(-13))/(6/9). Suppose r = 42 - 18. Factor 10*y**f - 9 + r*y - 15*y**2 - 64*y - 6.
5*(y - 3)*(y + 1)*(2*y + 1)
Let d(p) be the third derivative of p**8/2184 - 41*p**7/1365 + p**6/10 + 820*p**2. Factor d(j).
2*j**3*(j - 39)*(j - 2)/13
Let n(p) be the second derivative of 3*p**6 + 49*p**5/20 - 13*p**4/4 + p**3/3 - 782*p. Factor n(w).
w*(w + 1)*(5*w - 2)*(18*w - 1)
Let k = -96 - -98. Let f = 8 + 2. Factor 13*y + 2*y**2 + k + f*y - 27*y.
2*(y - 1)**2
Let v(x) be the first derivative of 8*x**5/5 + 49*x**4/2 + 64*x**3 - 371*x**2 - 196*x + 675. Factor v(m).
2*(m - 2)*(m + 7)**2*(4*m + 1)
Let u(l) = -4*l**3 - 28*l**2 - 4*l - 24. Let f be u(-7). Factor 1/5*i**5 + 2/5*i**2 + 1/5 + 2/5*i**3 - 3/5*i**f - 3/5*i.
(i - 1)**4*(i + 1)/5
Let x(u) = u + 1. Let g(b) = 13*b - 1. Let j be g(0). Let k(h) = h - 4 - 2*h - 2*h**2 - 5*h. Let i(v) = j*k(v) - 8*x(v). Factor i(y).
2*(y - 2)*(y + 1)
Let u(k) be the third derivative of 3/10*k**6 - 1/15*k**7 + 0 + 0*k - 2*k**2 + 3/7*k**4 - 4/21*k**3 - 109/210*k**5. Suppose u(z) = 0. Calculate z.
2/7, 1
Suppose 52*q - 246 = 66. Let u(s) be the first derivative of 0*s + 0*s**4 - 1/24*s**q + 0*s**2 + 1/20*s**5 + 0*s**3 + 3. Factor u(g).
-g**4*(g - 1)/4
Let f(w) = 4*w**3 + 40*w**2 + 79*w. Let h(x) = -5*x**3 - 40*x**2 - 78*x. Let t(a) = -6*f(a) - 5*h(a). Solve t(o) = 0 for o.
-2, 0, 42
Let m(j) be the third derivative of j**7/105 - 7*j**6/30 - j**5/30 + 7*j**4/6 - 21*j**2 + 2. Factor m(n).
2*n*(n - 14)*(n - 1)*(n + 1)
Suppose 4*n**3 + 2*n**2 + 13 - 14*n**2 - 2 + 3 + 2 = 0. What is n?
-1, 2
Find v, given that 15 - 29/2*v - 1/2*v**2 = 0.
-30, 1
Let p be 4 - (14 + 147/(-14)). Determine u so that -88*u + 32 - 19/2*u**3 - 13/2*u**4 + 145/2*u**2 - p*u**5 = 0.
-8, 1
Suppose 15 = 3*g, 4*g - 53 = 3*s + 6*g. Let q be ((-18)/s)/((-1)/(-7)). Factor 9 + 5*p**2 - q - 3*p**3 - 2*p - 3.
-p*(p - 1)*(3*p - 2)
Let q be 26/10 - 3 - 27/(-5). Factor -18*g**3 - 3*g**q - 3*g - 9*g**4 + 3*g**2 + 9*g**2 + 15*g**4 + 6*g**4.
-3*g*(g - 1)**4
Suppose 0 = -2*h + 6*x - 4*x, 5*x = -4*h + 36. Let n = 9/62 - -13/124. Find w such that 0*w**2 - 1/2*w**h + 0 + n*w**5 + 1/4*w**3 + 0*w = 0.
0, 1
Let a(b) = -b**2 - 18*b + 43. Let w be a(-19). Find l such that -14 - 32*l + l**2 - w + l**2 + 166 = 0.
8
Let x = -14 + 19. Factor 15 - 9 - 10 + 14*m - 2*m - x*m**2.
-(m - 2)*(5*m - 2)
Determine i, given that 3 - 670*i - 2*i**3 - 3 + 694*i + 10*i**2 + 12*i**2 = 0.
-1, 0, 12
Let h be (-6)/(-21) - 57/(-21). Suppose -3*l + 1 = -2*l. Solve -w**h - 4*w + 3*w**2 - 2 + 2 + l + w = 0 for w.
1
Let j be (-2)/(-4)*-2 - -4. Let g(p) = 2*p**3 - p**3 + 10*p**2 + 8*p + 2*p**3 - p**j. Let a(o) = o**2 + o. Let u(c) = 6*a(c) - g(c). Factor u(q).
-2*q*(q + 1)**2
Let q(r) be the first derivative of 10/7*r**2 - 3 + 4/7*r + 16/21*r**3. Factor q(z).
4*(z + 1)*(4*z + 1)/7
Let f(i) = 5*i**2 + 46*i - 33. Let n(b) = -8*b**2 - 91*b + 69. Let j(t) = -5*f(t) - 3*n(t). Factor j(d).
-(d - 42)*(d - 1)
Let i(w) = -81*w - 2833. Let o be i(-35). Factor 0 + 0*l - 1/5*l**3 - 1/5*l**4 + 0*l**o.
-l**3*(l + 1)/5
Suppose -s - 2*i + 0*i + 3 = 0, 3*i + 8 = s. Find u, given that -6*u + 6*u**3 + 11*u**2 + s*u**2 + 18*u - 2*u**3 = 0.
-3, -1, 0
Let p be (-1 + (-9)/(-6))*(-6 + 12). Suppose 4*q + w - 1 = -2, 1 = -w. Factor 6*b + b**2 + q*b - 2 - 2*b - p*b**2.
-2*(b - 1)**2
Let x(w) = 20*w**2 + 8*w + 28. Let t(k) = -13*k**2 - 5*k - 19. Let o(d) = 7*t(d) + 5*x(d). Let y be o(-3). Factor -u - 24*u**2 - 15*u**3 - y*u**3 + 16*u**3 - u.
-2*u*(6*u + 1)**2
Factor 0*g**2 + 0 + 4/7*g**5 - 10/7*g**4 + 0*g + 4/7*g**3.
2*g**3*(g - 2)*(2*g - 1)/7
Factor 0 - 4/3*f**2 - 8/3*f**3 + 0*f - 4/3*f**4.
-4*f**2*(f + 1)**2/3
Let b be ((-3)/(-36))/(7/2184*26). Factor 1/4*d**2 - b - 1/4*d**3 + d.
-(d - 2)*(d - 1)*(d + 2)/4
Let f(s) be the first derivative of -4*s**5/25 - 5*s**4 - 664*s**3/15 - 192*s**2/5 + 1152*s/5 + 301. Find h, given that f(h) = 0.
-12, -2, 1
Factor 2*z**2 + 30*z**3 - z**5 + 5*z**4 - 15 + 8*z**2 - 25*z - 4*z**5.
-5*(z - 3)*(z - 1)*(z + 1)**3
Solve 32/5*i**2 - 128/5*i - 2/5*i**3 + 0 = 0 for i.
0, 8
Let h(g) be the first derivative of 2/45*g**5 + 332/27*g**3 + 88/3*g**2 + 242/9*g - 5 + 4/3*g**4. Factor h(b).
2*(b + 1)**2*(b + 11)**2/9
Let o(c) be the third derivative of -c**6/40 - 13*c**5/20 - 23*c**4/8 - 11*c**3/2 + 6*c**2 + 20. Factor o(j).
-3*(j + 1)**2*(j + 11)
Let i(x) be the first derivative of -51 - 20*x - 10*x**2 - 5/3*x**3. Factor i(u).
-5*(u + 2)**2
Suppose -1397*u**5 + 3*u**3 + u**3 + 1396*u**5 = 0. Calculate u.
-2, 0, 2
Let q = 4876/153 + -538/17. Factor 4/9 - q*p**2 + 2/9*p.
-2*(p - 2)*(p + 1)/9
Suppose 2*i = 8 - 0. Suppose -i*l + 3 = -l. Determine z so that 2*z - 4 + 3*z**4 - 6*z**3 + l + 0*z**3 + 4*z = 0.
-1, 1
Let r(o) be the first derivative of 13*o**3 + 9*o - 9/4*o**4 - 39/2*o**2 + 4. Factor r(v).
-3*(v - 3)*(v - 1)*(3*v - 1)
Let j = 6263/70 - 447/5. Let o(d) be the second derivative of 0*d**2 - 1/4*d**4 + 9/20*d**5 + 0 + 3*d + j*d**7 + 0*d**3 - 3/10*d**6. What is x in o(x) = 0?
0, 1
Suppose -28*g - 3 = 22*g - 153. Factor 8/3*n**2 + 4/3*n**g + 2/9*n**4 + 2/3 + 20/9*n.
2*(n + 1)**3*(n + 3)/9
Let f = 72 + -790/11. Let -8/11*n + 4/11 + f*n**3 - 1/11*n**2 = 0. What is n?
-2, 1/2, 2
Let m(g) be the second derivative of g**6/50 + 3*g**5/25 - 3*g**4/20 - 7*g**3/5 - 12*g**2/5 + 341*g. Factor m(n).
3*(n - 2)*(n + 1)**2*(n + 4)/5
Let u(j) = -155*j**3 + 45*j**2 + 950*j - 615. Let d(k) = 7*k**3 - 2*k**2 - 43*k + 28. Let f(w) = -45*d(w) - 2*u(w). Factor f(n).
-5*(n - 2)*(n - 1)*(n + 3)
Let o = -3648/37 - -244978/2553. Let w = -30/23 - o. Factor -w*t**2 - 2/3 + 2*t**4 - 2/3*t**5 - 4/3*t**3 + 2*t.
-2*(t - 1)**4*(t + 1)/3
Suppose -v = -2*k + 4, -2*v + 0*k = 3*k - 20. Let n(f) be the first derivative of -f + 6 - 3/4*f**2 + 1/8*f**v + 0*f**3. Determine c, given that n(c) = 0.
-1, 2
Suppose -4*j - 4 + 20 = 0. Suppose j*t = 12*t - 16. Factor 0 + 0*i**t + 2/7*i - 2/7*i**3.
-2*i*(i - 1)*(i + 1)/7
Let i(h) = 39*h**2 - 1715*h - 44. Let r be i(44). Factor 2/7*q**3 + r + 4/7*q**2 + 2/7*q.
2*q*(q + 1)**2/7
Let n be -4 - (-11 - 2/(-2)). Let l(h) = -18*h**3 - 72*h**2 - 80*h - 24. Let m(z) = 90*z**3 + 362*z**2 + 400*z + 120. Let f(g) = n*m(g) + 28*l(g). Factor f(p).
4*(p + 3)*(3*p + 2)**2
Let d(i) be the first derivative of i**7/420 - i**6/240 - i**5/120 + i**4/48 - 7*i**2/2 - 7. Let s(t) be the second derivative of d(t). Factor s(q).
q*(q - 1)**2*(q + 1)/2
Suppose -4*z = -3*h - 30, -3*h - 18 = -6*z + 4*z. Suppose 3*i + 4*j = -6, -5*j - 19 = i - z. Solve -3 + 3*d**i + 9/2*d = 0.
-2, 1/2
Suppose 3*a = t - 2 + 7, 0 = 4*a + 4*t - 12. Suppose 3*w - a*y + 8 = 0, w + 12 = -0*w + 3*y. Find z, given that w - z**2 + 1/3*z**3 + 2/3*z = 0.
0, 1, 2
Let x(r) be the third derivative of -9*r**3 + 2*r**2 + 0*r - 3/40*r**6 + 0 + 4/5*r**5 - 15/8*r**4. Solve x(d) = 0 for d.
-2/3, 3
Factor 5/3*g**2 + 10 - 35/3*g.
5*(g - 6)*(g - 1)/3
Let m(f) be the second derivative of -1/5*f**6 - 1/42*f**7 + 0*f**3 + 1/2*f**4 + 0 - 39*f + 0*f**2 + 1/20*f**5. Factor m(b).
-b**2*(b - 1)*(b + 1)*(b + 6)
Let a be 18/(-4 + 7) + -4. Suppose 5*i = 5, -5*s + a*i = i - 309. Factor 2*x + 41 + s*x**2 - 20*x**3 - 53 - 4*x.
-2*(x - 3)*(2*x - 1)*(5*x + 2)
Suppose -1/3*o + 2/3*o**3 - 2/3 - 2/3*o**4 + 4/3*o**2 - 1/3*o**5 = 0. Calculate o.
-2, -1, 1
Suppose 4*q + 268 = 3*x, -9 + 1 = -4*q. Factor -x*t**2 - 4 + 5*t**3 - t**3 + 80*t**2 + 12*t.
4*(t - 1)**3
Let v be (-3 - -8) + 0 - 1. Factor 548*p**2 + 31*p**4 + 74*p**v + 24 - 212*p - 352*p**3 - 41*p**4.
4*(p - 3)*(p - 2)*(4*p - 1)**2
Let k(b) be the second derivative of 21*b**6/50 - 591*b**5/100 + 52*b**4/5 + 94*b**3/5 + 48*b**2/5 - 337*b. Find o such that k(o) = 0.
-1/3, -2/7, 2, 8
Let i(k) be the third derivative of k**6/960 + 13*k**5/480 + k**4/16 + 2*k**2 + 9. Factor i(w).
w*(w + 1)*(w + 12)/8
Let y(b) be the second derivative of b**4/21 - 2*b**3/3 + 20*b**2/7 + 121*b. Let y(u) = 0. What is u?
2, 5
Let t(f) = f - 47. Let z be t(51). Let x(k) be the third derivative of -z*k**2 + 4*k**3 + 7/4*k**4 + 0 + 3/20*k**5 + 0*k. Determine w, given that x(w) = 0.
-4, -2/3
Let h = -345/11 - -1413/44. Let j(l) be the first derivative of -13 + 0*l - l**3 + 3*l**2 - h*l**4. Suppose j(a) = 0. Calculate a.
-2, 0, 1
Let a(b) be the first derivative of b**9/13608 + b**8/7560 - b**7/1890 + b**3/3 - 11. Let m(w) be the third derivative of a(w). Determine o so that m(