**3 + 109*c**2. Factor u(d).
-3*(d - 2)*(3*d - 1)
Let w be -4 - 1 - (-2185)/414. Let j = 17/18 - w. Factor j*y + 4/9*y**2 - 4/9 - 2/3*y**3.
-2*(y - 1)*(y + 1)*(3*y - 2)/9
Let t(d) be the second derivative of -d**4/9 + 2*d**3/3 + 20*d**2/3 - 96*d. Factor t(q).
-4*(q - 5)*(q + 2)/3
Let x(z) be the second derivative of 27*z**5/50 - 143*z**4/20 + 28*z**3 + 24*z**2/5 + 71*z. Factor x(h).
3*(h - 4)**2*(18*h + 1)/5
Let m = 5 - -3. Let u = -6 + m. Solve 2 - 2 - 3*g + 0*g**u - 3*g**2 = 0.
-1, 0
Let h = 24 + -14. Let c be (4 + (-24)/h)/((-4)/(-10)). Factor 0*q - 2/3*q**c + 4/3*q**2 + 0*q**3 - 2/3.
-2*(q - 1)**2*(q + 1)**2/3
Let f(a) be the second derivative of -1/210*a**6 + 1/42*a**4 + 1/140*a**5 + 0*a**2 - 15*a + 0 + 0*a**3. Suppose f(h) = 0. Calculate h.
-1, 0, 2
Let b(j) be the first derivative of -5*j**4/12 - 5*j**3/6 - 6*j + 20. Let s(n) be the first derivative of b(n). Factor s(w).
-5*w*(w + 1)
Let u(x) be the second derivative of x**8/47040 - x**7/17640 - x**6/2520 - 7*x**4/3 - 22*x. Let h(i) be the third derivative of u(i). Factor h(d).
d*(d - 2)*(d + 1)/7
Find f, given that 6*f**2 + 215 - 107*f - 54*f - 181*f - 123*f + 16 = 0.
1/2, 77
Let z = -10 - -15. Factor -5*g**2 + 4*g**4 + 5*g**3 + z*g**4 - 3*g**4 - 5*g**5 - g**4.
-5*g**2*(g - 1)**2*(g + 1)
Let v(k) be the first derivative of -7*k**3/9 + 9*k**2 + 16*k/3 + 102. Find x, given that v(x) = 0.
-2/7, 8
Let p(o) = -11*o**4 - 9*o**3 + o**2 + 9*o + 5. Let r(i) = 6*i**4 + 5*i**3 - 5*i - 3. Let u(j) = -3*p(j) - 5*r(j). Factor u(n).
n*(n - 1)*(n + 1)*(3*n + 2)
Let r = 50/57 - 4/19. Let h = -11/6 - -5/2. Factor -2/3*x**2 + r - h*x**3 + 2/3*x.
-2*(x - 1)*(x + 1)**2/3
Let s(i) = -10*i**2 - 19*i - 4. Let u = 10 - 7. Let p(q) = u*q + 14*q**2 + 6*q**2 + 55*q + 10*q**2 + 12. Let k(a) = 5*p(a) + 16*s(a). Factor k(f).
-2*(f + 1)*(5*f + 2)
Let m(b) be the second derivative of -b**4/4 + 201*b**3/2 + 303*b**2 + 2*b + 27. Factor m(i).
-3*(i - 202)*(i + 1)
Let g(k) be the third derivative of -12*k**2 + 0*k + 1/228*k**4 + 0 - 1/570*k**5 + 0*k**3. Factor g(a).
-2*a*(a - 1)/19
Let x(p) be the first derivative of -p**4/7 - 152*p**3/21 + 160*p**2/7 + 252. What is m in x(m) = 0?
-40, 0, 2
Let y(l) be the second derivative of -l**5/110 - l**4/66 + 4*l**3/33 + 4*l**2/11 - 96*l. Suppose y(d) = 0. Calculate d.
-2, -1, 2
Let g = -7 + 11. Let q be ((-4)/(-6))/(g/30). What is t in -q*t**2 + 0*t**2 - 2*t**3 + 7*t**2 = 0?
0, 1
Factor 0 + 0*d + 1/5*d**3 + 8/5*d**2.
d**2*(d + 8)/5
Let m be ((-80)/(-28) + -3)/(-3). Let c(s) be the second derivative of 0*s**2 + 0*s**4 - m*s**3 + 1/70*s**5 + 4*s + 0. Factor c(q).
2*q*(q - 1)*(q + 1)/7
Let d(n) = -6*n**5 + 20*n**4 - 6*n**3 - 59*n**2 - 100*n + 37. Let z(u) = -u**5 + 4*u**4 - u**3 - 12*u**2 - 20*u + 6. Let s(a) = -2*d(a) + 11*z(a). Factor s(q).
(q - 2)*(q + 1)**2*(q + 2)**2
Let -29/3 + 205/6*k - 7/6*k**2 = 0. Calculate k.
2/7, 29
Let q = 1 - -8. Factor -2 + 5 + 4*r**2 + q*r + 3*r**3 + 5*r**2.
3*(r + 1)**3
Suppose 3*c - 2*c = 6. Factor -8*g - c*g**2 + 6 + 2*g**3 + 24*g - 18*g.
2*(g - 3)*(g - 1)*(g + 1)
Suppose 0 = 3*i - b, -7*i + 13*b = -4*i. Let -1/10*z**2 + 1/10*z + i = 0. Calculate z.
0, 1
Let j(y) = 6*y**4 - 6*y**3 - 12*y**2 + 12*y + 15. Let m(f) = -13*f**4 + 11*f**3 + 23*f**2 - 25*f - 31. Let t(u) = -7*j(u) - 3*m(u). Solve t(p) = 0.
-1, 1, 4
Factor -11/5*d + 1/5*d**2 + 0.
d*(d - 11)/5
Let q be ((-1)/(-4))/(204/544). Factor 4/3*a - 4/3*a**3 - q*a**2 + 0 + 2/3*a**4.
2*a*(a - 2)*(a - 1)*(a + 1)/3
Let -11*b + 131*b + 4*b**2 + 265*b + 477 - 21 - 149*b = 0. Calculate b.
-57, -2
Solve 0 + 2/5*q**2 - 238/5*q = 0.
0, 119
Suppose 19 = 3*w + 4. Let a(b) be the third derivative of -6*b**2 - 1/3*b**6 - 2/15*b**w + 0*b**3 + 0 - 5/21*b**7 + 0*b**4 + 0*b. Factor a(c).
-2*c**2*(5*c + 2)**2
Suppose -x = 4 - 7. Factor x*l**3 + 2*l**2 + 29*l**4 + 35*l**4 - 63*l**4.
l**2*(l + 1)*(l + 2)
Let r(d) be the second derivative of d**4/12 - 20*d**3/3 + 200*d**2 + 2*d + 14. What is j in r(j) = 0?
20
Let d(g) be the second derivative of 3/35*g**5 - 2/21*g**4 + 0*g**2 + 0 - 2/105*g**6 + 0*g**3 + 10*g. Factor d(i).
-4*i**2*(i - 2)*(i - 1)/7
Let m(v) = v**2 - 1. Let h be -1 + -1 + -1 + 9. Let q(k) = 4*k**2 - 4. Let l(u) = h*q(u) - 26*m(u). What is g in l(g) = 0?
-1, 1
Let y = 2048/615 + 2/615. Let w(n) be the first derivative of -y*n + 5/2*n**2 + 11 - 5/9*n**3. Factor w(h).
-5*(h - 2)*(h - 1)/3
Suppose -67 = -5*u - 27. Let z(p) be the first derivative of 2/21*p**3 + 0*p + u - 2/7*p**2. Factor z(h).
2*h*(h - 2)/7
Factor 56 - 58*m + 16*m**2 - 1/2*m**3.
-(m - 28)*(m - 2)**2/2
Let z be ((-5)/(-5) + -1)/((-92)/(-23)). Factor 2*l**3 + l - 1/2*l**4 - 5/2*l**2 + z.
-l*(l - 2)*(l - 1)**2/2
Let i be (-1 - 27)*43/(-172). Let g(c) be the third derivative of 23/360*c**6 + 13/72*c**4 - 1/90*c**i + 0 - 3/20*c**5 - 1/9*c**3 - c**2 + 0*c. Factor g(h).
-(h - 1)**3*(7*h - 2)/3
Let l(p) be the third derivative of -p**8/336 - p**7/84 + p**6/48 + p**5/24 - p**4/16 - 42*p**2. Solve l(d) = 0.
-3, -1, 0, 1/2, 1
Factor 66*q**2 + 3*q**4 + 36*q**2 - 28*q**3 - 23*q**3 + 24*q**2.
3*q**2*(q - 14)*(q - 3)
Factor -4/3*q**2 - 768 - 64*q.
-4*(q + 24)**2/3
Let n(y) be the third derivative of -3*y**6/160 + 43*y**5/80 - 53*y**4/32 + 13*y**3/8 - 78*y**2. Solve n(w) = 0.
1/3, 1, 13
Let c(u) be the second derivative of -u**7/28 + u**6/20 + 9*u**5/40 - u**4/8 - u**3/2 + 40*u. Solve c(t) = 0 for t.
-1, 0, 1, 2
Let a(k) = -k**3 + 23*k**2 - k - 9. Let p be a(23). Let x = p + 34. Factor -2/5*f**x - 6/5*f - 4/5.
-2*(f + 1)*(f + 2)/5
Let j be (-183)/(-793) + 4*68/624. Determine h, given that 2/3*h**3 - j*h - 4/9 + 2/9*h**2 + 2/9*h**4 = 0.
-2, -1, 1
Let i = 56027/7370 - 3/1474. Let n = 81/10 - i. Factor n*h**2 - 1/4*h**3 + 1/4*h - 1/2.
-(h - 2)*(h - 1)*(h + 1)/4
Let r be (13 - 2088/117) + 5. Find u, given that -2/13*u**2 - r*u + 0 = 0.
-1, 0
Let i(q) be the third derivative of 0*q**6 + 0*q + 3 - 1/80*q**5 + 3*q**2 + 0*q**4 + 0*q**3 + 1/280*q**7. Find f, given that i(f) = 0.
-1, 0, 1
Suppose -z - 3*z + 2*j = -6, -2*z + 3*j = -9. Let x(u) be the first derivative of -1/8*u**6 + 0*u**2 + z*u - 1/8*u**4 + 0*u**3 - 1/4*u**5 - 6. Factor x(w).
-w**3*(w + 1)*(3*w + 2)/4
Suppose 2*o + 16 = -2. Let x(a) = 2*a + 20. Let i be x(o). What is f in i*f**4 + 2*f + 2 - 18*f**2 - 10*f**4 + 6*f**3 + 16*f**3 = 0?
-1/4, 1
Let s(w) be the first derivative of -w**7/1260 - w**6/270 - w**5/180 - 9*w**3 + 23. Let h(o) be the third derivative of s(o). Factor h(q).
-2*q*(q + 1)**2/3
Determine r so that 45*r**4 - 20*r**5 - 302*r**3 + 50*r**4 + 227*r**3 = 0.
0, 1, 15/4
Suppose 0 = 3*g - 3977 + 3968. Factor 5/2*h**g + 1/2*h**5 + 0*h - h**2 + 0 - 2*h**4.
h**2*(h - 2)*(h - 1)**2/2
Let c = 462 - 2306/5. Let r be 2 - (6/(-3))/2. Let -1/5*h**5 - 2/5*h**2 - c*h**r + h + 4/5*h**4 - 2/5 = 0. Calculate h.
-1, 1, 2
Let 6*s**3 - 26*s**3 + 216 - 8003*s + 8335*s - 528*s**2 = 0. What is s?
-27, -2/5, 1
Let c = -40 - -42. Factor 6*d - d**3 + 0*d + 48*d**2 - 45*d**2 - c*d**3.
-3*d*(d - 2)*(d + 1)
Suppose -12*r + 18*r = -168. Let c be -3 + ((-384)/r)/1. Factor -3/7 + 30/7*t - c*t**2.
-3*(5*t - 1)**2/7
Find a such that -a**4 + 21*a**2 + 34*a + 12*a + 10*a**3 - 22*a**2 + 8*a - 35*a**2 - 27 = 0.
1, 3
Let d(s) be the third derivative of 1/14*s**4 + 13*s**2 + 3/14*s**3 + 0*s + 1/140*s**5 + 0. Solve d(k) = 0.
-3, -1
Suppose 15/2*k**2 - 9/2*k**3 + 1/2*k**4 - 7/2*k + 0 = 0. Calculate k.
0, 1, 7
Let f(r) be the first derivative of r**5/15 - r**4/12 - 2*r**3/9 + 189. Factor f(v).
v**2*(v - 2)*(v + 1)/3
Let k be 5 + ((-9)/6)/((-6)/(-8)). Factor -4*i**k - 2*i - 16*i**2 + 2*i + 8*i**2.
-4*i**2*(i + 2)
Let o(u) be the third derivative of -u**9/60480 + u**7/1680 - u**6/360 + 19*u**5/60 - 21*u**2. Let r(i) be the third derivative of o(i). Factor r(m).
-(m - 1)**2*(m + 2)
Let x(s) be the first derivative of 1/18*s**4 - 2*s + 1/60*s**5 + 3 + 0*s**2 + 1/18*s**3. Let i(b) be the first derivative of x(b). Factor i(d).
d*(d + 1)**2/3
Suppose 53*t - 52*t - 8 = -m, -3*t + 3*m - 12 = 0. Factor 16/13*j - 6/13 + 0*j**3 - 12/13*j**t + 2/13*j**4.
2*(j - 1)**3*(j + 3)/13
Let z(r) be the second derivative of r**7/840 + r**6/120 + r**5/60 + r**3/6 + r. Let l(q) be the second derivative of z(q). Determine o, given that l(o) = 0.
-2, -1, 0
Let c(w) be the second derivative of 45/8*w**2 - 35/8*w**3 - 1/8*w**6 + 25/24*w**4 + 3/8*w**5 + 0 - 5/1