s**5/24 - s**4/48 - s**3/2 + 5*s**2. Factor q(n).
(n - 3)*(n - 1)**2*(5*n + 2)/2
Let l be 7/(-70) - 1366/(-60). Factor 8/3 - 175/3*q**3 - l*q + 49/3*q**4 + 62*q**2.
(q - 2)*(q - 1)*(7*q - 2)**2/3
Find i such that -1/5*i**3 + 0 - 1/5*i + 2/5*i**2 = 0.
0, 1
Let h(p) be the first derivative of p**4/18 - 4*p**3/27 - p**2/9 + 4*p/9 - 9. Solve h(v) = 0 for v.
-1, 1, 2
Factor 4/11*n**2 - 2/11*n**3 - 16/11 + 8/11*n.
-2*(n - 2)**2*(n + 2)/11
Determine o so that 0 + 6/13*o**4 - 6/13*o**2 + 8/13*o + 2/13*o**5 - 10/13*o**3 = 0.
-4, -1, 0, 1
Let s(y) be the second derivative of 0*y**2 - 1/15*y**6 + 0 + 1/6*y**4 + 7*y - 1/10*y**5 + 0*y**3 + 1/21*y**7. Let s(i) = 0. Calculate i.
-1, 0, 1
Let y be ((-2)/3 + 1)/(5/6). Factor 0*g**2 - 6/5*g + 8/5*g**3 + y.
2*(g + 1)*(2*g - 1)**2/5
Let y(d) = d + 15. Let w be y(-7). Factor k + 19 + w*k**3 - 19 - 4*k**5 - 5*k.
-4*k*(k - 1)**2*(k + 1)**2
Let l(z) = -6*z**3 + z**2 - 4*z - 5. Let r(w) = 4*w + 6 - 2 + 0*w**3 + 5*w**3 + 0. Let t(m) = -4*l(m) - 5*r(m). Factor t(q).
-q*(q + 2)**2
Suppose -d - 2*m = -6*d + 6, -m + 2 = 0. Factor 0 + 2/13*s**d - 2/13*s + 2/13*s**3 - 2/13*s**4.
-2*s*(s - 1)**2*(s + 1)/13
Suppose -3*z - 5 = -4*z, -5*b + z = 5. Factor -2/9*f + b + 2/9*f**2.
2*f*(f - 1)/9
Factor 464*b**2 + 900*b**3 + 944*b**4 - 44*b**5 - 89*b**2 + 236*b**5 - 224*b**4.
3*b**2*(4*b + 5)**3
Let v(h) be the first derivative of -2*h**5/5 + 2*h**4/3 + 2*h**3/9 - 2*h**2/3 - 5. Solve v(p) = 0 for p.
-2/3, 0, 1
Let z = 14 + -20. Let f = z + 13/2. Determine y, given that 2*y**2 - 1/2*y + 2*y**4 + 0 - 3*y**3 - f*y**5 = 0.
0, 1
Suppose 0 = -t - 3*t + 8. Factor 6*k - 4*k**t + k - 4*k + k**2.
-3*k*(k - 1)
Let b(y) be the second derivative of y**8/30240 - y**6/3240 + y**4/3 + 2*y. Let j(p) be the third derivative of b(p). Factor j(d).
2*d*(d - 1)*(d + 1)/9
Find m, given that -2/5*m + 0*m**2 + 0 + 2/5*m**3 = 0.
-1, 0, 1
Let j be -2*(2/(-8) - 0). Let w = j - 0. Suppose 0*m + 1/2*m**2 - w = 0. What is m?
-1, 1
Let -220/23*h**2 - 286/23*h**3 - 90/23*h**4 + 16/23 - 8/23*h = 0. Calculate h.
-2, -1, -2/5, 2/9
Let t(w) = -w**3 - 5*w**2 - 2*w - 7. Let f be t(-5). Let c(m) = m**3 - 4*m**2 + 3*m. Let z be c(f). Factor -1/4 + 1/4*a**2 + z*a.
(a - 1)*(a + 1)/4
Factor -1/6*n**3 + 0 - 1/2*n - 2/3*n**2.
-n*(n + 1)*(n + 3)/6
Let -4/13*j**5 + 28/13*j**2 + 2/13 - 32/13*j**3 - 12/13*j + 18/13*j**4 = 0. What is j?
1/2, 1
Suppose -167*x + 2 = -166*x. Factor 3*n**4 + 0 - 3/2*n**3 - 3/2*n**5 + 0*n + 0*n**x.
-3*n**3*(n - 1)**2/2
Find l, given that -6/5*l**2 + 1/5*l**3 + 9/5*l + 0 = 0.
0, 3
What is h in 1/2*h - 1/2*h**3 + 1/2 - 1/2*h**2 = 0?
-1, 1
Let m(q) be the first derivative of -q**4/8 - q**3/2 + 2*q - 3. Factor m(u).
-(u - 1)*(u + 2)**2/2
Let i(h) be the third derivative of -h**7/245 - h**6/420 + h**5/105 - 2*h**2. Suppose i(c) = 0. Calculate c.
-1, 0, 2/3
Let t(b) = 6*b**4 + 6*b**3 - 8*b**2 + 4*b - 4. Let l(v) = -5*v**4 - 5*v**3 + 7*v**2 - 3*v + 3. Let k(y) = 4*l(y) + 3*t(y). Factor k(s).
-2*s**2*(s - 1)*(s + 2)
Let p(g) be the third derivative of g**5/300 - g**4/30 + g**3/10 - g**2. Factor p(l).
(l - 3)*(l - 1)/5
Suppose 6 - 22 = -4*p. Let -2*f**3 + 3*f**3 - f**2 + 3*f**p + 2*f**3 - 2*f**2 - 3*f**5 = 0. Calculate f.
-1, 0, 1
Let k(z) be the third derivative of z**5/30 + z**4/12 - 2*z**3/3 + 8*z**2. Let k(y) = 0. Calculate y.
-2, 1
Let l(d) be the second derivative of d**7/70 - 3*d**6/50 + 9*d**5/100 - d**4/20 + 14*d. Find x, given that l(x) = 0.
0, 1
Factor 180*u**2 + 0*u + 8 - 8*u - 178*u**2.
2*(u - 2)**2
Suppose -2*u = -3*u. Let g be (2 + -2)/4 + u. Suppose 2/7*i**3 + g*i**2 + 0 - 2/7*i = 0. Calculate i.
-1, 0, 1
Let p(d) = 8*d**5 + 5*d**4 - 24*d**3 + 16*d**2 + 5*d. Let r(h) = -4*h**5 - 3*h**4 + 12*h**3 - 8*h**2 - 3*h. Let y(n) = -3*p(n) - 5*r(n). Factor y(k).
-4*k**2*(k - 1)**2*(k + 2)
Let s be 18/(-12)*(2 - 4). Let 0*z + 1/4*z**s + 0 + 3/4*z**4 + 0*z**2 = 0. Calculate z.
-1/3, 0
Let f = 257/3210 - 5/107. Let x(t) be the third derivative of -1/6*t**4 + t**2 + f*t**5 + 0*t**3 + 0*t + 0. Find d such that x(d) = 0.
0, 2
Let p = 3 + -1. Determine b so that 2*b + 2*b**p - 3*b**2 + 2*b**3 + 2*b**2 - 5*b**2 = 0.
0, 1
Let z(w) = -w**3 - 9*w**2 - 12*w + 16. Let o be z(-7). Factor -3/4*s**3 - 11/4*s**2 - o*s + 1.
-(s + 2)**2*(3*s - 1)/4
Let m(s) be the second derivative of 2*s**6/15 - 2*s**4 - 16*s**3/3 - 6*s**2 - 12*s. Factor m(g).
4*(g - 3)*(g + 1)**3
Suppose 0 = 3*v + v - 28. Let j = v + -3. Solve 0*l + 2/7*l**3 + 0 + 4/7*l**j + 0*l**2 + 2/7*l**5 = 0 for l.
-1, 0
Suppose -5*c + 2*c = -6. Factor -4*o**4 + 2*o**3 + 4*o**4 - c*o**4.
-2*o**3*(o - 1)
Let p be 43/3 - (-4)/6. Let m be 6/p + 20/75. Determine f so that -m*f**5 + 4/3*f**3 + 0 - 2/3*f + 0*f**4 + 0*f**2 = 0.
-1, 0, 1
Let z(k) be the first derivative of -1/5*k**5 - 4 - 1/4*k**4 + 1/2*k**2 + 0*k + 1/3*k**3. Factor z(a).
-a*(a - 1)*(a + 1)**2
Suppose 10 = -5*h + 3*h, 8 = 4*f - 4*h. Let n be (f/6)/(15/(-12)). Factor 0*s - 2/5*s**2 + n.
-2*(s - 1)*(s + 1)/5
Suppose 16*x - 11*x = -14*x. Determine p so that 3/4*p**3 + 1/4*p**4 + 3/4*p**2 + 1/4*p + x = 0.
-1, 0
Let p = 0 + 3. Let 9*t**2 - p*t**2 + t + 2 + 5*t**3 - 2 = 0. What is t?
-1, -1/5, 0
Let b(l) be the first derivative of -4*l**5/25 - l**4 - 30. Find f, given that b(f) = 0.
-5, 0
Factor -42*k**5 + 3*k - 8*k**3 + k + 46*k**5.
4*k*(k - 1)**2*(k + 1)**2
Let t(p) be the third derivative of -p**8/4480 + p**7/5040 + p**6/720 - p**4/24 + 3*p**2. Let g(f) be the second derivative of t(f). Factor g(s).
-s*(s - 1)*(3*s + 2)/2
Let n(q) be the third derivative of q**5/60 + q**4/12 + q**3/6 - 8*q**2. Factor n(z).
(z + 1)**2
Let x(f) be the second derivative of f**6/45 - f**5/60 - f. Determine h so that x(h) = 0.
0, 1/2
Let w(c) be the first derivative of -c**6/27 - 2*c**5/45 + c**4/18 + 2*c**3/27 + 13. What is j in w(j) = 0?
-1, 0, 1
Suppose -4 = -c + 2*j, -2*c - 1 = -5*j - 8. Suppose u = -u + c. Factor 0*p**3 + p**2 + u*p**4 - 3*p**3 + 4*p**3 - 5*p**3.
p**2*(p - 1)*(3*p - 1)
Let r be ((-21)/(-24) + -2)/(21/(-28)). Find i, given that -3*i**5 + r - 6*i**2 + 9*i**4 + 9/4*i - 15/4*i**3 = 0.
-1/2, 1, 2
Let d(o) be the second derivative of 0 - 7/12*o**4 - 1/3*o**3 - 4*o + 0*o**2. Factor d(s).
-s*(7*s + 2)
Let g = -2 - -5. Suppose -g*b + b + m = 1, b + 23 = 5*m. Suppose -1/6 + 1/3*y - 1/6*y**b = 0. What is y?
1
Suppose y = -t - 2*t + 1, 0 = -3*y - 5*t + 7. Let w be -4*y/(-120)*3. Factor 0*a + w - 2/5*a**2.
-2*(a - 1)*(a + 1)/5
Let n(q) be the first derivative of -1/12*q**3 + 0*q + 1/8*q**2 + 4. Let n(z) = 0. What is z?
0, 1
Let o = 10407/4039 + -3/577. Let b = 2682/2345 + -2/2345. Factor b*g**2 - 4/7*g**3 - 24/7*g**4 + o*g**5 + 0 + 2/7*g.
2*g*(g - 1)**2*(3*g + 1)**2/7
Let k(t) = -t**4 + t**3 - t**2 - t + 1. Let a(m) = -4*m**4 - 6*m**3 + 20*m**2 - 30*m + 14. Let y(d) = -a(d) + 6*k(d). Let y(n) = 0. Calculate n.
1, 2
Let g(c) be the first derivative of -5/2*c**3 + 2 + 7/3*c**4 + 2*c + c**2. Let m(z) be the first derivative of g(z). Factor m(y).
(4*y - 1)*(7*y - 2)
Let a = -54 + 109/2. Factor a - 1/2*k**2 + 0*k.
-(k - 1)*(k + 1)/2
Let h be (-5)/(-6)*(-2)/(-5). Let r = -18/5 - -59/15. Factor -r*a + 0 - 1/3*a**2 + h*a**4 + 1/3*a**3.
a*(a - 1)*(a + 1)**2/3
Solve 4/7*f**2 - 12/7*f + 8/7 = 0 for f.
1, 2
Determine o, given that 6 - 3/2*o**2 + 0*o = 0.
-2, 2
Let w be ((-45)/(-12) + -3)*(-96)/(-18). Factor -13/2*u**2 - 1/2*u**w - 6*u - 3*u**3 - 2.
-(u + 1)**2*(u + 2)**2/2
Let c(v) be the second derivative of 2/21*v**7 - 3/20*v**5 + 0 - 5/12*v**4 - 5*v + 1/3*v**3 + 0*v**2 + 4/15*v**6. Let c(j) = 0. What is j?
-2, -1, 0, 1/2
Factor -4/3*a + 0 - 4/3*a**2.
-4*a*(a + 1)/3
Let g(t) = -t**3 - 2*t**2 + 5*t + 6. Let o be g(-3). Let i(r) be the third derivative of 1/330*r**5 + 0*r - 2/33*r**3 + 1/132*r**4 - 2*r**2 + o. Factor i(u).
2*(u - 1)*(u + 2)/11
Let f be (2/16*5)/1. Let s = f + 1/24. Factor 0 - s*p**3 - 2/3*p**2 + 0*p.
-2*p**2*(p + 1)/3
Solve 4/5*o**2 - 3/5*o - 1/5*o**3 + 0 = 0.
0, 1, 3
Let x be 42/153 + (-3)/9. Let v = 41/119 + x. Factor 0*h + 2/7 - v*h**2.
-2*(h - 1)*(h + 1)/7
Factor -t + 4*t**2 - 7 - 13 - 15*t.
4*(t - 5)*(t + 1)
Let h = 6 - 0. Let u be (((-72)/21)/h)/(-1). Factor 0 + u*l + 2/7*l**2.
2*l*(l + 2)/7
Factor -10/3*c**2 - 4/3*c - 2/3*c**4 + 0 - 8/3*c**3.
-2*c*(c + 1)**2*(c + 2)/3
Let i be 20/8*(2 + 0). Suppose i*y - 5 = 5. Determine d, given that 2/5*d + 2/5*d**3 + 0 - 4/5