7/5040 + l**4/8 + 2*l**2. Let s(b) be the second derivative of x(b). Factor s(t).
t**2*(t + 1)/2
Suppose -q - 8 = -5*q. Suppose 2*j + 65*j - 3*j - 16 - 28*j**q = 0. Calculate j.
2/7, 2
Let b = 48 - 17. Find g such that -13*g + 7*g**4 + g**4 + 29*g + 24*g**3 + g**5 + b*g**2 + g**2 = 0.
-2, 0
Let b be 1/(-4) + (-3)/(-12). Suppose b = -4*v + 28 - 4. Determine p, given that -1 - 18*p**2 + 15/2*p - v*p**4 + 35/2*p**3 = 0.
1/4, 2/3, 1
Factor 18*r + 3*r**2 + 14 + 8 + 2 + 3.
3*(r + 3)**2
Suppose 5*s + 2 = 12. What is h in s*h**2 - 4 - 8 + 0 + 7*h**2 + 3*h**3 = 0?
-2, 1
Let g = 4/15 - 9/40. Let r(k) be the second derivative of 0*k**2 + 0 - 1/12*k**3 - g*k**4 + k. Factor r(x).
-x*(x + 1)/2
Let c(u) = -3*u**2 - 7 + 7*u - 3*u + 0*u - 2*u**3 + 5*u. Let x(q) = 10*q**3 + 14*q**2 - 44*q + 34. Let f(m) = -14*c(m) - 3*x(m). Let f(z) = 0. Calculate z.
-2, 1
Let p = -6 - -11. Let w = 10 - p. Let 4*t + 3*t**4 + 0*t**4 - w*t**4 - 3*t - t**5 + 2*t**2 = 0. What is t?
-1, 0, 1
Let y(s) = 7*s**5 + s**4 + 7*s**3 + 5*s**2. Suppose -2*q - 6 = -16. Let w(z) = -3*z**5 - 3*z**3 - 2*z**2. Let l(o) = q*w(o) + 2*y(o). Solve l(j) = 0.
0, 1
Suppose -5*p + 5*a - 5 = -0*p, -a = -4. Factor -1/5*g**2 + 0 + 1/5*g**4 + 1/5*g - 1/5*g**p.
g*(g - 1)**2*(g + 1)/5
Suppose -25 = -0*r + 3*r + n, n + 1 = 0. Let x = -6 - r. Suppose -5*o**5 - 17*o**x - 5*o**3 + 4*o + 2*o**3 + 13*o**4 + 4*o**3 + 4 = 0. Calculate o.
-1, -2/5, 1, 2
Let a be -1 + 4/10 - -1. Suppose -a - 24/5*s**2 - 6/5*s**4 + 4*s**3 + 12/5*s = 0. Calculate s.
1/3, 1
Determine y so that -3 - y**2 - y - 4*y + 7*y + 2*y**2 = 0.
-3, 1
Let w = -277 + 282. Factor 2/5*r**w - 4/5*r**2 + 0 + 0*r**4 - 6/5*r**3 + 0*r.
2*r**2*(r - 2)*(r + 1)**2/5
Suppose 2/7*y**3 - 8/7 + 16/7*y - 10/7*y**2 = 0. Calculate y.
1, 2
Let h(a) = 6 + 2 + 14*a**3 + 3 + 11*a + 10*a**2. Let z = -6 - 16. Let s(i) = -i**3 - i**2 - i - 1. Let n(x) = z*s(x) - 2*h(x). Factor n(v).
-2*v**2*(3*v - 1)
Factor 0 + 4/5*z + 1/5*z**2.
z*(z + 4)/5
Let j = 41863/9394 - 43/122. Let y = j + -42/11. Determine f so that 0*f**4 + 4/7*f**3 + 0*f**2 - y*f**5 - 2/7*f + 0 = 0.
-1, 0, 1
Suppose 5*m - 6*m = 0. Let x(k) = -k + 2. Let y be x(m). Factor -2/11*z**3 + 0*z + 0 + 0*z**y.
-2*z**3/11
Factor -x - 8 - 2*x**2 - 5*x + 5*x**2 - x**2.
2*(x - 4)*(x + 1)
Let f(u) be the first derivative of -3*u**5/10 + u**4/6 + 2*u**3/3 - 2*u - 2. Let t(x) be the first derivative of f(x). Factor t(i).
-2*i*(i - 1)*(3*i + 2)
Let t = -26 - -31. Let b(m) be the third derivative of 0 + 1/4*m**4 - 2*m**2 + 0*m + 1/30*m**t + 2/3*m**3. Factor b(z).
2*(z + 1)*(z + 2)
Let f(j) = -j**5 + j**3 + j**2 + j + 1. Let p(g) = -7*g**5 + 7*g**3 + 5*g**2 + 5*g + 5. Let z(h) = 5*f(h) - p(h). Factor z(q).
2*q**3*(q - 1)*(q + 1)
Solve 2*p**2 + 0 - 1/2*p**5 - 4*p**3 + 5/2*p**4 + 0*p = 0 for p.
0, 1, 2
Let n = -8 + 20. Determine j so that -4*j - 12*j**4 + 0*j + 4*j - 3*j**5 - 3*j - 18*j**3 - n*j**2 = 0.
-1, 0
Let x be (3 - 5)/((-5)/2). Let j = -23/5 + 5. Factor j*h**2 + x*h**3 - 4/5*h - 2/5.
2*(h - 1)*(h + 1)*(2*h + 1)/5
Let h(g) be the first derivative of g**6/2 + 6*g**5/5 - 9*g**4/4 - 8*g**3 - 6*g**2 - 29. Find t, given that h(t) = 0.
-2, -1, 0, 2
Factor 12/7*p + 0 - 3*p**2.
-3*p*(7*p - 4)/7
Let u(o) be the third derivative of 1/6*o**5 + 0*o + 2*o**2 - 1/60*o**6 + 0 + 4/3*o**3 - 2/3*o**4. Determine g so that u(g) = 0.
1, 2
Factor 2/7 + 2/7*u**2 - 4/7*u.
2*(u - 1)**2/7
Suppose -r + 22 = 3*d, 0 = 2*d + 5*r - 6. Factor 3*a**4 + 3*a**3 - d*a**3 - 3*a**2 + 2*a**3 + 3*a**5.
3*a**2*(a - 1)*(a + 1)**2
Let c(u) be the second derivative of u**6/1080 + u**5/120 + u**4/36 - u**3/2 - 4*u. Let l(a) be the second derivative of c(a). Factor l(g).
(g + 1)*(g + 2)/3
Let x(i) be the second derivative of i**4/6 + 3*i**3/8 + i**2/8 + 7*i. Factor x(m).
(m + 1)*(8*m + 1)/4
Let i be (-12 - -10)*((-6)/(-8) - 1). Factor 3/4*s - i + 0*s**2 - 1/4*s**3.
-(s - 1)**2*(s + 2)/4
Let q = -9 - -12. Factor 2*m**3 + m**4 - 2*m**q + m**3 + 0*m**3.
m**3*(m + 1)
Suppose -4*x - 5 = 4*y - 41, 5*x - 33 = y. Let k = x + -5. Suppose -4/5*b + 2/5 + 2/5*b**k = 0. What is b?
1
Let f(q) be the first derivative of -q**3/5 + 3*q/5 + 3. What is s in f(s) = 0?
-1, 1
Let m(u) be the first derivative of u**6/180 - u**5/45 + u**4/36 + 3*u**2/2 - 1. Let r(p) be the second derivative of m(p). Solve r(i) = 0.
0, 1
Let h(m) be the first derivative of m**6/36 + m**5/15 + m**4/24 + 5. Factor h(r).
r**3*(r + 1)**2/6
Let a = 484 - 3386/7. Factor 4/7*t - 6/7*t**2 + 0 + a*t**3.
2*t*(t - 2)*(t - 1)/7
Let b be (30/(-8))/((-65)/40 + -1). Suppose -b*p**3 + 0 + 4/7*p**2 + 0*p = 0. What is p?
0, 2/5
Factor -p - 2/3 - 1/3*p**2.
-(p + 1)*(p + 2)/3
Let m(k) be the second derivative of -3*k - 1/18*k**4 + 1/3*k**2 - 1/60*k**5 + 1/18*k**3 + 0. Factor m(j).
-(j - 1)*(j + 1)*(j + 2)/3
Let v(l) be the third derivative of 2*l**2 + 0*l + 0 - 2/9*l**4 - 2/9*l**3 + 1/90*l**6 + 1/180*l**5. Factor v(h).
(h - 2)*(h + 2)*(4*h + 1)/3
Let w(k) be the first derivative of -3*k**5/20 + 27*k**4/16 - 27*k**3/4 + 81*k**2/8 - 18. What is y in w(y) = 0?
0, 3
Let h = 66 - 61. Let u(j) be the third derivative of 0 + 0*j + 1/33*j**4 + 1/660*j**6 + 3*j**2 - 2/165*j**h + 0*j**3. Let u(f) = 0. What is f?
0, 2
Let z = 10/23 + 94/207. Let f be 20/(-45) + (-4)/(-6). Factor z - 8/9*k + f*k**2.
2*(k - 2)**2/9
Suppose 3*v - 7 = 2. Factor -3*u**4 + 3*u**4 + 3*u**5 + u**4 + 2*u**4 - v*u**2 - 3*u**3.
3*u**2*(u - 1)*(u + 1)**2
Let z(h) be the second derivative of h**7/315 + h**6/45 + 2*h**5/45 + 5*h**2/2 - 5*h. Let c(i) be the first derivative of z(i). Determine t so that c(t) = 0.
-2, 0
Let o be (1 - (-4)/(-3))*-6. Suppose -2*a - 4*a**o + 3*a - 6*a - 7*a = 0. What is a?
-3, 0
Let v = 5 + -5. Let x(u) be the third derivative of -2*u**2 + 0 + 0*u - 1/504*u**8 + 0*u**4 - 1/90*u**5 + v*u**3 + 1/315*u**7 + 1/180*u**6. Factor x(l).
-2*l**2*(l - 1)**2*(l + 1)/3
Let c(y) = 9*y**3 + 10*y**2 + 3*y - 1. Let k(z) = -z**2 + z - 1. Let m(g) = -5*c(g) + 5*k(g). Let m(d) = 0. Calculate d.
-1, -2/9, 0
What is u in -2*u**2 + 4/3 + 2/3*u**3 - 2/3*u + 2/3*u**4 = 0?
-2, -1, 1
Let a = -8 + 10. Let q(r) = -r**3 + 1. Let z(p) = -p**4 - p**3 - 3*p**2 + 4*p + 1. Let t(n) = a*z(n) + 6*q(n). Solve t(w) = 0 for w.
-2, -1, 1
Let z(m) be the second derivative of -m**6/180 + m**5/60 - m**3/2 + m. Let h(w) be the second derivative of z(w). Factor h(b).
-2*b*(b - 1)
Let x = 3/380 - -1/2280. Let r(g) be the third derivative of 0*g**4 + 0*g**6 + 0*g - 1/420*g**7 + 0*g**3 + 2*g**2 + x*g**5 + 0. Let r(z) = 0. What is z?
-1, 0, 1
Let v = -16 + 20. Let d(q) be the first derivative of -1/3*q**3 + 0*q + v + q**2. Suppose d(c) = 0. What is c?
0, 2
Let w = 22 - 21. Let d(c) = 4*c**2 - 1. Let a be d(w). What is j in 1/4*j**2 + 0*j + 0 + 1/4*j**a = 0?
-1, 0
Let u(w) be the second derivative of -w**4/48 + w**2/8 + 5*w. Factor u(q).
-(q - 1)*(q + 1)/4
Let r = -21/2 - -11. Let c(a) be the first derivative of -2*a + 1/3*a**3 - 1 + r*a**2. Factor c(w).
(w - 1)*(w + 2)
Let y(k) = 10*k**4 + 3*k**3 - 10*k**2 - 10*k. Let g(l) = 3*l**4 + l**3 - 3*l**2 - 3*l. Let h(z) = -7*g(z) + 2*y(z). Find b, given that h(b) = 0.
-1, 0, 1
Factor -32 + 98*h**3 + 24*h + 28*h**4 + 62*h**3 + 204*h**2 + 16*h.
4*(h + 1)**2*(h + 4)*(7*h - 2)
Let v(x) = -4*x**3 - 3*x**2 - 4*x. Let i be ((-2)/3)/((-2)/(-6)). Let t(r) = r**3 + r**2 + r. Let w(c) = i*v(c) - 10*t(c). Factor w(u).
-2*u*(u + 1)**2
Suppose 0 = 4*m - 16, 0 = k - 2*m - 0*m + 6. Suppose 3*f - 10 = -5*x, 2*x - k*f = 4 - 0. Factor -v + 1/3*v**x + 2/3.
(v - 2)*(v - 1)/3
Factor -6*n**4 - 15/2*n**3 + 0 - 3/2*n**5 - 3*n**2 + 0*n.
-3*n**2*(n + 1)**2*(n + 2)/2
Factor -1024 - 2*m**3 - 48*m**2 - 117*m - 60*m - 207*m.
-2*(m + 8)**3
Let a(l) be the third derivative of -l**7/280 - l**6/60 - l**5/40 + l**3/6 + 2*l**2. Let r(z) be the first derivative of a(z). Factor r(i).
-3*i*(i + 1)**2
Let u(x) be the second derivative of -3*x**7/14 + 7*x**6/10 + 3*x**5/20 - 7*x**4/4 + x**3 + 6*x. Let u(k) = 0. Calculate k.
-1, 0, 1/3, 1, 2
Let w be (1/(-2))/(2/(-8)). Let p be w - 5 - -1 - -7. Let -l**4 + 0*l**2 + 5/3*l**p + 0 - 2/3*l**3 + 0*l = 0. What is l?
-2/5, 0, 1
Let n(h) be the second derivative of -3*h**5/20 - h**4 - 3*h**3/2 + 16*h + 2. Factor n(f).
-3*f*(f + 1)*(f + 3)
Let r(d) be the first derivative of 8 - 2/9*d**3 - 1/3*d - 1/2*d**2 + 1/5*d**5 + 1/6*d**4 + 1/18*d**6. What is f 