0. Calculate f.
7
Let i = 83/6 + -69/5. Let k(t) be the second derivative of 1/12*t**4 - 1/6*t**3 + 9*t + 0*t**2 + 1/20*t**5 + 0 - i*t**6. Factor k(d).
-d*(d - 1)**2*(d + 1)
Suppose 9*d + 6 = 33. Find f such that -164*f**2 + 6*f**d - 4*f**5 - 2*f**3 + 164*f**2 = 0.
-1, 0, 1
Let c = 14268 - 14265. Let n(r) be the first derivative of 3/4*r**4 + 3*r**2 - 35 - c*r**3 + 0*r. Factor n(t).
3*t*(t - 2)*(t - 1)
Suppose 4*d = o - 12, 55 - 43 = 2*d + 4*o. Let j be (-12)/d - (7 + -4). What is x in 6/5*x**j - 6/5*x**2 + 0*x + 0 = 0?
0, 1
Let v(b) be the first derivative of b**6/39 - 2*b**5/65 - 3*b**4/13 - 4*b**3/39 + 5*b**2/13 + 6*b/13 - 1719. Find o, given that v(o) = 0.
-1, 1, 3
Let r(m) = -51*m + 261. Let a be r(5). Determine x, given that -12*x**2 + 8*x**2 + 0*x**3 - 3*x**4 + a*x**3 + 28*x**2 - 36*x + 9*x**2 = 0.
-3, 0, 1, 4
Let s(z) be the second derivative of 0 + 4*z**2 + 1/21*z**7 + 4/5*z**5 + 126*z - 3*z**3 + 1/3*z**4 - 2/5*z**6. Factor s(d).
2*(d - 4)*(d - 1)**3*(d + 1)
Let b(o) = 6*o**4 - 4*o**3 - 12*o**2 + 12*o + 4. Let i(w) = 7*w**4 - 4*w**3 - 13*w**2 + 11*w + 5. Let s(y) = -5*b(y) + 4*i(y). Find k, given that s(k) = 0.
-2, 0, 2
Solve 204 - 3826/13*q - 232/13*q**2 + 6/13*q**3 = 0 for q.
-13, 2/3, 51
Factor 1388*c - 3*c**2 - 2131947 + 3589*c + 233*c - 152*c.
-3*(c - 843)**2
Solve 2/11*y**3 + 18/11*y**2 - 24/11*y - 40/11 = 0.
-10, -1, 2
Find k, given that -2619/5 - 3/5*k**2 - 882/5*k = 0.
-291, -3
Let z = 480 - 506. Let h be (689/z - -4)*(-1)/5. Factor -7/4*o**3 + 0 - 2*o + 3/4*o**4 - h*o**2.
o*(o - 4)*(o + 1)*(3*o + 2)/4
What is f in -3*f**4 + 5*f**2 - 143*f**3 + 45*f**2 - f**4 - 2*f**2 + 187*f**3 = 0?
-1, 0, 12
Factor -396*f**3 + 548942 + 548934 - 400*f**2 + 4*f**4 - 1097876.
4*f**2*(f - 100)*(f + 1)
Let q be (-24)/15 + (-540)/150*4/(-6). Factor -1/5*a**2 - q - 4/5*a.
-(a + 2)**2/5
Let v(s) be the first derivative of -305/4*s**4 + 140*s**3 + 14*s**5 + 0*s - 5/6*s**6 + 43 - 90*s**2. Factor v(c).
-5*c*(c - 6)**2*(c - 1)**2
Let d(b) be the third derivative of -b**5/30 + 659*b**4/6 - 434281*b**3/3 - 4*b**2 + 105*b. Factor d(u).
-2*(u - 659)**2
Suppose 13/5*d**2 + 9/5*d**3 + 3/5 - 16/5*d**4 - 13/5*d + 4/5*d**5 = 0. What is d?
-1, 1/2, 1, 3
Let v(q) = 2*q**4 + 450*q**3 + 1971*q**2 - 5230*q + 2832. Let n(o) = -2*o**4 - 226*o**3 - 985*o**2 + 2614*o - 1416. Let h(d) = -5*n(d) - 3*v(d). Factor h(u).
4*(u - 59)*(u - 1)**2*(u + 6)
Determine v so that -9/7*v**2 + 3/7*v**4 - 6/7*v**3 + 12/7*v + 12/7 = 0.
-1, 2
Let l(g) = 10*g**3 - 93*g**2 + 667*g - 7. Let q(z) = 7*z**3 - 62*z**2 + 443*z - 5. Let a(s) = -5*l(s) + 7*q(s). Find r, given that a(r) = 0.
0, 13, 18
Let p(a) be the second derivative of -3/8*a**2 - 1/6*a**3 - 2 - 1/48*a**4 - 35*a. Factor p(i).
-(i + 1)*(i + 3)/4
Let j = -105 + 91. Let h = j - -17. Solve -r**2 + 4*r**4 + 4*r**3 + r**3 - 9*r**h - 7*r**2 = 0.
-1, 0, 2
What is s in -18*s**3 + 4104*s**2 + 937 + 6972*s**2 + 7390*s + 295 = 0?
-1/3, 616
Let p(o) = -o**2 - o + 4. Let y(d) = 1. Let b(z) = -p(z) + 3*y(z). Let g(l) = -3*l**2 + 17*l + 48. Let k(a) = 2*b(a) - g(a). Determine u so that k(u) = 0.
-2, 5
Let y(f) be the first derivative of 3*f**4/4 + 829*f**3 + 514185*f**2/2 - 516675*f + 4986. Suppose y(s) = 0. Calculate s.
-415, 1
Let j(h) = -6*h**2 - 20*h + 246. Let t(k) = -3*k**2 - 9*k + 114. Let m(s) = -2*j(s) + 5*t(s). Factor m(n).
-(n + 6)*(3*n - 13)
Let t(s) be the first derivative of -s**4/2 - 86*s**3 - 380*s**2 - 504*s - 383. What is g in t(g) = 0?
-126, -2, -1
Let l(r) be the second derivative of 1/21*r**3 + 0*r**2 - 2 - 34*r + 1/84*r**4. Solve l(h) = 0 for h.
-2, 0
Suppose -40*t = 36*t - 285*t + 418. Factor 0 + 28/9*a - 2/9*a**t.
-2*a*(a - 14)/9
Factor 332/3*u**2 - 178*u - 1/3*u**4 - 14*u**3 + 245/3.
-(u - 5)*(u - 1)**2*(u + 49)/3
Let l(r) be the second derivative of -5*r**4/12 - 4180*r**3/3 - 1747240*r**2 - 1003*r. Let l(n) = 0. What is n?
-836
Let y(t) be the third derivative of -t**8/672 + t**7/42 - 3*t**6/20 + 9*t**5/20 - 9*t**4/16 - 165*t**2. What is r in y(r) = 0?
0, 1, 3
Suppose -4*d - 18 = -2, -d + 653 = 3*l. Factor -8*c**4 + 24*c**4 + 32*c**3 + l*c**2 + 2*c**5 - 219*c**2.
2*c**3*(c + 4)**2
Find k such that -84*k**2 + k + 112*k**2 + 313*k**2 - 4*k + 298*k**2 = 0.
0, 1/213
Let s(t) be the first derivative of -t**7/14 + 7*t**6/30 - 13*t**5/40 + t**4/4 - t**3 - 5*t**2/2 + 61. Let q(p) be the third derivative of s(p). Factor q(j).
-3*(2*j - 1)**2*(5*j - 2)
Suppose 5*s - 33 = 42. Factor 21*l**3 - 446*l**2 + s*l**4 + 17*l**5 - 14*l**5 + 455*l**2.
3*l**2*(l + 1)**2*(l + 3)
Factor 9720*q**3 + 0*q**4 - 4829*q**3 - 4*q**4 - 4895*q**3 + 12*q**2 - q - 8 + 5*q.
-4*(q - 1)**2*(q + 1)*(q + 2)
Let z be 2 + 1 - (-2 - -2). Suppose -3*v + 132 = z*c, -3*c = -4*v + v - 150. What is u in c*u - 47*u + 80 + 40*u + 5*u**2 = 0?
-4
Suppose -14*k + 6 = -13*k. Factor -3*y**4 - 2 + 1680*y + k*y**3 + 5 - 1686*y.
-3*(y - 1)**3*(y + 1)
Let b(q) be the second derivative of -q**5/20 - 25*q**4/6 - 176*q**3/3 - 336*q**2 - 12*q - 31. What is w in b(w) = 0?
-42, -4
Let g(s) be the second derivative of 14*s**2 - s**4 + 4*s + 6 + 3*s**3 - 1/10*s**5. Factor g(k).
-2*(k - 2)*(k + 1)*(k + 7)
Let i(l) = 5*l**2 - 1. Let j(w) = -8*w - 7. Let k be j(-1). Let v be i(k). Factor -2*t**4 - 13*t**4 - 3*t**5 + 3*t**v.
-3*t**4*(t + 4)
Let k(p) = 4*p - 184. Let g be k(47). Factor -3 + 58*a + 3 - g*a**2 - 5 + 3*a**2 - 64*a.
-(a + 1)*(a + 5)
Factor -272/3 - 46*u - 1/3*u**2.
-(u + 2)*(u + 136)/3
Let t(l) = l + 8. Let h(m) = -m**4 + 26*m**3 + 31*m**2 - 108*m - 140. Let f(v) = -h(v) - 4*t(v). Solve f(r) = 0.
-2, -1, 2, 27
Let s be 31*3*(-6)/72 + 8. Let j(p) be the first derivative of 1/6*p**3 + 13 + 0*p + 0*p**2 + 1/10*p**5 - s*p**4. Factor j(o).
o**2*(o - 1)**2/2
Suppose -2*s + 63*s = -74298. Let m = -1218 - s. Determine t so that m + 0*t + 6/7*t**3 - 4/7*t**2 - 2/7*t**4 = 0.
0, 1, 2
Let d = 26491/106636 + 42/26659. Factor -7/4*t**2 + 3 - t - d*t**3.
-(t - 1)*(t + 2)*(t + 6)/4
Factor -1/6*o**4 + 0*o**2 + 0 + o**3 + 0*o - 1/6*o**5.
-o**3*(o - 2)*(o + 3)/6
Let d(t) be the second derivative of t**5/50 + 23*t**4/6 - 314*t. Factor d(x).
2*x**2*(x + 115)/5
Let v(f) be the third derivative of -8*f**6/5 - 28*f**5/5 + 255*f**4/8 + 225*f**3 - 2*f**2 + 960*f. Factor v(k).
-3*(k - 2)*(8*k + 15)**2
Let u(i) be the first derivative of -405/7*i - 81/14*i**2 + 12 - 33/14*i**4 + 1/14*i**6 + 90/7*i**3 - 9/35*i**5. Factor u(c).
3*(c - 3)**3*(c + 1)*(c + 5)/7
Solve 258/5*z**2 + 2/5*z**3 - 1056/5 - 160*z = 0.
-132, -1, 4
Let w be 203/7 + (-4214)/147. Determine y, given that w*y + 4 - 1/3*y**2 = 0.
-3, 4
Let p be 5/40 + (-1)/8. Suppose p = -i + 114 - 74. Determine u so that -18*u**2 + 4*u + i*u**4 - u**5 + 33*u**3 - 3*u**2 + 4*u**5 - 59*u**4 = 0.
0, 1/3, 1, 4
Let x(t) be the first derivative of -t**6/2340 + t**5/52 + 17*t**4/78 + 69*t**3 - 10. Let v(z) be the third derivative of x(z). Factor v(l).
-2*(l - 17)*(l + 2)/13
Let u(a) be the third derivative of -a**6/960 + 13*a**5/80 + 499*a**4/192 + 35*a**3/4 + 2*a**2 + 15*a - 3. Factor u(k).
-(k - 84)*(k + 1)*(k + 5)/8
Let k(t) be the second derivative of 0*t**3 + 5 - 1/378*t**7 + 2/27*t**4 - 5*t - 1/135*t**6 + 1/45*t**5 + 0*t**2. Let k(n) = 0. Calculate n.
-2, 0, 2
Let p(m) = 2*m**4 + 10*m**3 - 6*m**2 - 6*m + 16. Let t = 918 + -922. Let n(w) = -w**4 - w**2 - w - 1. Let s(c) = t*n(c) - p(c). Suppose s(y) = 0. Calculate y.
-1, 1, 2, 3
Factor -13*d**3 + 37*d + 0 + 71/3*d**2 + 1/3*d**4.
d*(d - 37)*(d - 3)*(d + 1)/3
Let y(c) be the first derivative of 11/7*c**2 - 28 + 24/7*c - 2/21*c**3. Solve y(m) = 0 for m.
-1, 12
Let p(w) be the first derivative of -70*w**5/3 - 59*w**4/2 + 346*w**3/9 + 59*w**2 + 4*w/3 - 2564. Find s, given that p(s) = 0.
-1, -2/175, 1
Let b(y) be the first derivative of -y**6/15 - y**5/10 + 41*y - 78. Let q(j) be the first derivative of b(j). Let q(v) = 0. Calculate v.
-1, 0
Solve 375/2*g**4 + 4593/2*g**2 + 576 + 3/4*g**5 - 7671/4*g - 1143*g**3 = 0.
-256, 1, 3
Let m(k) = -8*k**3 + 8*k**2. Let g(z) = -z**3 + z**2. Suppose 2*j + 95 = -3*j. Let b = 18 + j. Let o(n) = b*m(n) + 10*g(n). Solve o(c) = 0 for c.
0, 1
Factor -2*h**2 + 2*h**2 + 140*h**3 + 4*h**5 - 17346*h**4 + 17298*h**4.
4*h**3*(h - 7)*(h - 5)
Let -2*c**5 + 256*c**4 - 14*c**4 + 500094 + 548100*c**2 - 24572*c**3 - 1024002*c + 140*c**4 = 0. Calculate c.
1, 63
Suppose -282*d - 69*d + 1755 = 