 0. Calculate j.
-1, 3
Let z(d) be the third derivative of 5*d**8/336 + d**7/21 + d**6/24 + 11*d**2. Factor z(o).
5*o**3*(o + 1)**2
Let i = -60452552/1533 + 276048/7. Let w = 4/73 + i. Factor w*g + 2/3 + 2/3*g**2.
2*(g + 1)**2/3
Let z = -516 + 3604/7. Let o = -17/21 - z. Factor -4/3*d + o + 5/3*d**2 - 2/3*d**3.
-(d - 1)**2*(2*d - 1)/3
Suppose 3*p = 2*v + 18, 0 = 4*v + 4*p + 2 - 6. Let s(l) = 5*l**2 - 2*l - 4. Let t(u) = 4*u**2 - 2*u - 3. Let f(c) = v*s(c) + 4*t(c). Factor f(i).
i*(i - 2)
Suppose -5*p + 0 = 20. Let t be ((-10)/p - 0)*2. Factor -2/5*r**4 + 0 + 0*r + 0*r**3 + 0*r**2 + 6/5*r**t.
2*r**4*(3*r - 1)/5
Let r(p) be the third derivative of -p**7/2520 + p**6/120 - 3*p**5/40 - p**4/4 + p**2. Let k(c) be the second derivative of r(c). Factor k(m).
-(m - 3)**2
Let v(z) be the first derivative of 3/4*z - 1 + 3/16*z**4 - 3/8*z**2 - 1/4*z**3. Suppose v(d) = 0. What is d?
-1, 1
Factor -2*v + 6*v**4 - 3*v**5 + 0*v**2 - 2*v**2 + 5*v - 4*v**2.
-3*v*(v - 1)**3*(v + 1)
Let v = 18 + -8. Suppose 6*m - m = v. Factor 6 - 4*s - m*s**2 - 5 - 1.
-2*s*(s + 2)
Let k(c) be the third derivative of c**7/2520 - c**6/360 - c**4/24 - 5*c**2. Let n(l) be the second derivative of k(l). Factor n(x).
x*(x - 2)
Factor -2/15*p**3 + 0*p + 0 - 2/15*p**2.
-2*p**2*(p + 1)/15
Let u(m) = m - 3. Let z be u(3). Let -o + 2*o**4 + o + z*o = 0. What is o?
0
Let q(o) be the third derivative of 0*o**4 + 0*o + 1/90*o**5 + 1/504*o**8 - 1/315*o**7 + 4*o**2 + 0 - 1/180*o**6 + 0*o**3. Factor q(n).
2*n**2*(n - 1)**2*(n + 1)/3
Let d(u) be the first derivative of -3*u**4 + 9*u**3 - 3*u**2 + 22. Find i, given that d(i) = 0.
0, 1/4, 2
Let x(r) be the first derivative of -1/8*r**2 + 1/12*r**3 - 1/20*r**5 + 0*r - 2 + 1/16*r**4. Factor x(l).
-l*(l - 1)**2*(l + 1)/4
Factor 5