*a**4 + 16/7*a - 16/7*a**2 + i + 4/21*a**3. Factor v(j).
4*(j - 1)*(j + 2)*(3*j - 2)/7
Let s(w) = -5*w**3 + 77*w**2 + 243*w - 5769. Let j(m) = -m**2 + m - 3. Let z(r) = -3*j(r) + s(r). Factor z(g).
-5*(g - 12)**2*(g + 8)
Let j(l) be the second derivative of l**7/21 + 44*l**6/15 + 314*l**5/5 + 435*l**4 - 1575*l**3 - 6750*l**2 + 4*l + 54. Factor j(b).
2*(b - 2)*(b + 1)*(b + 15)**3
Let p(y) be the first derivative of -128 - 5*y + 3/4*y**2 + 1/6*y**3. Determine k, given that p(k) = 0.
-5, 2
Let a(s) be the second derivative of s**4/24 + 13*s**3 + 155*s**2/4 - 7513*s. Factor a(y).
(y + 1)*(y + 155)/2
Suppose -37*s + 178 - 30 = 0. Let c(y) be the first derivative of -6/65*y**5 - 15 + 1/13*y**2 + 10/39*y**3 - 4/13*y - 1/26*y**s. Let c(z) = 0. Calculate z.
-1, 2/3, 1
Let -1938/7 + 652/7*r - 2/7*r**2 = 0. What is r?
3, 323
Factor -1800 - 57*l**3 + 42*l**4 + 707*l + 1873*l - 722*l**2 - 26*l**4 - 8*l**4 - 9*l**4.
-(l - 2)*(l - 1)*(l + 30)**2
Let v(d) be the second derivative of -d**8/5040 - d**7/630 - d**6/360 + d**3/3 - 3*d**2/2 - 11*d. Let k(q) be the second derivative of v(q). Factor k(b).
-b**2*(b + 1)*(b + 3)/3
Let c(d) be the second derivative of -1/9*d**3 + 1/90*d**6 + 1/120*d**5 - 1/8*d**4 - 14*d + 1/3*d**2 + 2. Solve c(k) = 0.
-2, -1, 1/2, 2
Let t(z) = 23*z - 39. Let b(r) = -r - 1. Let u(s) = 6*b(s) - t(s). Let p be u(1). Let -1/3*o**3 + 0 + 0*o**p + 1/6*o + 1/6*o**5 + 0*o**2 = 0. Calculate o.
-1, 0, 1
Let b(t) be the second derivative of -t**4/18 + 8*t**3 - 69*t**2 - 22*t + 42. Find p such that b(p) = 0.
3, 69
Let w = -484/19 + 8549/38. Let q = w - 197. Let -45/4*t**3 - 45/4*t + q*t**4 + 5/2 + 35/2*t**2 = 0. Calculate t.
1/2, 1, 2
Let q(v) = -v**2 - 12848*v + 4211999. Let u(h) = -2572*h + 842400. Let k(g) = -2*q(g) + 11*u(g). Factor k(y).
2*(y - 649)**2
Suppose -923*a + 897*a + 49 + 81 = 0. Let o(u) be the first derivative of 19 + 0*u**2 + 0*u + 1/4*u**4 - 2/3*u**3 + 1/5*u**a. Factor o(d).
d**2*(d - 1)*(d + 2)
Let a = -54 + 63. Suppose 3*c = -2*z + 2 + a, -c - 3 = -z. Solve 10*x**2 + 7*x**3 + z*x + 6*x**4 - 8*x**4 - x**3 - 2*x**5 = 0 for x.
-1, 0, 2
Let z be (-15 - 1134) + (1 - 1)/1. Let a = z + 3449/3. Let 26/9*d**2 + 2/3 + 26/9*d + a*d**3 = 0. Calculate d.
-3, -1, -1/3
Let d(s) = -4*s**2 - 53*s - 45. Suppose 18 = -2*w + 4*z, -4*z - z = -5. Let p(q) = -4*q**2 - 54*q - 47. Let m(c) = w*d(c) + 6*p(c). Find u such that m(u) = 0.
-11, -3/4
Let u be ((-3)/5)/((-3636)/16160). Let v(w) be the first derivative of -w**2 + 18 + u*w**3 + 1/2*w**4 - 8*w. Determine b, given that v(b) = 0.
-4, -1, 1
Let s(w) be the third derivative of 9/10*w**5 - 1/112*w**8 - 37/40*w**6 + 2/7*w**7 + 0*w**4 + 0 + 0*w**3 + 2*w + 23*w**2. Factor s(k).
-3*k**2*(k - 18)*(k - 1)**2
Let r(n) be the third derivative of -n**5/12 - 35*n**4/24 - 5*n**3 + 280*n**2 - 3. Factor r(x).
-5*(x + 1)*(x + 6)
Let v = -507 - -1022. Let b = v - 513. Factor 19/6*a - 4/3*a**b - 5/6*a**3 - 1.
-(a - 1)*(a + 3)*(5*a - 2)/6
Let -1/3*o**4 + 0 + 23/3*o**3 + 53/3*o**2 - 25*o = 0. Calculate o.
-3, 0, 1, 25
Suppose 0 = 3*y + 3*f + 9, 15 = -10*y + 6*y - 3*f. Let r(x) = -5*x**2 - 50*x - 39. Let m(t) = -9*t**2 - 99*t - 79. Let q(b) = y*m(b) + 11*r(b). Factor q(n).
-(n - 45)*(n + 1)
Let t be -549*15/(-5670) - (-6)/28. Factor -t*c**3 + 2*c**2 - 8/3 + 4/3*c + 1/3*c**4.
(c - 2)**3*(c + 1)/3
Factor -2*j + 6/13*j**2 + 28/13.
2*(j - 2)*(3*j - 7)/13
Let x = 10613 - 31838/3. Factor -4/3 - x*h**2 + 4/3*h.
-(h - 2)**2/3
Let f be ((-66220)/(-90) - -6) + 6/27. Let v = f + -740. Factor 3/7 + 6/7*g - 9/7*g**v.
-3*(g - 1)*(3*g + 1)/7
Let u = -8459/10 - -846. Let m(w) be the second derivative of 1/6*w**3 + 0 + 1/15*w**6 + w**2 - u*w**5 - 1/3*w**4 + 18*w + 1/42*w**7. Let m(a) = 0. Calculate a.
-2, -1, 1
What is r in 28*r**2 + 310 + 19462*r**3 - 178*r**2 - 165*r - 19457*r**3 = 0?
-2, 1, 31
Factor 8542*j**2 + 2*j**3 - 2 - 17167*j**2 + 8498*j**2 + 2 - 64*j.
j*(j - 64)*(2*j + 1)
Let q = 73 - 78. Let m(c) be the second derivative of -c**4/12 - c**3 - c. Let k(y) = -3*y**2 - 13*y. Let r(x) = q*m(x) + 2*k(x). Solve r(i) = 0 for i.
0, 4
Find a, given that -3/4*a**3 + 945/2 + 90*a**2 + 2253/4*a = 0.
-5, -1, 126
Suppose 5*u + 5 = 2*l, -l - 1789 + 1786 = 3*u. Determine t, given that -3/2*t**3 + 0*t + l + 12*t**2 = 0.
0, 8
Let h = 80/123 - 232/861. Let o(s) be the first derivative of 7 + h*s**3 - 2/7*s - 5/28*s**4 - 1/14*s**2. Factor o(w).
-(w - 1)**2*(5*w + 2)/7
Factor 1/4*s**2 + 34*s - 137/4.
(s - 1)*(s + 137)/4
Find l such that 65/3*l**2 - 44/3 - 8*l - 1/3*l**5 + 25/3*l**3 - 7*l**4 = 0.
-22, -1, 1, 2
Let b(w) = 2*w**3 - w**2 - w. Let f(y) = 63*y**2 + 5*y**3 - 19*y - 30*y**2 - 24*y**2 - 27*y**2. Let a(p) = -2*b(p) + f(p). Factor a(x).
x*(x - 17)*(x + 1)
Let f(x) be the third derivative of 1/6*x**5 + 0 - 5/8*x**4 - 1/72*x**6 + 7*x**2 + 0*x - 1/6*x**3. Let k(g) be the first derivative of f(g). Solve k(w) = 0.
1, 3
Let g(j) = -j**5 + 7*j**4 - j**3 - 2*j**2. Let z(v) = -8*v**5 - 479*v**4 - 3*v**3 - 6*v**2. Let l(n) = -3*g(n) + z(n). Let l(y) = 0. What is y?
-100, 0
Let w(q) = 14*q + 50. Let v(j) = -3*j. Let c(f) = -6*v(f) - w(f). Let z be c(13). Find u, given that 2/5*u**z - 36/5*u + 162/5 = 0.
9
Let q(k) be the first derivative of k**8/420 - k**7/42 - 46*k**3/3 - 53. Let c(d) be the third derivative of q(d). Factor c(l).
4*l**3*(l - 5)
Factor -72/7 - 150/7*w - 81/7*w**2 + 3/7*w**4 + 0*w**3.
3*(w - 6)*(w + 1)**2*(w + 4)/7
Factor -9/4*m**3 - 3/4*m**4 + 0 - 24*m + 27*m**2.
-3*m*(m - 4)*(m - 1)*(m + 8)/4
Let t(c) be the third derivative of -c**6/40 + 7*c**5/5 - 139*c**4/8 - 84*c**3 - c**2 - 214. Solve t(x) = 0 for x.
-1, 8, 21
Let o be (6/99)/(20 + 19306/(-966)). Determine x, given that -o*x + 4/11*x**2 - 24/11 = 0.
-1/2, 12
Let c be (-2 + (-8)/(-6))/((-11)/99). Let a be 2/(4/c) + (-5 - -6). What is n in -242*n**2 - 30 - 20*n**a - 82*n**3 - 83*n**3 - 58*n**2 - 185*n = 0?
-6, -1, -1/4
Factor m**3 - 33*m**2 - 21*m**2 + 0 + m + 50*m**2 + 6.
(m - 3)*(m - 2)*(m + 1)
Find l such that 1123632*l**2 + 1413*l + 256 + 1176*l + 7854330*l**3 + 26787*l + 6471978*l**3 = 0.
-4/153
Let p = 478209 - 1434626/3. Factor 0 + 0*a**2 + p*a**3 + 0*a + 1/3*a**4.
a**3*(a + 1)/3
Let k(d) = -57*d**3 - 564*d**2 - 2085*d - 690. Let s(g) = 60*g**3 + 565*g**2 + 2086*g + 707. Let c(l) = 7*k(l) + 6*s(l). Factor c(y).
-3*(y + 7)**2*(13*y + 4)
Let j(d) be the first derivative of -d**6/18 - 17*d**5/15 - 22*d**4/3 - 200*d**3/9 - 104*d**2/3 - 80*d/3 + 825. Factor j(i).
-(i + 1)*(i + 2)**3*(i + 10)/3
Let u = 88096 - 176177/2. Factor u*g - 13 - 1/2*g**2.
-(g - 13)*(g - 2)/2
Let u(l) = -10*l**3 + 25*l**2 + 420*l - 445. Let c(i) = 15*i**3 - 40*i**2 - 629*i + 668. Let d(a) = 5*c(a) + 7*u(a). Let d(o) = 0. Calculate o.
-5, 1, 9
Let i(v) be the second derivative of -v**6/180 + v**5/40 + v**4/8 + 5*v**3/36 - 8*v + 81. Factor i(d).
-d*(d - 5)*(d + 1)**2/6
Let a(i) = 6*i**2 - 2535*i + 7533. Let p(h) = -15*h**2 + 5070*h - 15033. Let g(s) = -7*a(s) - 3*p(s). Suppose g(w) = 0. What is w?
-848, 3
Suppose 7458 = 13*d - 3345. Let y = d + -5815/7. Factor -y*n + 2/7*n**2 - 4/7.
2*(n - 2)*(n + 1)/7
Let x(z) be the third derivative of -8*z**2 + 25/12*z**4 + 1/10*z**5 + 0*z + 1 - 6*z**3. Factor x(m).
2*(m + 9)*(3*m - 2)
Let j(r) = 13*r**3 - r**2 + r. Let c(w) = -44*w**3 + 2*w**2 - 4*w. Let t(y) = -3*c(y) - 10*j(y). Factor t(h).
2*h*(h + 1)**2
Solve 4/7*j**3 - 144/7*j**2 + 492/7*j + 640/7 = 0 for j.
-1, 5, 32
Find v such that 522*v**2 - 24192 - 677/4*v**3 + 67/8*v**4 - 1/8*v**5 + 11664*v = 0.
-7, 2, 24
Let h(w) be the first derivative of -22*w**3/9 - 6437*w**2/3 - 780*w - 11185. Factor h(o).
-2*(o + 585)*(11*o + 2)/3
Let y(c) = 12*c - 25. Let s be y(3). Factor 121 + s*q**2 + 22*q - 10*q**2 + 0*q**2.
(q + 11)**2
Let r(b) = b**4 + 10*b**3 + 27*b**2 - 13*b - 28. Let n(w) = -1. Let a(o) = o**2 - o - 6. Let h(m) = a(m) - 5*n(m). Let i(z) = 6*h(z) - 2*r(z). Factor i(v).
-2*(v - 1)*(v + 1)*(v + 5)**2
Let l(b) be the first derivative of 0*b**2 - 1/38*b**4 + 0*b + 2/57*b**3 - 2/95*b**5 + 1/57*b**6 - 151. Suppose l(q) = 0. Calculate q.
-1, 0, 1
Let h be (-7 + (-1270)/(-70))/(-23 + 16 + 10). Factor h*p + 44/7 - 20/7*p**2 - 2/7*p**3.
-2*(p - 2)*(p + 1)*(p + 11)/7
Let s(f) = -2*f**3 + 4*f**2 + 2*f + 10. Let i be s(0). Let r be (6/i)/(4/20). Find k, given that 28*k**r - 516/5*k**2 + 304/5*k - 48/5 = 0.
2/7, 2/5, 3