45/(-6). Let x(r) = 693*r + 1390. Let z be x(-2). Factor 6*n**2 - p*n**2 + 6*n**3 - 3*n**5 + 4 - 10 + 6*n**z - 148*n + 169*n.
-3*(n - 1)**4*(n + 2)
Let q(z) be the second derivative of 1/12*z**4 - 2 - 9/2*z**2 + 0*z**3 - 2*z. Factor q(t).
(t - 3)*(t + 3)
Let r = 1 + -1. Suppose 2*p + 2*z - 8 = 0, 19*z = 17*z + 4. Determine a, given that 0 - 1/5*a + r*a**p + 1/5*a**3 = 0.
-1, 0, 1
Let i(z) be the first derivative of 3*z**6/4 + 186*z**5/5 - 251*z**4/8 + 7*z**3 + 74. Suppose i(s) = 0. What is s?
-42, 0, 1/3
Let m(x) = 3*x + 24. Let f be (-2)/8 - 243/36. Let s be m(f). Factor -2*r - 5*r**3 + s*r**3 + 4*r**3 + 0*r**3.
2*r*(r - 1)*(r + 1)
Let x be ((-12)/(-54))/(5/(-15))*2/(-4). Let i(m) be the first derivative of -1/4*m**2 + x*m**3 + 0*m - 1/8*m**4 - 9. Factor i(l).
-l*(l - 1)**2/2
Let h(q) = 12*q - 7. Let l(d) = -7*d + 3. Let g(a) = 4*h(a) + 7*l(a). Let f be g(-7). Solve 1/6*j**5 + 0*j**4 + f*j**2 + 0 + 1/6*j - 1/3*j**3 = 0 for j.
-1, 0, 1
Let d be (-2)/6 - ((-74)/105 + 28/392). Let r(b) be the first derivative of d*b**2 + 4/5*b**3 + 7/20*b**4 + 3 - 2/5*b. What is z in r(z) = 0?
-1, 2/7
Let -93*i - 12*i**3 - 2664*i**2 - 2834*i**2 + 5123*i**2 = 0. What is i?
-31, -1/4, 0
Find o, given that 2528/17 + 142/17*o**2 - 1232/17*o + 2/17*o**3 = 0.
-79, 4
Suppose -5 = -o - 3. Let c = 52 + -33. Let -2*t**o + 15*t - c*t - 17*t + 5*t**2 + 18 = 0. Calculate t.
1, 6
Let b(p) be the second derivative of -3*p**5/20 + 3147*p**4/2 - 6602406*p**3 + 13851847788*p**2 + 4551*p. Let b(o) = 0. What is o?
2098
Let u(d) be the first derivative of -5*d**3/3 - 5*d**2 + 75*d - 5178. Factor u(h).
-5*(h - 3)*(h + 5)
Factor 10*d**3 - 785*d**2 - 270*d**2 + 22247*d - 20687*d.
5*d*(d - 104)*(2*d - 3)
Let t be (32 + 4)*(-2)/(-4). Let v be 4/(-10) - t*(-6)/45. Factor 14*w**v + 4*w**5 + 18*w**2 + 2*w**4 - 5*w**4 - 16*w**3 - 5*w**4.
4*w**2*(w - 2)**2*(w + 2)
Let o = 7151 - 28603/4. Let u(h) be the second derivative of 0 + 19*h + 10/3*h**3 + o*h**5 - 5/3*h**4 + 0*h**2. Determine j so that u(j) = 0.
0, 2
Let i(v) = -3*v**3 - 23*v**2 - 3*v - 17. Let j(w) = -w**3 - 8*w**2 - w - 6. Let c = -366 + 383. Let a(d) = c*j(d) - 6*i(d). Factor a(p).
p*(p + 1)**2
Find d such that 227*d**2 + 137 + 5*d**3 - 492 + 829*d - 352*d**2 + 11*d - 365 = 0.
1, 12
Let b(a) be the second derivative of -a**6/70 - 159*a**5/140 - 234*a**4/7 - 2754*a**3/7 - 7534*a. Find k, given that b(k) = 0.
-18, -17, 0
Let l(y) = 9*y**2 + 21*y + 17. Suppose 5 = 2*p - 5. Let w(m) = -14*m**2 - 32*m - 26. Let s(h) = p*w(h) + 8*l(h). Factor s(d).
2*(d + 1)*(d + 3)
Let -2960/7*x - 2/7*x**2 - 1095200/7 = 0. What is x?
-740
Let v = -456 - -460. Factor -2*y**2 + 7*y**2 - 3*y**3 - 3*y**2 + 0*y**2 + 5*y**4 - 4*y**v.
y**2*(y - 2)*(y - 1)
Let f(a) be the third derivative of -1/9*a**4 - 1/90*a**5 + 0*a - 4/9*a**3 + 85*a**2 + 0. Factor f(w).
-2*(w + 2)**2/3
Let u(x) = 574*x**2 + 13202*x + 3. Let q be u(-23). Factor -16/11 + 2/11*m**q - 14/11*m**2 + 28/11*m.
2*(m - 4)*(m - 2)*(m - 1)/11
Suppose 160*x - 166*x + 35 - 5 = 0. Factor 0*s + 0*s**2 + 6/5*s**3 - 3/5*s**x + 0 - 3/5*s**4.
-3*s**3*(s - 1)*(s + 2)/5
Let n(t) be the third derivative of 0 + 8/315*t**7 + 0*t - 35*t**2 + 1/36*t**4 + 0*t**3 - 1/12*t**6 + 1/15*t**5. Factor n(s).
2*s*(s - 1)**2*(8*s + 1)/3
Let b(t) be the second derivative of t**8/3360 + t**7/630 - t**6/24 - 3*t**5/5 - t**4/4 + t**3/2 + 180*t. Let m(u) be the third derivative of b(u). Factor m(h).
2*(h - 4)*(h + 3)**2
Let s(p) be the third derivative of -p**6/150 + 3*p**5/25 - p**4/2 + 14*p**3/15 + 1143*p**2. Solve s(r) = 0 for r.
1, 7
Let r be (5 + -2)*-1*-1. Let k(t) = -4*t**3 + 80*t**2 + 3*t - 57. Let u be k(20). Factor -26*n**4 - u*n - 6 + 23*n**4 - 2*n**3 + 3*n**r + 9*n**2 + 2*n**3.
-3*(n - 2)*(n - 1)*(n + 1)**2
Factor 63/4*t**2 - 1/2 + 61/4*t.
(t + 1)*(63*t - 2)/4
Let l(z) be the third derivative of z**6/24 + 37*z**5/30 + 365*z**4/24 + 100*z**3 + 529*z**2. Determine o so that l(o) = 0.
-5, -24/5
Let 11*y**2 + 19*y**2 - 16*y**2 - 1692*y + 14*y**2 + 720 = 0. What is y?
3/7, 60
Let o(b) be the second derivative of 5*b**4/12 + 650*b**3/3 + 42250*b**2 + 5*b - 52. Factor o(f).
5*(f + 130)**2
Let w be (-75795)/(-1395) - (49 + 0). Factor -2/9*n**2 + 0 + w*n.
-2*n*(n - 24)/9
Let -78*s**2 + 18*s**2 + 13*s**2 + 4*s**2 - 137*s**2 - 138*s**3 - 75*s - 36*s**4 - 3*s**5 = 0. What is s?
-5, -1, 0
Determine k, given that -51*k**2 + 9*k**4 - 5 + 7 + 3*k**3 + 57*k - 8 - 12 = 0.
-3, 2/3, 1
Determine o, given that 866/7*o - 216/7 + 8/7*o**3 - 872/7*o**2 = 0.
1/2, 108
Let i be -49 + 54 + 82/14. Let y = 284/21 - i. Factor y*l**4 + 8/3*l + 16/3 - 20/3*l**2 - 2/3*l**3 - 2/3*l**5.
-2*(l - 2)**3*(l + 1)**2/3
What is x in 0 + 8/7*x - 2/7*x**5 - 10/7*x**4 - 6/7*x**3 + 10/7*x**2 = 0?
-4, -1, 0, 1
Let x(f) be the first derivative of -f**6/1620 - f**5/135 + 7*f**4/36 + 65*f**3/3 + f**2 - 43. Let k(d) be the third derivative of x(d). Solve k(r) = 0.
-7, 3
Find a, given that -401 - 293 + 3*a**2 + 262 - 246*a + a**3 - 16*a**2 = 0.
-9, -2, 24
Let r(c) = 2*c**3 - 8*c**2 - 11*c + 8. Let i be r(5). Factor -3*g - 13*g**3 - 90 - 16*g**2 + 32*g**3 - 18*g**i + 72*g.
(g - 10)*(g - 3)**2
Let v(i) = -3*i**3 - 857*i**2 - 37796*i - 105846. Let a(k) = -2*k**3 - 858*k**2 - 37794*k - 105849. Let n(q) = 2*a(q) - 3*v(q). Factor n(c).
5*(c + 3)*(c + 84)**2
Let n = 213 + -205. Let i be (116/(-232))/((-2)/n). Suppose 0 + 0*c + 4/3*c**3 - 1/6*c**4 + 3/2*c**i = 0. Calculate c.
-1, 0, 9
Solve -652/3*w + 0 - 4/3*w**3 + 656/3*w**2 = 0 for w.
0, 1, 163
Let y(p) be the second derivative of p**6/320 + p**5/40 + p**4/16 - 29*p**2 - 15*p. Let m(b) be the first derivative of y(b). Factor m(g).
3*g*(g + 2)**2/8
Let s(a) be the second derivative of 0 - 1/6*a**3 + 0*a**4 + 1/80*a**5 + 1/480*a**6 - 13*a**2 + 4*a. Let o(b) be the first derivative of s(b). Factor o(k).
(k - 1)*(k + 2)**2/4
Let m(c) = c + 6 - 10 + 4*c + 11*c**2. Let z(i) = 0 + 40*i**2 - 8*i**2 + 15*i - 13. Let w(d) = -17*m(d) + 6*z(d). Find x, given that w(x) = 0.
-2, 1
Find m, given that -8298879*m**3 + 26*m - 66*m**5 + 8299085*m**3 - 98*m - 72*m**2 + 140*m**4 = 0.
-1, -6/11, 0, 2/3, 3
Let r = -2/1160407 + 2320824/5802035. Determine u so that -3/5 + 1/5*u + 1/5*u**5 - r*u**3 - 3/5*u**4 + 6/5*u**2 = 0.
-1, 1, 3
Suppose -2*d = -o - 6, 10 - 22 = -4*o - 4*d. Let c(t) be the third derivative of -t**3 + 0 - 1/24*t**4 + o*t - 21*t**2 + 1/45*t**5 + 1/360*t**6. Factor c(j).
(j - 2)*(j + 3)**2/3
Let h(c) be the first derivative of -47 + 0*c + c**2 - 2/3*c**3. Solve h(s) = 0.
0, 1
Let k(u) be the second derivative of u**4/2 - 245*u**3/9 + 18*u**2 + 516*u. Factor k(c).
2*(c - 27)*(9*c - 2)/3
Let m be -9 - -24 - 4*1. Suppose 3 = -4*b + m. Factor -4*r + 6*r - 7*r - 6 - 2*r**b - 3*r.
-2*(r + 1)*(r + 3)
Factor -44755*p**2 + 44683*p**2 - 284*p**3 - 1 + 16*p**4 + 1 + 0.
4*p**2*(p - 18)*(4*p + 1)
Let v(i) = -10*i + 19*i**2 + 436 - 850 + 425. Let a(p) = 23*p**2 - 10*p + 11. Let c(q) = 5*a(q) - 6*v(q). Factor c(k).
(k - 1)*(k + 11)
Let l(y) be the first derivative of -y**5/5 - 15*y**4/8 + 8*y**3/3 + 69*y**2/4 + 20*y - 15637. Solve l(v) = 0 for v.
-8, -1, 5/2
Let l(o) be the second derivative of o**6/6 - 11*o**5/12 - 5*o**4/8 - 37*o**2 - 6*o + 3. Let w(v) be the first derivative of l(v). Suppose w(a) = 0. What is a?
-1/4, 0, 3
Let w(r) be the second derivative of -1/5*r**5 + 0*r**2 + 2 + 30*r**3 + 44/3*r**4 + 8*r. Factor w(l).
-4*l*(l - 45)*(l + 1)
Let u be (-5)/(-8)*((-7)/350)/(3/(-2)). Let o(j) be the third derivative of -1/8*j**4 + u*j**5 + 5/12*j**3 + 14*j**2 + 0*j + 0. Find g, given that o(g) = 0.
1, 5
Let b(p) = -2*p**3 - 7*p - 10. Let f be b(-2). Let -28*w**4 + 8*w**2 - f*w**2 - 6*w**5 - 32*w**3 + 7*w**5 - 9*w**5 = 0. Calculate w.
-3/2, -1, 0
Let p be 11 - (7 + -3) - -3. Suppose -6*l - 32 = -p*l. Determine q, given that 7*q + 11*q + 8*q - l - 20*q + 2*q**2 = 0.
-4, 1
Let v(c) be the second derivative of -c**6/90 + 617*c**5/60 - 154*c**4/9 + 19*c - 115. Factor v(t).
-t**2*(t - 616)*(t - 1)/3
Let q(d) be the first derivative of 4/3*d**3 - 30 - 16*d**2 + 64*d. Find o, given that q(o) = 0.
4
Let h be (-9)/6*(12 + -4 + -20). Suppose 67*c + h*c = 0. Let -1/4*d**2 + c + 2*d**3 + 0*d - 4*d**4 = 0. What is d?
0, 1/4
Factor 84 + 3*t**2 + 9 + 876*t + 81 - 42 - 948*t.
3*(t - 22)*(t - 2)
Let b(n) = -133*n**2 + 5648*n + 2690427. Let g(y) = 47*y**2 - 1882*