Factor k(i).
-2*i*(i + 2)/3
Let z(n) = -n**2 + n + 1. Let t(u) = 5*u + 9*u + 3*u**3 - 3*u**2 + 11 + 2*u**2. Let w(l) = 4*t(l) - 44*z(l). Factor w(c).
4*c*(c + 3)*(3*c + 1)
Let s(q) be the third derivative of 14*q**2 - 2/27*q**3 - 1/108*q**4 + 0 + 1/270*q**5 + 0*q. Factor s(u).
2*(u - 2)*(u + 1)/9
Factor -235298/11 + 2/11*z**3 - 294/11*z**2 + 14406/11*z.
2*(z - 49)**3/11
Let g = -14396/327 - -39/109. Let d = -43 - g. Suppose -d + 2/3*a**2 + 2/3*a - 2/3*a**3 = 0. What is a?
-1, 1
Let h(x) = -2*x**3 + 33*x**2 - 48*x + 117. Let f be h(15). Let 553/5*s**3 + 92/5*s + f*s**4 + 8/5 + 358/5*s**2 + 81/5*s**5 = 0. Calculate s.
-2, -1, -2/9
Let w(k) be the first derivative of k**3 + 45*k**2/2 + 42*k + 227. Find r such that w(r) = 0.
-14, -1
Suppose -44*q - 5 = -45*q. Let k(z) be the first derivative of 0*z + q - 3/4*z**4 + z**3 + 3*z**2. Suppose k(h) = 0. Calculate h.
-1, 0, 2
Let g = 1/2044 - 1075/108332. Let a = g - -851/318. Factor 2/3*w**3 - 8/3 + 2/3*w**2 - a*w.
2*(w - 2)*(w + 1)*(w + 2)/3
Let o(x) be the third derivative of 4*x**5/15 + 7*x**4/2 + 10*x**3/3 - 19*x**2 - 3*x. Find p, given that o(p) = 0.
-5, -1/4
Suppose -249/8*i**3 + 3/8*i**5 + 123/4*i - 21 + 75/8*i**4 + 93/8*i**2 = 0. Calculate i.
-28, -1, 1, 2
Let j(n) be the second derivative of -n**5/4 - 485*n**4/12 + 985*n**3/6 - 495*n**2/2 + 151*n + 1. Factor j(t).
-5*(t - 1)**2*(t + 99)
Factor -227 - 12*z**2 + 22*z**2 - 8*z**2 - 350*z - 118 - 7*z**2.
-5*(z + 1)*(z + 69)
Let g = -883 - -886. Determine t, given that 8/5*t**4 + 6/5*t**g + 0 - 18/5*t**2 + 4/5*t = 0.
-2, 0, 1/4, 1
Let w(x) = -x**2 + 32*x - 31. Let p be w(1). Let u(g) be the first derivative of 0*g**2 + 2/3*g**6 + p*g**3 + 0*g + 9 + g**4 - 8/5*g**5. Factor u(f).
4*f**3*(f - 1)**2
Let z = 164359/10 + -16421. Let b = z + -72/5. Solve -1/2*a**2 + a - b = 0 for a.
1
What is r in -1/2*r**4 - 14*r - r**3 + 6 + 19/2*r**2 = 0?
-6, 1, 2
Suppose -4 = -2*i + i. Factor 80 + 2*c**4 + i*c**3 - 80 - 6*c**2.
2*c**2*(c - 1)*(c + 3)
Let r(l) be the third derivative of l**7/525 + l**6/200 + l**5/300 - 85*l**2. Factor r(g).
g**2*(g + 1)*(2*g + 1)/5
Let h(a) be the first derivative of -a**4/12 - 7*a**3/9 - 8*a**2/3 - 4*a + 139. Factor h(s).
-(s + 2)**2*(s + 3)/3
Let p(f) be the third derivative of f**7/13860 - f**6/792 - 2*f**4/3 - 8*f**2. Let q(w) be the second derivative of p(w). Factor q(m).
2*m*(m - 5)/11
Let x(g) be the third derivative of -5*g**6/9 - 16*g**5/9 - 23*g**4/12 - g**3 - 11*g**2. Factor x(i).
-2*(i + 1)*(10*i + 3)**2/3
Factor -48/7 - 4*h**2 - 80/7*h + 8/7*h**3 + 4/7*h**4.
4*(h - 3)*(h + 1)*(h + 2)**2/7
Let s = -6/1355 + 1373/4065. Factor 0 + 1/3*c + s*c**2.
c*(c + 1)/3
Let i be 8/48 - 46/(-12). Suppose -3*c - i*u + 14 = 0, -3*u + 4 = -4*u. Factor 5*x + c*x**2 + 5*x**3 + 5*x - 5*x.
5*x*(x + 1)**2
Factor 6 + 8*h + 209*h**2 + 200*h**2 - 407*h**2.
2*(h + 1)*(h + 3)
Factor 50/3*a**3 - 1/3*a**4 - 300*a**2 - 5625 + 2250*a.
-(a - 15)**3*(a - 5)/3
Suppose 5*k + 5*m + 20 = 0, m = 4*k - 0*k - 4. Suppose 4*b + 3*n - 9 = -k, -5*b = 3*n - 12. Factor 0 - 196/5*i**5 + 0*i - 16/5*i**2 - 128/5*i**b - 308/5*i**4.
-4*i**2*(i + 1)*(7*i + 2)**2/5
Suppose 0 = 3*g - g. Suppose g = -2*j + 8, 3*j = 2*t + 2*j - 4. What is f in -8*f + 2*f**t + 0*f**4 + 5 + 4*f**2 + 8*f**3 + 0*f**4 - 11 = 0?
-3, -1, 1
Let n = -2805431/5 + 568388. Let a = n - 7270. Suppose 81/5*v**4 + 72/5*v + 12/5 + 33*v**3 + 3*v**5 + a*v**2 = 0. Calculate v.
-2, -1, -2/5
Suppose -z = -4*z + 243. Factor -27*d**2 - 81 - 3*d**5 + 0*d**4 - 30*d**3 - 21*d**4 + z*d**2 + 81*d.
-3*(d - 1)**2*(d + 3)**3
Let y(r) = -3*r**2 - 23*r + 26. Let o(z) = 2*z**2 - 2*z. Let s(x) = -3*o(x) - 3*y(x). Let s(a) = 0. What is a?
-26, 1
Let c(i) be the second derivative of i**5/35 + 32*i**4/21 - 22*i**3/7 - 174*i. Determine v, given that c(v) = 0.
-33, 0, 1
Let h(u) be the second derivative of -1/6*u**6 - 1 - u + 0*u**2 - 1/4*u**5 + 5/12*u**4 + 5/6*u**3. Let h(r) = 0. Calculate r.
-1, 0, 1
Let d be (-4)/(-2) + (2 - 2). Suppose -s = 4*b - 3, s + 5*b - d = 1. Factor -3*l - l**2 - 2 + s*l**4 + 0*l**2 + 0*l + 5*l**3 - 2*l.
(l - 1)*(l + 1)**2*(3*l + 2)
Let b = 235/9 + -461/18. Solve 1/2*s**2 - b + 0*s = 0.
-1, 1
Let l be (-6)/4 - 92/(-8). Determine t, given that 4*t**3 - 5*t - l*t**4 + 6*t**3 - 10 + 23*t**2 - 3*t**2 - 5*t**5 = 0.
-2, -1, 1
Let y(m) be the third derivative of -m**8/168 - m**7/35 - m**6/30 - 6*m**2 - 2. Factor y(n).
-2*n**3*(n + 1)*(n + 2)
Let d = -32 + 31. Let q be (14/12 + d)*10. Let 0*u + 4*u**4 + 2/3*u**2 + 0 + 3*u**3 + q*u**5 = 0. Calculate u.
-1, -2/5, 0
Let r = 8667/14 + -619. Let c(i) be the second derivative of 3/10*i**5 - 1/2*i**4 + 6*i + 1/10*i**6 + 0 - 1/2*i**3 - r*i**7 + 3/2*i**2. Factor c(j).
-3*(j - 1)**3*(j + 1)**2
Let h(u) be the second derivative of u**5/30 - u**4/2 + 3*u**3 + 16*u**2 + 25*u. Let y(v) be the first derivative of h(v). Factor y(o).
2*(o - 3)**2
Let v(m) = 9*m + 7. Let k(l) = -5*l - 3. Let s(b) = 11*k(b) + 6*v(b). Let j be s(9). Suppose 2*z**2 + j*z - z + 7*z = 0. Calculate z.
-3, 0
Let a(n) be the first derivative of -2*n**3/15 + 4*n**2 - 40*n - 275. Factor a(r).
-2*(r - 10)**2/5
Let m(t) be the first derivative of t**4/6 + 28*t**3/3 + 196*t**2 + 12*t + 20. Let s(h) be the first derivative of m(h). Factor s(b).
2*(b + 14)**2
Let f = 1168/4527 - 18/503. Factor 2/9*b - 2/9*b**2 - 2/9*b**3 + f.
-2*(b - 1)*(b + 1)**2/9
Find a such that 35/3*a + 1/9*a**3 + 2*a**2 + 200/9 = 0.
-8, -5
Let d(c) be the first derivative of 2*c**3/21 + 10*c**2/7 - 48*c/7 - 15. Find o such that d(o) = 0.
-12, 2
Let w(z) be the first derivative of z**5/150 - z**4/60 - 11*z**2/2 + 5. Let s(t) be the second derivative of w(t). Factor s(p).
2*p*(p - 1)/5
Let y(l) be the first derivative of l**6/360 - l**5/10 + 2*l**3 + 2*l + 23. Let f(p) be the third derivative of y(p). Solve f(h) = 0 for h.
0, 12
Suppose 19*b - 16*b + 9 = d, 0 = -2*d + 3*b + 12. Let y(n) be the first derivative of 2*n**2 + 8/3*n + 1 + 4/9*n**d. Let y(z) = 0. What is z?
-2, -1
Factor 2/11*b**2 - 2/11*b**3 + 8/11*b - 8/11.
-2*(b - 2)*(b - 1)*(b + 2)/11
Suppose -3*x - 265 = 5*d, -3*x - 215 - 58 = 3*d. Let m = x + 95. Let 2/7*k**3 + 0*k + m - 2/7*k**2 = 0. What is k?
0, 1
Let d(o) be the second derivative of 7*o**5/100 - 19*o**4/60 + 4*o**3/15 + 2*o**2/5 - 6*o. Solve d(w) = 0.
-2/7, 1, 2
Let n(z) = 4*z**2 - 12*z - 4. Let u(j) = 30*j**2 + j + 15 - 31*j**2 - 15. Let l(d) = 2*d + 4. Let f be l(-5). Let k(x) = f*u(x) - n(x). Solve k(m) = 0.
-2, -1
Let -2/11*r**2 + 294/11 - 92/11*r = 0. Calculate r.
-49, 3
Let k = 4675/2 - 2337. Factor k*p - 1/2*p**2 + 0.
-p*(p - 1)/2
Let p(b) be the second derivative of b**8/13440 + b**7/5040 - b**6/720 + 4*b**4/3 - 9*b. Let w(s) be the third derivative of p(s). Suppose w(h) = 0. What is h?
-2, 0, 1
Let b = -70 - -202. Let z = -1186/9 + b. Factor -z*i**3 + 2/9*i**4 + 2/9*i + 0 - 2/9*i**2.
2*i*(i - 1)**2*(i + 1)/9
Suppose -2*t = -2*g - 18, -t - 2*t + 25 = -5*g. Find a, given that -t*a**3 + 4*a**2 + 6*a + 12*a**3 + 2 + 2*a**2 = 0.
-1
Let s(o) = 11*o**4 - 2*o**3 + o**2 - o. Let y(j) = 5*j**4 - j**3. Let h(p) = -4*s(p) + 9*y(p). Find c, given that h(c) = 0.
-2, 0, 1, 2
Factor 5798*a**2 - 2982*a - 3803*a**2 + 0*a**4 + 5*a**4 + 777*a + 205*a**3.
5*a*(a - 1)*(a + 21)**2
Let o(s) = 60*s**5 + 81*s**4 + 12*s**3 + 9*s**2 + 9*s - 9. Let d(c) = 15*c**5 + 20*c**4 + 3*c**3 + 2*c**2 + 2*c - 2. Let i(u) = -9*d(u) + 2*o(u). Factor i(k).
-3*k**3*(k + 1)*(5*k + 1)
Let f(x) be the second derivative of x**5/4 - 65*x**4/12 - 325*x**3/6 - 255*x**2/2 + 380*x - 2. Factor f(j).
5*(j - 17)*(j + 1)*(j + 3)
Let t = 2306 - 2302. Let v(b) be the second derivative of 0*b**2 + 0*b**3 + 0 + 1/9*b**t - 13*b + 1/15*b**5. Solve v(j) = 0 for j.
-1, 0
Suppose -5*m + 7 + 13 = 0. Determine u, given that 5*u - u**2 + 7*u + m*u**2 = 0.
-4, 0
Suppose 0 = -6*z + 7*z - 2. Let -3*s**z + 2*s + s - 6*s**2 + 0*s = 0. What is s?
0, 1/3
Let l(n) = 3*n**4 + 3*n**3 + 6*n**2 - 12*n - 6. Let u(f) = 3*f**4 + 5*f**3 + 5*f**2 - 11*f - 6. Let y(h) = -2*l(h) + 3*u(h). Solve y(q) = 0.
-2, -1, 1
Suppose -189/4 - 225/4*g + 3/4*g**5 - 33/4*g**4 + 39/2*g**2 + 39/2*g**3 = 0. Calculate g.
-1, 3, 7
Let r(o) = -o**2 + 2072*o - 2071*o - 3 + 2. Let n(i) be the second derivative of 5*i**4/3 + 9*i**2 + i. Let g(t) = 2*n(t) + 28*r(t). Factor g(v).
4*(v + 2)*(3*v + 1)
Let h be (144/540)/(22/1