 + m**4/12 - 4*m**3/3 - 6*m**2. Let t be p(5). Factor 1/3*u**3 + u**t + 2/3*u + 0.
u*(u + 1)*(u + 2)/3
Let y(n) be the first derivative of 3*n**7/280 - n**6/160 - n**5/40 + 23*n**2/2 - 12. Let w(l) be the second derivative of y(l). Factor w(c).
3*c**2*(c - 1)*(3*c + 2)/4
Factor 15*s**4 - 20*s**5 + 43*s**5 - 18*s**5 + 5*s**3 - 15*s**2 - 10*s.
5*s*(s - 1)*(s + 1)**2*(s + 2)
Let o(w) = -2*w**4 + 54*w**3 - 142*w**2 + 140*w - 46. Let h(n) = 10*n**4 - 271*n**3 + 709*n**2 - 700*n + 230. Let s(u) = -2*h(u) - 11*o(u). Factor s(q).
2*(q - 23)*(q - 1)**3
Factor -74/9*r - 2/9*r**2 + 76/9.
-2*(r - 1)*(r + 38)/9
Suppose -6 - 15 = -7*m. Determine c so that 2*c + 13*c + 2*c**4 + 2*c**m - 10*c**2 - 9*c + 0*c = 0.
-3, 0, 1
Let j(f) be the first derivative of -f**6/300 + f**5/60 + 11*f**4/120 + 2*f**3/15 + 8*f**2 - 19. Let c(l) be the second derivative of j(l). Factor c(i).
-(i - 4)*(i + 1)*(2*i + 1)/5
Let n(x) be the second derivative of 0*x**2 + 0 + 0*x**3 - 2/147*x**7 - 16/105*x**6 + 48*x + 0*x**4 - 16/35*x**5. Factor n(i).
-4*i**3*(i + 4)**2/7
Let q(j) be the first derivative of -1/10*j**2 + 0*j + 4/25*j**5 - 3/10*j**4 + 4/15*j**3 - 9 - 1/30*j**6. Suppose q(h) = 0. What is h?
0, 1
Factor -5616/7*i - 3124/7*i**2 - 216/7*i**3 - 4/7*i**4 - 2704/7.
-4*(i + 1)**2*(i + 26)**2/7
Let x(w) = -10*w + 5*w - w - 1 + 5*w. Suppose 0 = -c - 2 + 4. Let d(h) = 3*h**2 + 8*h + 5. Let l(y) = c*x(y) + d(y). Determine b so that l(b) = 0.
-1
Solve 16/5*g**5 + 108/5*g**3 + 0 + 0*g + 54/5*g**2 - 18*g**4 = 0.
-3/8, 0, 3
Let x = -218 + 221. Let k be x - (-20)/(-6)*10/12. Factor 2/9*f**3 + 2/9 - 2/9*f - k*f**2.
2*(f - 1)**2*(f + 1)/9
Factor 33 + 3*p**3 - 9 + 54*p**2 + 6*p - 122*p**2 + 53*p**2.
3*(p - 4)*(p - 2)*(p + 1)
Suppose 58*j = 60*j. Let -3*p**4 - 2*p**5 - 2*p**2 + 5*p**4 + j*p**3 + 2*p**3 = 0. What is p?
-1, 0, 1
Let g = 11088 + -33575/3. Let t = g + 105. Factor -8/3 + 1/3*k**3 - t*k + 2/3*k**2.
(k - 2)*(k + 2)**2/3
Let r(d) be the first derivative of d**6/6 - 4*d**5/15 - 13*d**4/6 - 8*d**3/3 - d**2/6 + 4*d/3 + 170. Find p, given that r(p) = 0.
-1, 1/3, 4
Let 25/3*s**2 + 0 + 5*s**4 - 10*s**3 - 5/6*s**5 - 5/2*s = 0. What is s?
0, 1, 3
Let k = 1687/6 + -281. Let p(q) be the second derivative of -1/3*q**3 + 1/3*q**2 - 1/30*q**5 - 6*q + k*q**4 + 0. Factor p(y).
-2*(y - 1)**3/3
Suppose 31 = -5*j - 39. Let r be 22/(-6) + (-10 - j). Factor 0*u + 1/3*u**2 - r.
(u - 1)*(u + 1)/3
Let z(c) be the third derivative of 0 + 1/60*c**5 + 0*c + 1/240*c**6 + 0*c**4 + 3*c**2 + 0*c**3. Factor z(k).
k**2*(k + 2)/2
Suppose -4*v = 6 - 190. Factor 2 + 2*z**2 + v*z - 4 - 46*z.
2*(z - 1)*(z + 1)
Let 123*z + z**2 - 38*z + 150 + 4*z**2 = 0. What is z?
-15, -2
Let f be 0/((-108)/(-18))*(-2)/4. Factor 4/9*a + 2*a**2 + f + 10/9*a**4 + 8/3*a**3.
2*a*(a + 1)**2*(5*a + 2)/9
Let p be 0/(-1) - -22*2/4. Let v = p - 9. Determine t, given that 12/7*t**5 + 2/7 - 4/7*t + 26/7*t**4 + 8/7*t**3 - 12/7*t**v = 0.
-1, 1/3, 1/2
Let h(i) = i**2 + 9*i + 5. Let b be h(-9). Factor -1 - v**3 - 33*v - 14 - 21*v**2 + 3*v**3 - b*v**3.
-3*(v + 1)**2*(v + 5)
Let h(g) be the first derivative of -45*g**4/4 - 530*g**3/3 + 60*g**2 + 104. Factor h(l).
-5*l*(l + 12)*(9*l - 2)
Suppose -3*a + 7 = -4*f - 19, 2*a - 4*f = 24. Determine x, given that -1/8*x**3 - 3/8*x**a + 0 - 1/4*x = 0.
-2, -1, 0
Suppose 0*c - 3*c - 6 = 3*z, -4*c - 5*z - 10 = 0. Suppose -5*g - 2*r - 8 = c, 0 = 6*g - 3*g - 4*r - 16. Factor g*a**3 + 0*a + 3/5*a**2 - 3/5*a**4 + 0.
-3*a**2*(a - 1)*(a + 1)/5
Suppose 12*d + 8*d - 220 = 0. Factor p - 10*p**2 + 5*p**2 + 10*p**2 - d*p.
5*p*(p - 2)
Let l be (-5418)/(-2160) + (-20)/8. Let t(s) be the third derivative of 0 + 0*s + 1/240*s**6 + s**2 - 1/24*s**4 - l*s**5 + 0*s**3. What is v in t(v) = 0?
-1, 0, 2
Let q(i) be the second derivative of i**5/60 + i**4/2 - i**3/18 - 3*i**2 - 3*i - 3. Factor q(d).
(d - 1)*(d + 1)*(d + 18)/3
Suppose 3*k - 18 = -2*v - 2*k, -10 = -3*v + k. Factor -15*x**2 + 10*x + 0*x - 2*x**3 + 3*x**3 + v*x**3.
5*x*(x - 2)*(x - 1)
Let l(w) = -26*w - 23. Let v be l(4). Let u = 389/3 + v. Factor -2*f**2 - 2/3*f**3 + 0*f + u.
-2*(f - 1)*(f + 2)**2/3
Let 29/2*t**2 + 9/4 - 21/2*t**3 - 37/4*t - 1/4*t**5 + 13/4*t**4 = 0. Calculate t.
1, 9
Let r(y) be the first derivative of -y**6/1620 + y**5/90 + 7*y**4/108 + 10*y**3 - 2. Let h(b) be the third derivative of r(b). Factor h(s).
-2*(s - 7)*(s + 1)/9
Let r = -788/5 + 2384/15. Let d(l) be the first derivative of 0*l**2 - 3 + r*l**3 + 0*l. Determine n, given that d(n) = 0.
0
Let h be -374 - -375 - (-6)/4. Factor 3/2*y**4 - 9/2*y + y**2 + 5*y**3 - 1/2*y**5 - h.
-(y - 5)*(y - 1)*(y + 1)**3/2
Let f(i) be the second derivative of 2/45*i**6 + 0*i**2 + 1/15*i**5 + 0*i**3 + 1/36*i**4 - 17*i + 0. Factor f(g).
g**2*(2*g + 1)**2/3
Let d = 14 + -12. Let -3*i**2 - 6*i - 7*i**2 + 6*i**d + 5*i**2 = 0. Calculate i.
0, 6
Let z(s) be the first derivative of 3/8*s**4 + s - 1/4*s**2 - 2/3*s**3 + 18. Factor z(t).
(t - 1)**2*(3*t + 2)/2
Let k be (-20)/(-14) - (-28)/49. Factor 20*j - j**4 + 44*j**k - 9*j**4 + 11*j**2 + 25*j**3.
-5*j*(j - 4)*(j + 1)*(2*j + 1)
Let a = 403 - 398. Let i(w) be the third derivative of -1/280*w**7 + 1/1344*w**8 + 1/80*w**a + 0*w - 3*w**2 + 0*w**3 - 1/48*w**4 + 0 + 1/480*w**6. Factor i(r).
r*(r - 2)*(r - 1)**2*(r + 1)/4
Solve -686 + 112*c + 2*c**5 - 6*c**5 + 2*c**3 + 0*c**5 + 20*c**4 + 638 - 14*c**3 - 68*c**2 = 0.
-2, 1, 2, 3
Let q(f) = 2*f**2 + 17*f - 11. Let r be q(-10). Let 0*w**3 + 0*w**2 + 8*w**4 + 3*w - r*w + 4*w**3 - 32*w**2 = 0. What is w?
-2, -1/2, 0, 2
Let d be -2 + 4 - (3 + -1). Let b = d + 4. Factor -3*p**3 + 3*p**2 + 3*p**5 + 10*p**4 + 9*p**4 - 22*p**b.
3*p**2*(p - 1)**2*(p + 1)
Let t = 323/20 - 16. Let c(u) be the first derivative of -1/2*u**3 + 3/4*u**4 + 27/4*u + t*u**5 - 5 - 9/2*u**2. Factor c(h).
3*(h - 1)**2*(h + 3)**2/4
Suppose -69*r + 16 = -65*r. Let w be ((-25)/(-40))/(r/16). Factor 15/4*j + w + 5/4*j**2.
5*(j + 1)*(j + 2)/4
Let o(p) = 2*p**2 + 3*p - 4. Let w be o(2). Suppose -16*k + w*k = 0. Factor 2/3*x**5 - 4/3*x**4 + 4/3*x**2 - 2/3*x + k + 0*x**3.
2*x*(x - 1)**3*(x + 1)/3
Suppose -12 + 5 = -2*s + 5*i, 32 = 5*s + 2*i. Let n be 3*1/s*8/1. Find b, given that -14/13*b**3 - 40/13*b + 36/13*b**2 + 2/13*b**n + 16/13 = 0.
1, 2
Let k = 9 - 3. Suppose 0 = -2*w + 5*w - k. Factor -26*r**2 - 8*r + 8*r**3 + 16*r**4 - 12 + 11 + 11*r**w.
(r - 1)*(r + 1)*(4*r + 1)**2
Let u be (75/(-5))/(567/(-42)). Determine j so that -u*j**4 + 8/3*j - 8/3*j**3 + 8/9 + 2/9*j**2 = 0.
-2, -1, -2/5, 1
Let t(v) = 2*v**3 + 3*v**2 - 4*v + 1. Let h be t(2). Let u be (3/10)/(h/28). Factor 0 - 2/5*g + u*g**2.
2*g*(g - 1)/5
Suppose 0 = 7*s - 2*s - 10. Suppose s*w - 9 = w. Solve -2*m**4 + m**4 + 0 - w*m**2 + 8*m**3 - 3*m**3 - 2 + 7*m = 0 for m.
1, 2
Let n(o) be the first derivative of -6*o + 13*o**3 + 27/4*o**4 - 33/5*o**5 - 27/2*o**2 - 17. Solve n(c) = 0.
-1, -2/11, 1
Let t = 10709635/101781 - 4/33927. Let h = t - 105. Factor -4/9 + 2/9*b + h*b**2.
2*(b - 1)*(b + 2)/9
Factor -2/11*n**4 + 0*n**2 - 64/11*n + 12/11*n**3 + 0.
-2*n*(n - 4)**2*(n + 2)/11
Let r(o) = -o**2 + 4. Let q be r(0). Let z(k) = -3*k**2 + 42*k - 37. Let d be z(13). Solve 2*c**4 + 4*c**4 + 8*c**3 + 3*c**d - 2*c - 3*c**q = 0 for c.
-2, -1, 0, 1/3
Let d(r) be the second derivative of -r**7/105 + 13*r**6/225 - 17*r**5/150 + r**4/30 + 8*r**3/45 - 4*r**2/15 - 72*r. Find l, given that d(l) = 0.
-2/3, 1, 2
Let m(a) be the second derivative of -a**6/30 - 7*a**5/60 - a**4/12 + a**3/6 + a**2/3 - 149*a. Factor m(j).
-(j + 1)**3*(3*j - 2)/3
Suppose 4*u = 5*j + 33, u + j = -4*j - 23. Suppose -2*l = 3*v - 15, 0*l - v + 5 = u*l. Factor 0 + 3/5*d**2 + 3/5*d**4 + 6/5*d**3 + l*d.
3*d**2*(d + 1)**2/5
Let n(w) be the first derivative of w**4/20 - 3*w**3/10 - 2*w - 21. Let g(r) be the first derivative of n(r). What is p in g(p) = 0?
0, 3
Suppose v + 15 = -4*m - 13, 0 = -3*v. Let x = -1 - m. Find y, given that 2*y**4 - 6*y**3 + 0*y + 3*y + x*y**2 - 5*y = 0.
0, 1
Let u = -32 + 36. Factor 3*j**5 - j**3 - 2*j**u + 3*j**4 - j**2 - 2*j**5.
j**2*(j - 1)*(j + 1)**2
Find m, given that 70/9*m**5 + 698/3*m**3 + 734/9*m**4 + 100/9*m + 0 + 890/9*m**2 = 0.
-5, -2/7, -1/5, 0
Let l(t) be the second derivative of 30*t + 0*t**2 + 11/24*t**4 + 2/5*t**5 + 0 + 7/60*t**6 + 1/6*t**3. Factor l(v).
v*(v + 1)**2*(7*v + 2)/2
Let c(a) be the third derivative of 15*a**5/22 +