l**2 + 0.
2*l*(l + 1)/3
Factor 6 - 5*j + 5*j**3 + 3*j**4 - 11 - 15*j**2 + 2*j**4 + 15.
5*(j - 1)**2*(j + 1)*(j + 2)
Suppose 7*l + 2*l - 27 = 0. Let u(v) be the second derivative of 1/24*v**l + 0 - 1/120*v**6 - 2*v - 1/80*v**5 + 1/16*v**4 - 1/4*v**2. Factor u(s).
-(s - 1)**2*(s + 1)*(s + 2)/4
What is p in -2*p**2 + 4*p**2 - 4*p**3 + 0*p**2 + 2*p**2 = 0?
0, 1
Let h = 101 + -99. Let d(u) be the third derivative of 0*u**5 + 0*u - 3*u**h - 1/3*u**3 + 1/6*u**4 + 1/105*u**7 - 1/30*u**6 + 0. Find v, given that d(v) = 0.
-1, 1
Let y be 124/44 + (-6)/(-33). Let c(b) be the second derivative of -1/12*b**4 + 0 + 1/3*b**y - b - 1/2*b**2. Factor c(i).
-(i - 1)**2
Let c(y) = -y**2 + 7*y - 4. Let x be c(6). Let 3*d**x + 30 + 7*d - 3 + 11*d = 0. Calculate d.
-3
Suppose 6/5*b + 0 - 3/5*b**2 = 0. Calculate b.
0, 2
Factor 4*t**5 - 3*t**5 - 2*t**4 + t**4.
t**4*(t - 1)
Let w(x) be the third derivative of x**6/120 - x**4/24 + x**3/6 - x**2. Let a(r) = 18*r**2 + 56*r + 52. Let n(d) = a(d) + 2*w(d). Solve n(s) = 0.
-3
Find j, given that 2/11*j - 2/11*j**3 + 4/11*j**2 - 4/11 = 0.
-1, 1, 2
Factor 19*t**3 + 8*t - 17*t**3 - 6*t**4 - 16*t**3.
-2*t*(t + 1)*(t + 2)*(3*t - 2)
Let p be 90/(-210)*3/((-9)/4). What is a in -2/7*a**2 + p + 6/7*a**3 - 2/7*a**4 - 6/7*a = 0?
-1, 1, 2
Let u = 7/10 + -11/30. Factor 0 - 1/3*r + 1/3*r**2 - u*r**4 + 1/3*r**3.
-r*(r - 1)**2*(r + 1)/3
Suppose -4 = -28*r - 4. Factor r*z - 1/4*z**2 + 0.
-z**2/4
Let h be -1*25/(-15) + -1. Let s(u) be the first derivative of h*u**3 + 1 - 4*u + u**2. Find i such that s(i) = 0.
-2, 1
Let a be (2/12)/(1/94). Let q = 16 - a. Find g, given that q*g - 1/3*g**2 + 2/3 = 0.
-1, 2
Let i = -1572 + 7863/5. Factor -i - 48/5*a**2 + 24/5*a.
-3*(4*a - 1)**2/5
Let o(q) be the first derivative of 2*q**3/33 + 5. Factor o(d).
2*d**2/11
Let z(g) = -3*g**5 + 3*g**4 - 5*g**3 - 3*g**2 - 4*g. Let f(j) = -j**5 - j**3 + j**2 - j - 1. Let y(u) = 12*f(u) - 3*z(u). Determine t so that y(t) = 0.
-2, -1, 1
Let f(c) = c**2 - 5*c. Let i be f(5). Suppose -2*d + 0*d + 14 = i. Let -d + 3*t**2 - t**2 + 5 = 0. Calculate t.
-1, 1
Let d(q) = 3*q - 24. Let l be d(8). Let i(j) be the first derivative of 0*j - 1/6*j**4 - 3 + l*j**2 - 1/9*j**3 - 1/15*j**5. Suppose i(o) = 0. Calculate o.
-1, 0
Let x = -4 - -9. Let t be 5*(-2 + 12/x). Factor a**4 + 3*a**3 + a - a**t - 2*a**3 - 2*a**3.
a*(a - 1)**2*(a + 1)
Let o be (-4)/(-6)*(2 - 1/2). Factor -m**2 + o + 3/2*m**3 - 3/2*m.
(m - 1)*(m + 1)*(3*m - 2)/2
Let k(p) be the third derivative of -1/120*p**6 + 3*p**2 - 5/24*p**4 + 1/3*p**3 + 0*p + 1/15*p**5 + 0. Factor k(g).
-(g - 2)*(g - 1)**2
Let u be ((-24)/40)/((-6)/20). Let m(y) be the first derivative of 1/3*y**u + 4/9*y**3 + 0*y + 1. Factor m(k).
2*k*(2*k + 1)/3
What is a in 22*a + 9*a**2 + 16*a + 4*a + 0*a + 24 = 0?
-4, -2/3
Let y be (-2 - -1)/(1/(-4)). Determine g so that g + y*g**4 - 3 + 4*g**2 + 12*g**3 - 5 - 13*g = 0.
-2, -1, 1
Suppose -4*u + 1 = 2*q - 27, -u - 3 = -2*q. Let t(z) = -3*z**2 + 7*z - 5. Let s(v) = 4*v**2 - 8*v + 6. Let l(w) = u*s(w) + 6*t(w). Factor l(y).
2*y*(y + 1)
Let d be (-706)/(-6) + (-10)/(-30). Let w = d - 347/3. Factor 0 + 2/3*k + w*k**4 - 4*k**3 + k**2.
k*(k - 1)**2*(7*k + 2)/3
Let v(f) be the first derivative of -f**3/9 + f**2/3 + f - 5. Factor v(y).
-(y - 3)*(y + 1)/3
Let c(q) be the second derivative of 1/2*q**5 - 11/24*q**4 + q**2 - 2*q - 11/60*q**6 + 1/42*q**7 - 1/3*q**3 + 0. Determine g, given that c(g) = 0.
-1/2, 1, 2
Suppose -44*l - 16*l**2 + 6 + 4*l**2 + 23*l = 0. What is l?
-2, 1/4
Let u(o) be the third derivative of -o**8/2352 + 2*o**7/735 - o**6/140 + o**5/105 - o**4/168 - 8*o**2. Factor u(m).
-m*(m - 1)**4/7
Let t(z) be the first derivative of 1/6*z**2 - 1/12*z**4 - 1/3*z - 6 + 1/9*z**3. Determine o so that t(o) = 0.
-1, 1
Let j be 0/4 + (-8)/(-12) - -2. Factor j*h - 2*h**2 - 2/3.
-2*(h - 1)*(3*h - 1)/3
Let p(j) be the third derivative of 1/420*j**7 + 0*j**4 - 1/60*j**5 + 0*j**6 + 1/12*j**3 + 0 + 2*j**2 + 0*j. Solve p(t) = 0.
-1, 1
Let l(i) be the first derivative of -2*i + 0*i**3 + 4*i**2 - 1/2*i**4 - 1/10*i**5 - 4. Let d(a) be the first derivative of l(a). Factor d(p).
-2*(p - 1)*(p + 2)**2
Let a(y) = y**2 + 8*y + 1. Let t be a(-8). Let d be (3 - 0) + t + -2. Solve 2*g**5 + d*g**3 + 4*g**4 - 2*g + 2*g = 0 for g.
-1, 0
Let h(m) = -6*m - 28. Let q be h(-5). Let p(w) be the second derivative of 0*w**q + 1/18*w**4 - 1/9*w**3 + 2*w + 0. What is n in p(n) = 0?
0, 1
Let w(k) be the third derivative of k**8/60480 - k**7/7560 - k**6/720 + k**5/10 + 2*k**2. Let c(t) be the third derivative of w(t). Find l, given that c(l) = 0.
-1, 3
Let u be (3 - 44/15)*1. Let v(f) be the second derivative of -f + 0*f**2 + u*f**3 + 0 - 1/30*f**4. Determine x so that v(x) = 0.
0, 1
Let l = 3422/4265 - 2/853. Find c, given that l + c**3 - 1/5*c**5 - 8/5*c - 1/5*c**4 + 1/5*c**2 = 0.
-2, 1
Let q(v) = -v**4 - 3*v**3 - 2*v. Let d(s) = s**4 + 4*s**3 + 3*s. Let u(k) = -2*d(k) - 3*q(k). Determine g, given that u(g) = 0.
-1, 0
Solve 3*c**5 + 18*c**4 - 1 - 5 + 27*c**3 + 6 = 0 for c.
-3, 0
Factor -2*c**4 - 4*c**4 + 6*c**3 + 3*c**4.
-3*c**3*(c - 2)
Let a(f) = 8*f**3 + 5*f - 8*f**4 - 15*f**2 + f**4 + 5*f**4 + 1. Let o(w) = w**2 + w - 1. Let l(g) = a(g) + 3*o(g). Suppose l(c) = 0. Calculate c.
1
Suppose 2*m = 5*m - 12. Let r = 10 + -8. Determine f so that 4*f - 2*f**2 - 2*f**3 + r*f**4 + 0*f + 0*f**m - 2*f = 0.
-1, 0, 1
Factor -12 + 44*x**2 + 21*x - 9*x - 48*x**2 + 4.
-4*(x - 2)*(x - 1)
Let j(d) = -4*d**3 + 3*d**2 + d. Let a(v) = -v**3 + v**2. Let x be (2 + -3)/(2 + -1). Let n = -4 - -9. Let i(h) = n*a(h) + x*j(h). Factor i(r).
-r*(r - 1)**2
Let a = 19/39 + -2/13. Suppose 5*c = 2*c + v + 9, -2*v - 3 = -c. Suppose l**4 + 0 - 7/3*l**c + 5/3*l**2 - a*l = 0. Calculate l.
0, 1/3, 1
Let c = -41 + 33. Let d be -1*(2 + c/4). Suppose -1/2*x + x**3 + 0*x**2 + 0*x**4 - 1/2*x**5 + d = 0. What is x?
-1, 0, 1
Suppose 4*z + 3*f = 24, -5*z + 9 = f - 21. Suppose -x + 5*w + 10 = 0, 5*x - 3*w = -z*w - 6. Factor -6 - 3*o**2 + x*o + 4*o + o**2 + 4.
-2*(o - 1)**2
Factor -r**5 + 0*r**2 + 13*r**3 - 2*r**5 - 9*r**4 - 22*r**3 - 3*r**2.
-3*r**2*(r + 1)**3
What is y in 0*y + 8/7*y**2 + 0 - 2/7*y**3 = 0?
0, 4
Factor 10*i**3 + 21/2*i**2 - 1/2 + 0*i.
(i + 1)*(4*i + 1)*(5*i - 1)/2
Let t(b) be the third derivative of -b**7/350 - b**6/40 - 7*b**5/100 - 3*b**4/40 + 9*b**2. Find a, given that t(a) = 0.
-3, -1, 0
Let a = 41/119 - 1/17. Suppose 0 = -2*k + 4*k. Factor 2/7*g + k + a*g**2.
2*g*(g + 1)/7
Suppose 4*n = -2*d + 2*n - 10, -4*d + 4*n + 20 = 0. Solve 1/3*x - x**2 + d + x**3 - 1/3*x**4 = 0 for x.
0, 1
Let f(q) be the first derivative of -2*q**3/9 + q**2 - 4*q/3 - 2. Factor f(v).
-2*(v - 2)*(v - 1)/3
Let m(p) be the second derivative of -p**7/14 + 9*p**5/20 + p**4/2 - 3*p. Factor m(v).
-3*v**2*(v - 2)*(v + 1)**2
Let j(s) be the second derivative of s**8/36960 + s**4/6 + 3*s. Let z(a) be the third derivative of j(a). Factor z(h).
2*h**3/11
Let o(n) = 2*n**2 - 9*n + 7. Let v(g) = -g - 4. Let h be v(-6). Let r(s) = -2*s - s + 2*s**h + 8 - 7*s. Let z(t) = 6*o(t) - 5*r(t). Factor z(f).
2*(f - 1)**2
Let z(y) be the first derivative of -y**4/16 + 5*y - 5. Let c(o) be the first derivative of z(o). What is f in c(f) = 0?
0
Let x(k) be the second derivative of 0 + 6*k + k**2 - 1/6*k**4 + 1/6*k**3 - 1/20*k**5. Factor x(w).
-(w - 1)*(w + 1)*(w + 2)
Factor -3/4*r**3 + 0 - 1/4*r**2 + 1/4*r**4 + 1/4*r**5 + 1/2*r.
r*(r - 1)**2*(r + 1)*(r + 2)/4
Let g(d) = 2*d**3 - 8*d**2 + 2*d. Let w(o) = 2*o**3 - 9*o**2 + 3*o. Let y(r) = 3*g(r) - 2*w(r). Factor y(x).
2*x**2*(x - 3)
Let i(r) = -r**5 - r**3 + r**2 + r - 1. Let j(q) = 19*q**5 - 120*q**4 + 203*q**3 - 160*q**2 + 66*q - 14. Let k(c) = 6*i(c) - j(c). Find o such that k(o) = 0.
2/5, 1, 2
Let y(h) be the second derivative of -h**6/540 + h**4/36 - 2*h**3/3 + 5*h. Let b(g) be the second derivative of y(g). Factor b(v).
-2*(v - 1)*(v + 1)/3
Factor -2/11*u**2 - 2/11*u + 4/11.
-2*(u - 1)*(u + 2)/11
Factor 2*o - 1/3*o**2 + 7/3.
-(o - 7)*(o + 1)/3
Let w(y) be the first derivative of 3*y**5/5 - 3*y**4/4 - y**3 + 3*y**2/2 + 1. Factor w(c).
3*c*(c - 1)**2*(c + 1)
Let j be (7/(-42))/(6/(-9)). Let h(l) be the first derivative of 1/2*l - 1/8*l**4 + 1 - 1/6*l**3 + j*l**2. Solve h(z) = 0.
-1, 1
Let a = 2 - 5/3. Factor 2/3*n**3 + 0 + n**2 + a*n.
n*(n + 1)*(2*n + 1)/3
Let w(s) b