9*k. Let g be i(2). Let z = g + -14. Let -x**4 - 3*x**2 - z*x**4 - 9*x**3 - 4*x**4 - 3*x**5 + 0*x**4 = 0. Calculate x.
-1, 0
Let m(t) be the first derivative of 3/4*t**3 + 3/4*t**4 - 11 - 9/4*t - 3/2*t**2. Factor m(s).
3*(s - 1)*(s + 1)*(4*s + 3)/4
Suppose -108 + 28 = -16*p. Let x(f) be the third derivative of 5*f**2 + 1/80*f**p + 0*f - 3/32*f**4 + 1/4*f**3 + 0. Factor x(d).
3*(d - 2)*(d - 1)/4
Let x = -1/1290 - -323/645. Find d such that -1/2*d - 1 + x*d**2 = 0.
-1, 2
Suppose 644*a + 170 - 24*a**4 + 5*a**5 + 12*a**4 - 639*a + 135*a**4 - 10*a**3 - 340*a**2 + 47*a**4 = 0. What is a?
-34, -1, 1
Let x(u) be the third derivative of u**9/120960 - u**7/2520 - u**5/10 + 3*u**2. Let v(z) be the third derivative of x(z). Factor v(n).
n*(n - 2)*(n + 2)/2
Let b be (-142)/4*440/(-660). Let 34/3*c**2 - 17*c**4 + 8/3 - b*c**3 + 44/3*c + 12*c**5 = 0. Calculate c.
-2/3, -1/4, 1, 2
Let l(v) = 4*v**2 + 5*v - 20. Let i be l(4). Let t = i + -176/3. Factor t*h**3 + 8/3*h**2 + 2/3*h**5 + 0*h + 10/3*h**4 + 0.
2*h**2*(h + 1)*(h + 2)**2/3
Let i = -173 + 176. Let k be 380/120 + (-2)/i. Factor 45/2*s**4 + 10*s + k - 5*s**2 - 30*s**3.
5*(s - 1)**2*(3*s + 1)**2/2
Let j(x) be the second derivative of 5/2*x**3 + 25/6*x**4 + 3/4*x**5 + 0*x**2 + 0 - 10*x. Suppose j(g) = 0. Calculate g.
-3, -1/3, 0
Factor 1/6*n**4 + 1/3*n**3 - 1/3*n - 2/3*n**2 + 1/2.
(n - 1)**2*(n + 1)*(n + 3)/6
Let x(t) be the first derivative of -4/3*t**4 + 13 - 40/9*t**3 + 23/6*t**2 - t. Factor x(k).
-(k + 3)*(4*k - 1)**2/3
Let b(q) be the first derivative of 1/2*q - 22 + 4/9*q**3 + 11/12*q**2. Factor b(l).
(l + 1)*(8*l + 3)/6
Let j(y) = -7*y + 6. Let d be j(3). Let a = d - -27. Suppose 18*m**3 + m + 12*m**4 + m + m + a*m**2 + 3*m**5 = 0. What is m?
-1, 0
Let o(b) = b**3 - 799*b**2 - 21659*b - 57633. Let n(q) = -200*q**2 - 5412*q - 14408. Let v(w) = -9*n(w) + 2*o(w). Factor v(g).
2*(g + 3)*(g + 49)**2
Let x(z) be the third derivative of 0*z + 3/8*z**4 - 1/112*z**8 + 0 - 2/35*z**7 + 0*z**3 - 1/20*z**6 - 8*z**2 + 1/5*z**5. Solve x(v) = 0 for v.
-3, -1, 0, 1
Let n = 85 - 82. Let s be 8/((-240)/(-126)) - n. Determine i so that 0*i + s*i**2 + 0 - 27/5*i**3 = 0.
0, 2/9
Let q be (-2 + 2 + -1)*-6. Suppose -2 = 3*w + 5*r + 7, 14 = 4*w - 2*r. Factor -q*p**2 + 2*p**w + 2*p**2 - 4*p.
-2*p*(p + 2)
Let s be 2/5 + 22296/60. Find g such that 243*g**4 + 17 - s*g + 2 + 1107*g**3 + 29 + 444*g**2 = 0.
-4, -1, 2/9
Let r(x) = -x**2 + 13*x - 6. Let j be r(12). Let s = -19 - -21. Factor 2*g**3 - 9*g - 2*g**2 - 3*g**4 + 9*g**3 - g**2 + j - s*g**3.
-3*(g - 2)*(g - 1)**2*(g + 1)
Determine v so that 1/8*v**2 + 1/8*v**4 + 0 + 3/4*v - 1/2*v**3 = 0.
-1, 0, 2, 3
Let u(a) be the first derivative of 5*a - 1/4*a**4 + 0*a**3 + 6*a**2 + 2. Let m(y) be the first derivative of u(y). Factor m(s).
-3*(s - 2)*(s + 2)
Suppose 11*d - 10*d = 0. Let b be 594/231 - d/2. Factor 0*i - 2/7*i**4 + 0 - 12/7*i**3 - b*i**2.
-2*i**2*(i + 3)**2/7
Let v = 1/114 + 55/228. Solve v*o**2 + 1/2 + 3/4*o = 0 for o.
-2, -1
Let b(w) be the second derivative of w**8/7560 - w**6/1620 + 13*w**3/3 + 17*w. Let s(n) be the second derivative of b(n). Factor s(d).
2*d**2*(d - 1)*(d + 1)/9
Let a(d) = -d**3 + d**2 - d + 1. Let c(h) = 8*h**3 - 44*h**2 - 70*h - 46. Let l(u) = -14*a(u) - 2*c(u). Solve l(i) = 0 for i.
-1, 39
Let s be -25 + 51 - 1200/(-140). Factor -s - 2/7*x**2 - 44/7*x.
-2*(x + 11)**2/7
Let x = -23446/3 - -7818. Factor 20/3*q**3 - 32/3*q**2 + x + 4/3*q.
4*(q - 1)**2*(5*q + 2)/3
Let q = -111 - -115. Let i(n) be the third derivative of 0*n + 1/12*n**q + 2*n**2 + 0 + 1/6*n**3 + 1/60*n**5. Factor i(w).
(w + 1)**2
Let s be 22/(-165) + 5/(2 - -13). Factor -s*u**2 + 1/5*u**3 + 0*u + 0.
u**2*(u - 1)/5
Factor 123*r**3 + 89*r**3 + 116*r**2 - 92*r**3 + 6*r**4 + 22*r**4 + 24*r.
4*r*(r + 1)*(r + 3)*(7*r + 2)
Let q be ((-44)/12 - -8)/(2/(-30)). Let m be (-2)/(-13) - 16/q. Let 2/5*d**2 - m*d**4 - 2/5*d + 2/5*d**3 + 0 = 0. Calculate d.
-1, 0, 1
Let j(g) be the third derivative of -g**6/360 - 67*g**5/60 - 4489*g**4/24 - 300763*g**3/18 + g**2 + 69*g. What is n in j(n) = 0?
-67
Let v be (2 - -2)/(-2) - -2. Factor -14*q + 6*q - q**2 + v*q**2 - 3*q**2.
-4*q*(q + 2)
Let m(o) = -o**2 - 5. Let z(q) = -6*q**2 + 7*q - 7. Let x(d) = 5*m(d) - z(d). Factor x(s).
(s - 9)*(s + 2)
Let s be (-90)/(-27) + 8/(-6). Factor 16*k**s - 24*k**4 - k**3 + 46*k**4 - 18*k**4 + 17*k**3.
4*k**2*(k + 2)**2
Suppose -5*k + 30 = 4*b, 0 = -68*k + 72*k + 4*b - 28. Let z(y) be the second derivative of -1/4*y**4 + 0 + 6*y**k + 7*y + 3/2*y**3. Solve z(l) = 0.
-1, 4
Let y = -349/9 + 4171/63. Factor -48/7*c**2 - 4/7*c**3 - y*c - 256/7.
-4*(c + 4)**3/7
Let m = 3445 - 3445. Find g, given that 0*g + 4/7*g**3 + 16/7*g**2 + m = 0.
-4, 0
Suppose 7*z + 4*p = 3*z + 4, 2*z = 2*p - 2. Let w(n) be the first derivative of 1/2*n**3 - 5 - 3/4*n**2 + z*n. Factor w(a).
3*a*(a - 1)/2
Suppose i - 10*s + 13*s = -10, 3*i = 2*s + 14. Let v(t) be the second derivative of -6*t + 0 - 1/24*t**4 - 9/4*t**i - 1/2*t**3. Determine j so that v(j) = 0.
-3
Suppose -23 = -4*u + 1. Factor -12*i - 7*i**4 + 6*i**3 + 4*i**4 + 3*i**2 + u*i.
-3*i*(i - 2)*(i - 1)*(i + 1)
Let v be (468/(-27) - -14)*6/(-4). Let k(s) be the third derivative of -s**3 + 2*s**2 + 0 + 7/30*s**6 + 1/6*s**4 + 1/35*s**7 + 0*s + 8/15*s**v. Factor k(r).
2*(r + 1)**2*(r + 3)*(3*r - 1)
Let f(m) be the second derivative of -m**6/30 + 3*m**5/20 - m**4/12 - m**3/2 + m**2 - 30*m + 1. Factor f(a).
-(a - 2)*(a - 1)**2*(a + 1)
Suppose -570*a + 397*a = -692. Determine r, given that 0 + a*r**2 + 32/3*r**3 - 20*r**4 + 16/3*r**5 + 0*r = 0.
-1/4, 0, 1, 3
Let i = 520/9 - 6742/117. Factor -2/13 - 2/13*t + 2/13*t**3 + i*t**2.
2*(t - 1)*(t + 1)**2/13
Let h = 210/13 - -163/39. Let r = h + -20. Find o such that o - r*o**2 - 2/3 = 0.
1, 2
Let c be 2/(-7)*(385/66 + -6). Let f(v) be the second derivative of -1/3*v**4 - c*v**7 + 0 + 0*v**6 + 2*v**2 - v**3 + 2/5*v**5 + 3*v. Factor f(o).
-2*(o - 1)**3*(o + 1)*(o + 2)
Let w(o) be the third derivative of -2 + 0*o - 11/90*o**6 + 2/45*o**5 + 5/9*o**4 + 7/9*o**3 - 26*o**2 - 11/315*o**7 + 1/252*o**8. Solve w(j) = 0 for j.
-1, -1/2, 1, 7
Suppose -5*k + h - 2*h = -118, -2*h + 121 = 5*k. Suppose -2*z + k = 3*d - 2, -z + d = -15. Suppose c - 2 - z*c**2 + 3*c + 12*c**2 = 0. What is c?
1
Let p(y) be the first derivative of 1 + 1/3*y**3 + 0*y + 0*y**2. Let d(a) = 4*a**2 - 9*a + 6. Let k(c) = -d(c) + p(c). Factor k(m).
-3*(m - 2)*(m - 1)
Suppose 480 - 35/2*x**5 - 1425/2*x**3 - 550*x**2 - 200*x**4 + 1000*x = 0. Calculate x.
-4, -3/7, 1
Let f(z) be the first derivative of -z**4/2 - 108*z**3 - 8748*z**2 - 314928*z + 179. Factor f(w).
-2*(w + 54)**3
Let u(w) be the third derivative of -5*w**2 + 0 + 1/6*w**6 + 37/30*w**5 + 5*w**4 + 12*w**3 + 1/105*w**7 + 0*w. Factor u(t).
2*(t + 2)**2*(t + 3)**2
What is o in 35*o**4 + 4193*o**2 + 4202*o**2 + 5*o**5 + 40*o**3 - 8475*o**2 = 0?
-4, 0, 1
Factor 0 - 12*x**2 + 0*x**4 + 9*x**3 - 3/2*x**5 + 9/2*x.
-3*x*(x - 1)**3*(x + 3)/2
Factor 32/3*n + 1/6*n**4 + 16/3 + 11/6*n**3 + 7*n**2.
(n + 1)*(n + 2)*(n + 4)**2/6
Let n(r) be the second derivative of -r**4/12 + 5*r**3/3 - 25*r**2/2 - 106*r - 6. Find z, given that n(z) = 0.
5
Let t(b) = -17*b**3 - 4*b**2 + 5*b - 2. Let m be t(1). Let u be -8 + 9 + m/26. What is c in 0*c**3 + 2/13*c + 0 + 4/13*c**4 - 2/13*c**5 - u*c**2 = 0?
-1, 0, 1
Let r(z) be the third derivative of -1/40*z**5 + 0 + 1/672*z**8 + 1/140*z**7 - 1/24*z**4 + 0*z**3 - 26*z**2 + 1/240*z**6 + 0*z. Factor r(x).
x*(x - 1)*(x + 1)**2*(x + 2)/2
Let s(j) = -j**2 + 6*j - 5. Let x be (-48)/(-20) + 12/20. Let i(k) = 3 - x*k + 0*k + 0*k. Let h(c) = -5*i(c) - 3*s(c). Determine a so that h(a) = 0.
0, 1
Let n = 178/915 + 1/183. Let s(k) be the second derivative of 0 + 2*k - 1/10*k**4 - 1/5*k**2 - n*k**3 - 1/50*k**5. What is o in s(o) = 0?
-1
Let w = 33 - 16. Let o(n) = -25 + 37*n**2 + 22*n - 9 + 36*n**2 - w*n**2. Let d(h) = -5*h**2 - 2*h + 3. Let g(t) = 68*d(t) + 6*o(t). Solve g(i) = 0 for i.
-1, 0
Let j = 213 - 381. Let f be 96/j + (-5)/(-7). Solve f*l**2 + 1/7*l**3 + 3/7 - 5/7*l = 0 for l.
-3, 1
Let n be (-2 - 27/(-15))/(-1)*9. Let r(j) be the first derivative of 3*j**3 + 0*j + 3/2*j**2 + 4 - n*j**5 - 3/4*j**4. Factor r(t).
-3*t*(t - 1)*(t + 1)*(3*t + 1)
Let t be (9/(-15))/(18 - 2016/105). Determine f so that t*f**2 + 2*f + 2 = 0.
-2
Suppose 2*y - 96