9*u**2 - 225*u = 0.
-74, -1
Solve -3*d**4 - 141*d**2 - 3*d**3 + 156*d**2 + 18*d - 3*d**3 = 0 for d.
-3, -1, 0, 2
Suppose 5*p - 3*h + 25 = 0, 4*p + 5*h + 11 = -9. Let n(i) = i**4 - i**2. Let s(v) = 3*v**4 + 6*v**3 - 9*v**2. Let y(w) = p*n(w) + s(w). Factor y(t).
-2*t**2*(t - 2)*(t - 1)
Let t(z) be the second derivative of 0 + 11/30*z**4 - 3/140*z**7 - 14*z + 47/200*z**5 + 0*z**2 + 1/5*z**3 + 1/50*z**6. Solve t(l) = 0.
-1, -2/3, 0, 3
Let y be (-144)/252 - 814/(-364). Let b = y - 21/26. Suppose -26/7*f**3 + 8/7*f**5 + b*f**4 - 4/7 + 18/7*f - 2/7*f**2 = 0. What is f?
-2, -1, 1/4, 1
Let l(w) be the third derivative of w**8/7560 - w**7/1890 + w**6/1620 + 3*w**3/2 + 19*w**2. Let c(j) be the first derivative of l(j). Factor c(p).
2*p**2*(p - 1)**2/9
Let r = 4 - 2. Factor 32*b**5 - r + 0 + 12*b**2 - 10*b**4 - 2*b - 4*b**3 - 26*b**5.
2*(b - 1)**3*(b + 1)*(3*b + 1)
Let a(m) = 5*m**4 - 121*m**3 + 342*m**2 + 24*m - 436. Let k(d) = -d**3 - 3*d**2 - d - 1. Let p(i) = a(i) + 4*k(i). Determine f so that p(f) = 0.
-1, 2, 22
Let u = -1416 - -1416. Factor 2/7*c - 2/7*c**3 + 2/7*c**4 - 2/7*c**2 + u.
2*c*(c - 1)**2*(c + 1)/7
Let j(t) = -4*t**4 - 4*t**3 - 36*t**2 + 60*t + 56. Let a(o) = -3*o**4 - 5*o**3 - 35*o**2 + 60*o + 58. Let g(c) = -8*a(c) + 7*j(c). Factor g(h).
-4*(h - 3)**2*(h + 1)*(h + 2)
Let k(s) be the first derivative of -s**4/4 - 10*s**3/3 - 25*s**2/2 + 246. Factor k(r).
-r*(r + 5)**2
Factor 0*x**2 - 3 - 7/2*x + 1/2*x**3.
(x - 3)*(x + 1)*(x + 2)/2
Let l(m) be the second derivative of -5*m**7/168 - 7*m**6/24 + 9*m**5/8 + 155*m**4/6 + 380*m**3/3 + 240*m**2 + 248*m. Solve l(v) = 0.
-4, -1, 6
Let t = -6201/2 - -3101. Factor 3/8*i + 1/8*i**2 - t.
(i - 1)*(i + 4)/8
Let p = -38 - -74. Factor p*x**2 + 6*x - 32*x**2 - 2*x.
4*x*(x + 1)
Let x(k) be the third derivative of 2*k**7/105 + 19*k**6/60 - 11*k**5/10 + k**4/12 + 11*k**3/3 - 18*k**2 + 4*k. Suppose x(b) = 0. Calculate b.
-11, -1/2, 1
Let q(j) = -21*j**3 - 174*j**2 - 420*j + 588. Let r(p) = -5*p**3 - 43*p**2 - 105*p + 147. Let s(i) = -2*q(i) + 9*r(i). Factor s(d).
-3*(d - 1)*(d + 7)**2
Let x(i) be the second derivative of -i**4/4 + 18*i**3 - 486*i**2 + 319*i. Suppose x(a) = 0. Calculate a.
18
What is d in -1/5*d**2 - 41/5 + 42/5*d = 0?
1, 41
Let o(n) be the first derivative of -3*n**5/10 + 3*n**4/8 + 10*n**3 - 305. Factor o(k).
-3*k**2*(k - 5)*(k + 4)/2
Let d be (-1)/(3/954*-1). Let n = -318 + d. Factor n - 4/3*b + 2/3*b**2.
2*b*(b - 2)/3
Let y(r) = r + 10. Let i be y(-10). Factor -4*k**3 - 7 - 8*k - 12*k**2 - 4*k + i*k**2 + 3.
-4*(k + 1)**3
Let a(g) = 14*g**4 - 44*g**3 - 53*g**2 + 1029*g + 1024. Let i(z) = 40*z**4 - 132*z**3 - 158*z**2 + 3086*z + 3072. Let y(q) = -14*a(q) + 5*i(q). Factor y(n).
4*(n - 8)**2*(n + 1)*(n + 4)
Factor 3*p**3 + 62*p - 20 - 10 + 2*p**3 + 0*p**2 - 34*p**2 - 3*p**3.
2*(p - 15)*(p - 1)**2
Find h, given that 13*h**4 - 22*h**4 - 10*h**3 - 2*h**3 + 5*h**4 + 36*h**2 + 108*h = 0.
-3, 0, 3
Let y(a) be the first derivative of a**4/12 + 49*a**3/9 - 101*a**2/6 + 17*a - 134. What is f in y(f) = 0?
-51, 1
Let t be 6/39 - 48/(-26). Suppose -r**4 + 2*r**2 - 12*r**3 + 5*r**4 + 12*r - 6*r**t = 0. Calculate r.
-1, 0, 1, 3
Let b = 3921/9247 + 6/1321. Let 6/7 - 3/7*v**2 + b*v = 0. What is v?
-1, 2
Let q(u) be the third derivative of -2*u**7/315 + u**6/15 + 8*u**5/15 + 13*u**4/9 + 2*u**3 - 84*u**2. Factor q(a).
-4*(a - 9)*(a + 1)**3/3
Let t(c) be the third derivative of -c**6/120 + 3*c**5/20 - 5*c**4/8 - 25*c**3/6 + 40*c**2. Determine z so that t(z) = 0.
-1, 5
Let j(s) be the second derivative of -s**8/672 + s**7/420 + s**6/240 - s**5/120 - 3*s**2 - 5*s. Let g(x) be the first derivative of j(x). Solve g(a) = 0 for a.
-1, 0, 1
Factor 0 - 128/7*c - 4/7*c**2.
-4*c*(c + 32)/7
Let c(y) be the third derivative of 0*y + 0*y**5 + 0 + 1/56*y**7 - 10*y**2 - 1/48*y**6 - 5/1344*y**8 + 0*y**4 + 0*y**3. Factor c(m).
-5*m**3*(m - 2)*(m - 1)/4
Let s(j) be the third derivative of -j**5/20 - j**4/4 + 34*j**2. Determine r, given that s(r) = 0.
-2, 0
Let j(s) be the second derivative of s**6/90 - s**5/6 + 10*s**3/3 - 26*s. Let u(d) be the second derivative of j(d). Suppose u(c) = 0. Calculate c.
0, 5
Let n(w) = -w + 1. Let d(j) = -2*j**3 + 11*j - 1. Suppose -2*o + 5 = -2*a + 3, -8 = -4*a - 2*o. Let f(g) = a*d(g) + 5*n(g). Factor f(q).
-2*(q - 2)*(q + 1)**2
Let d(v) be the second derivative of -486*v**5/5 - 63*v**4 + 104*v**3 - 40*v**2 - 24*v. Factor d(w).
-4*(6*w + 5)*(9*w - 2)**2
Let u(q) be the first derivative of -q**2 + 1/3*q**6 + 0*q**4 - 17 + 0*q + 4/3*q**3 - 4/5*q**5. Factor u(g).
2*g*(g - 1)**3*(g + 1)
Let k(w) be the first derivative of w**3/4 + 117*w**2/8 + 111*w/2 - 256. Determine j so that k(j) = 0.
-37, -2
Suppose 0 = 8*g - g - 42. Solve 2*h**3 - g*h**3 - 6*h - 4*h**3 - 7*h**3 - 21*h**2 = 0 for h.
-1, -2/5, 0
Factor -324/5 - 18/5*u + 6/5*u**2.
6*(u - 9)*(u + 6)/5
Let a = -79057/4 - -19765. Factor 0 + a*v**3 + 9/4*v**2 + 3/2*v.
3*v*(v + 1)*(v + 2)/4
Let g(z) be the second derivative of 5*z**7/42 - 7*z**6/30 - 23*z**5/20 - 5*z**4/12 + z**3 + 139*z. Find y, given that g(y) = 0.
-1, 0, 2/5, 3
Let x(n) be the third derivative of -n**6/480 - n**5/120 + n**4/12 + 21*n**2 - n. Determine f so that x(f) = 0.
-4, 0, 2
Factor -88*z + 363*z**2 + 16/3.
(33*z - 4)**2/3
Let s be 187/(-204)*135/(-99). Factor 0*h**2 + 1/2*h**3 + s*h**5 + 0*h + 7/4*h**4 + 0.
h**3*(h + 1)*(5*h + 2)/4
Suppose -2*f + 5*f = -3. Let c = 3 + f. Factor 3*r**2 + 3*r**3 - 3*r**3 + r**2 - c*r**3 - 2*r.
-2*r*(r - 1)**2
Factor -172*n**2 + 4 + 84*n**2 - 6*n + 90*n**2.
2*(n - 2)*(n - 1)
Let j(z) = z**5 + 4*z**4 + z**3 - 2*z + 2. Let a(i) be the third derivative of i**7/70 - i**4/8 + i**3/2 + 16*i**2. Let o(h) = -2*a(h) + 3*j(h). Factor o(y).
3*y**3*(y + 1)**2
Solve 19 - 4*u + 80*u**2 - 52*u**3 - 4 - 39 + 0 = 0.
-6/13, 1
Let q = 17961/2 - 8980. Let i = -3 + 7. Factor -1/2*r + 1 + 1/2*r**i - 3/2*r**2 + q*r**3.
(r - 1)**2*(r + 1)*(r + 2)/2
Let y(n) = -10*n**5 + 10*n**3 + 11*n - 11. Let s(l) = l**5 - l**3 - l + 1. Let t = 93 - 49. Let z(k) = t*s(k) + 4*y(k). Factor z(i).
4*i**3*(i - 1)*(i + 1)
Factor -43*a**2 + 138 + 51*a**2 + 60*a**2 - 368*a + 64*a**2 + 95*a + 3*a**3.
3*(a - 1)**2*(a + 46)
Suppose -3*h = -0*h + 5*t - 78, 0 = -3*t. Factor 4*s**2 - 2*s - h*s + 9*s**3 - 6 - 10*s**2 + 7*s.
3*(s - 2)*(s + 1)*(3*s + 1)
Let h = -97 - -114. Factor h - 81*k + 7 + 219*k + 33*k**2.
3*(k + 4)*(11*k + 2)
Suppose -5*m = -8 - 7, -4*r + 33 = -5*m. Let f be (36/(-378))/((-2)/r). Solve 2/7*v**3 + 2/7*v + 0 - f*v**2 = 0.
0, 1
Let -25/3*u + 8 + 1/3*u**2 = 0. What is u?
1, 24
Let z(n) = -3*n + 26. Let r be z(8). Factor v - 3*v**r - 1 + 1 + 5*v**2 + v**3.
v*(v + 1)**2
Let i(z) be the second derivative of -z**7/6300 + 11*z**6/3600 - z**5/120 - z**4 - z. Let x(b) be the third derivative of i(b). Determine l so that x(l) = 0.
1/2, 5
Let g(y) be the first derivative of -5*y**6/24 + 3*y**5/2 - 35*y**4/24 - 5*y**3 - 9*y**2/2 - 14. Let v(u) be the second derivative of g(u). Factor v(z).
-5*(z - 3)*(z - 1)*(5*z + 2)
Let k(o) be the first derivative of -o**4/16 + 43*o**3/12 - 551*o**2/8 + 1805*o/4 + 606. Factor k(l).
-(l - 19)**2*(l - 5)/4
Let w = -34716/5 - -6944. Factor 0*i + 0 - w*i**2 - 8/5*i**4 + 2*i**3 + 2/5*i**5.
2*i**2*(i - 2)*(i - 1)**2/5
Suppose 89*j = -6585 + 6852. Find s such that -6/11*s**2 + 4/11*s + 2/11*s**j + 0 = 0.
0, 1, 2
Let d(u) be the first derivative of u**5/60 + u**4/24 - u**3 - 5*u**2 - 17. Let m(h) be the second derivative of d(h). Factor m(w).
(w - 2)*(w + 3)
Let k(z) = 12*z**4 - 10*z**3 - 26*z**2 - 16*z + 3. Let q(u) = -60*u**4 + 48*u**3 + 132*u**2 + 80*u - 14. Let f(t) = -14*k(t) - 3*q(t). Factor f(j).
4*j*(j - 2)*(j + 1)*(3*j + 2)
Suppose -2*u - 10 = -7*u. Suppose j + 3*j**u - 2 + 8*j**3 - j**2 - 5*j**3 - 4*j**3 = 0. Calculate j.
-1, 1, 2
Let i(t) be the second derivative of -t**4/16 - 3*t**3/16 - 3*t**2/16 - t - 18. Solve i(v) = 0 for v.
-1, -1/2
Factor 1/3*z**3 - 2 - 4/3*z**2 - 11/3*z.
(z - 6)*(z + 1)**2/3
Let r(y) be the second derivative of 0*y**2 + 1/30*y**5 - 1/180*y**6 + 1/3*y**3 + 0 - 6*y - 1/12*y**4. Let m(w) be the second derivative of r(w). Factor m(g).
-2*(g - 1)**2
Suppose -5*h**3 - 30 - 56*h + 98*h - 7*h = 0. Calculate h.
-3, 1, 2
Let t be (-546)/(-143) - (-2)/11. Let j be 17/3 - t/6. Factor 3*n**j + 0 - 3*n**3 + 1 - 1.
3*n**3*(n - 1)*(n + 1)
Le