8*j**4 + 111*j**2 + 0*j**3. Factor a(k).
-2*k*(k - 1)**3*(k + 2)/3
Determine s so that -160*s**3 - 20*s - s**4 + 428*s**3 - 248*s**3 + 97*s**2 - 96 = 0.
-4, -1, 1, 24
Let y = 10917/35438 - 1/2726. Let z(m) be the first derivative of 5/13*m**2 - 14/39*m**3 - 21 + y*m. Factor z(i).
-2*(i - 1)*(7*i + 2)/13
Suppose 60 = 3*u + 589*j - 586*j, -90 = -5*j. Find n such that 20/7*n - 24/7 - 4/7*n**3 + 8/7*n**u = 0.
-2, 1, 3
Let g(w) be the second derivative of -w**6/30 - 151*w**5/80 - 415*w**4/24 + 217*w**3/24 + 166*w + 1. Suppose g(p) = 0. What is p?
-31, -7, 0, 1/4
Let l(v) be the third derivative of 18*v**2 + 0*v**3 + 0*v + 0 - 1/4*v**4 + 1/70*v**7 + 0*v**6 - 3/20*v**5. Factor l(j).
3*j*(j - 2)*(j + 1)**2
Factor 21*s**4 + 41*s**4 + 19*s**4 - 76*s**4 + 540 + 1185*s + 60*s**3 + 55*s**3 + 755*s**2.
5*(s + 1)**2*(s + 9)*(s + 12)
Let f be 22/77 + (-153)/(-910) + (-9)/30. Let 2/13*d**2 + 0*d - f*d**3 + 0 = 0. Calculate d.
0, 1
Let d = -265819/9 + 29537. Determine v so that 28/9 + 94/9*v**3 - 94/9*v + d*v**4 - 14/3*v**2 = 0.
-7, -1, 2/7, 1
Let h(s) be the first derivative of 7*s**4/4 - 15*s**3 + 4*s**2 + 60*s + 3697. Factor h(u).
(u - 6)*(u + 1)*(7*u - 10)
Suppose 3*u = 4*r - 5, 3*u = -2*r + 6*u + 1. Factor 7*i**2 - 15*i**r - 205 + 3*i**2 - 150*i - 920.
-5*(i + 15)**2
Suppose 4462*h - 38901 - 7393 = 770*h + 9086. Determine s so that 0 + 24*s**2 + 3/4*s**4 - 39/4*s**3 - h*s = 0.
0, 1, 2, 10
Suppose 51 = -68249*y + 68266*y + z, 5*y - z - 37 = 0. Factor 1/4*d**3 + y*d - 3 - 7/4*d**2.
(d - 3)*(d - 2)**2/4
Let f(w) be the first derivative of -w**5/60 + 7*w**4/36 - 7*w**3/9 + 4*w**2/3 - w - 58. Let g(p) be the first derivative of f(p). Find h such that g(h) = 0.
1, 2, 4
Suppose -16*l = -34*l + 36. Suppose 0 = -9*j + 4*j + 2*x + 5, 4*x = l*j + 14. Factor -4/3*y - 32/3*y**j - 14/3*y**4 + 0 - 22/3*y**2.
-2*y*(y + 1)**2*(7*y + 2)/3
Let u = -475 + 477. Factor -39 + u*a**2 - 15*a - 37*a - 17 + 0*a**2 + 2.
2*(a - 27)*(a + 1)
Let g(f) = f**5 + 1. Let l be ((-20)/6)/5*30/20. Let i(o) = -2*o**4 + 2*o**3 + 2*o**2 + 2. Let m(q) = l*i(q) + 2*g(q). Factor m(y).
2*y**2*(y - 1)*(y + 1)**2
Factor 224/5*h**2 + 2/5*h**3 + 872/5*h + 864/5.
2*(h + 2)**2*(h + 108)/5
Factor -2/3*a**3 + 0 + 68/3*a**2 - 80*a.
-2*a*(a - 30)*(a - 4)/3
Suppose -d = -3*x - 17, 7*x = 4*x - 4*d - 22. Let u be (875/(-28))/(-5) + x. Find s such that u*s**3 + 1/2*s + 0 - 3/4*s**2 = 0.
0, 1, 2
Let l = 4/2847 - -917/22776. Let y(a) be the third derivative of 0*a + l*a**6 - 5/3*a**3 - 5/24*a**4 + 0 + 7*a**2 + 1/6*a**5. Factor y(b).
5*(b - 1)*(b + 1)*(b + 2)
Let b(p) be the second derivative of -p**6/5 - 29*p**5/5 - 92*p**4/3 + 170*p**3/3 + 75*p**2 + 8*p - 46. Solve b(j) = 0 for j.
-15, -5, -1/3, 1
Factor 1960/3 - 756*s + 104*s**2 - 4/3*s**3.
-4*(s - 70)*(s - 7)*(s - 1)/3
Let i(q) be the first derivative of -13*q**4/22 + 472*q**3/33 - 257*q**2/11 + 68*q/11 - 230. Suppose i(h) = 0. Calculate h.
2/13, 1, 17
Let z(b) be the second derivative of -b**4/12 + b**3/3 - 13*b**2/2 - 2*b + 29. Let g(o) = o**2 - 3*o + 11. Let m(t) = 4*g(t) + 3*z(t). Solve m(d) = 0.
1, 5
Let s(f) be the first derivative of -f**6/2 + 36*f**5/5 + 195*f**4/4 - 366*f**2 - 576*f - 630. Let s(l) = 0. Calculate l.
-3, -2, -1, 2, 16
Let t be (-10 - -11)*6/3. Let l(u) be the second derivative of -12*u + 0 - 4/3*u**3 + 5*u**t - 1/6*u**4. Solve l(q) = 0.
-5, 1
Let n = 15503/85448 + 3/7768. Factor -512/11 - n*u**2 - 64/11*u.
-2*(u + 16)**2/11
Suppose 2*m = k + 433, 5*m + 3*k - 1110 = -0*k. Suppose m = 32*h - 293. Factor 28/5*w**3 + h*w + 104/5*w**2 - 32/5.
4*(w + 2)**2*(7*w - 2)/5
Find g, given that -117*g**2 + 1/2*g**3 + 9126*g - 237276 = 0.
78
Let n(u) be the second derivative of -u**4/3 + 4540*u**3/3 - 2576450*u**2 - 6474*u. Factor n(d).
-4*(d - 1135)**2
Suppose -3*d - 5*g = -2*d - 19, 5*d + 2*g = 26. Let n(q) = -q**3 + 12*q**2 + 10*q + 42. Let r be n(13). Factor 14*h - d*h**2 - 6*h + 64*h**r - 66*h**3 + 16.
-2*(h - 2)*(h + 2)**2
Let w be ((-120)/(-14))/((-210)/(-490)) - -2*3. Let t(k) be the first derivative of 0*k - 1/3*k**3 - w + 5/2*k**2. Let t(y) = 0. Calculate y.
0, 5
Factor 596/9 + 302/9*u + 2/9*u**2.
2*(u + 2)*(u + 149)/9
Suppose 21*c**2 - 35*c**2 - c**3 + 8*c**2 - 144 + 60*c + 14*c**2 = 0. What is c?
-6, 2, 12
Let t = 32893/329220 + -10/1829. Let z(u) be the third derivative of 4/45*u**5 - t*u**4 + 2/45*u**3 + 0 + 0*u - 4/225*u**6 - u**2. What is f in z(f) = 0?
1/4, 2
Let p(g) be the first derivative of -1/90*g**4 + 0*g**2 + 2/45*g**3 + 15*g - 11. Let w(q) be the first derivative of p(q). Find u such that w(u) = 0.
0, 2
Let y be -27*(-578)/459 - 30. Factor 0*r**2 + 0*r + 9/8*r**y + 3/2*r**3 + 0 - 3/8*r**5.
-3*r**3*(r - 4)*(r + 1)/8
Suppose o - 2*m - 20 = 0, -63827*o + 63830*o = -2*m - 12. Determine h, given that -o - 2/3*h**2 + 8/3*h = 0.
1, 3
Let q(a) be the second derivative of -a**4/4 - 277*a**3/2 - 414*a**2 - 1534*a. Factor q(w).
-3*(w + 1)*(w + 276)
Let t(v) be the second derivative of -3*v**5/20 - 1035*v**4/4 - 357075*v**3/2 - 123190875*v**2/2 - 980*v. Determine i so that t(i) = 0.
-345
Let n(m) be the third derivative of m**5/360 - 61*m**4/48 - 185*m**3/18 - 2504*m**2. Factor n(d).
(d - 185)*(d + 2)/6
Let q(l) be the first derivative of 2*l**3/9 + 353*l**2 + 1638. Let q(h) = 0. Calculate h.
-1059, 0
Let r(l) = -l**2 + 3*l + 9. Let m be r(-1). Let q(z) be the first derivative of 16 - 4/33*z**3 + 12/11*z**2 + 2/55*z**m + 18/11*z - 2/11*z**4. Factor q(g).
2*(g - 3)**2*(g + 1)**2/11
Suppose 0 = w - 3*i - 20, 2*w + 5*i = 8*i + 28. Let -10650*x**3 + x + 10654*x**3 - x + w*x**2 = 0. Calculate x.
-2, 0
Let i be 3 - (2/(7 - 5) - 18). Suppose 95*f + i = 100*f. Factor -2/3*w**f + 8/3*w**3 + 4/3*w + 0 - 10/3*w**2.
-2*w*(w - 2)*(w - 1)**2/3
Let f(w) be the third derivative of -w**7/210 - 7*w**6/120 + w**5/12 + 25*w**4/8 - 23*w**2 + 12*w. What is g in f(g) = 0?
-5, 0, 3
Let i(c) be the first derivative of 2/39*c**3 + 0*c - 38 - 1/26*c**4 + 0*c**2. Factor i(d).
-2*d**2*(d - 1)/13
Let w(j) be the second derivative of -j**5/140 - j**4/14 - 2*j**3/7 - 29*j**2/2 - j - 25. Let c(n) be the first derivative of w(n). Factor c(f).
-3*(f + 2)**2/7
Let m(a) = 11*a**3 - 27*a**2 - 6*a + 47. Let w(g) = 9*g**3 - 35*g**2 - 5*g + 51. Let s(t) = 4*m(t) - 5*w(t). Find d, given that s(d) = 0.
-1, 1, 67
Let c be (-46)/253*(-22 + 11). Determine d so that 5/2*d**4 - 10*d**3 + 15*d + 5/2*d**c + 0 = 0.
-1, 0, 2, 3
Let k = -541 + 577. Let c be (8 - 12)/(k/(-10)). Let 10/9*y + 4/9 - 4/9*y**2 - c*y**3 = 0. What is y?
-1, -2/5, 1
Let t(h) be the second derivative of 0 + 75*h - 9/8*h**2 - 5/16*h**3 - 1/32*h**4. Factor t(v).
-3*(v + 2)*(v + 3)/8
Suppose 3*b - 5 + 4 = -5*o, 2*b + o = 3. Factor -20*h**3 + 3*h**5 + 41*h**3 + 12*h**4 + 6*h**b - 6*h**3.
3*h**2*(h + 1)**2*(h + 2)
Let s(w) = 17*w**2 + 13*w + 7. Let q be s(7). Let l = q - 926. Factor -13/2*p**4 + 5/2*p**l + 1/2*p**2 + 0 - p + 9/2*p**3.
p*(p - 1)**3*(5*p + 2)/2
Suppose -287*n = -1948*n - 1182*n. Factor 0*f**2 + n - 8/9*f + 2/9*f**3.
2*f*(f - 2)*(f + 2)/9
Let n(r) be the second derivative of -15/2*r**2 + 2/5*r**6 + 1/28*r**7 + 6/5*r**5 + 1/4*r**4 + 2*r + 5 - 17/4*r**3. Suppose n(a) = 0. Calculate a.
-5, -2, -1, 1
Let v(x) = -x**3 + 213*x**2 + 400*x + 6453. Let q be v(215). Let 0*a + q*a**3 + 12/5*a**4 + 0 + 6/5*a**2 + 3/5*a**5 = 0. What is a?
-2, -1, 0
Let j = -368 + 370. Let i(u) be the second derivative of 7*u + 0 - 1/5*u**j + 1/30*u**4 - 1/45*u**3 + 1/150*u**5. Find b, given that i(b) = 0.
-3, -1, 1
Solve -2/3*q**2 + 154/3 - 152/3*q = 0 for q.
-77, 1
Let j(m) = m**4 - m. Let y(o) = 4*o**4 - 4*o**3 - 6*o**2 + 6*o + 8. Let h be 10/25 + 3/5. Let k(a) = h*y(a) - 2*j(a). What is q in k(q) = 0?
-1, 2
Let n(j) = -7*j**3 + 51*j**2 + 40*j. Let c(h) = -20*h**3 + 150*h**2 + 119*h. Let x(w) = -6*c(w) + 17*n(w). Find q, given that x(q) = 0.
-1, 0, 34
Let a(y) be the third derivative of 1/360*y**6 + 1/45*y**5 + 5*y + 3*y**2 + 0*y**4 + 0 + 1/2016*y**8 - 1/252*y**7 + 0*y**3. Factor a(n).
n**2*(n - 4)*(n - 2)*(n + 1)/6
What is v in 17*v**3 - 161 + 82*v + 105 - 25*v**2 - 5*v**3 - 13*v**3 = 0?
-28, 1, 2
Suppose -1 + 2 = -g + 2*q, 2*g = -4*q + 14. Suppose -2*n = 2*p - 2, -4*n - 3*p + g = -3. Factor 9*c**4 - 117*c - 171/4*c**n - 3/4*c**5 + 201/2*c**2 + 54.
-3*(c - 3)**2*(c - 2)**3/4
Let p(n) be the second derivative of -15/8*n**2 + 60*n + 0