20/2*1/3. Let x = -225975 + 225977. Factor -z*f**2 - x*f + 4/3.
-2*(f + 1)*(5*f - 2)/3
Suppose 21 = c - g, -2*c - 3*g + 2*g + 36 = 0. Suppose 0 = -s - c + 22. Factor -10 + 5*v - 4*v + 25*v**2 + 10*v**s + 5*v - v.
5*(v + 1)*(v + 2)*(2*v - 1)
Let l(x) = 1986*x + 25826. Let h be l(-13). Factor h*b + 2/7*b**2 + 56.
2*(b + 14)**2/7
Let h be (-44)/(-2) + (676/13)/13. Find k, given that h*k**3 - 5*k**5 - 13945 - 6*k**4 + 13949 + 2*k**2 - 18*k - 3*k**5 = 0.
-2, -1, 1/4, 1
Let w be ((22/(-12) + 2)*(-87)/174)/(-2). Let a(v) be the third derivative of 0*v**3 + 5/8*v**4 - 17*v**2 + w*v**6 + 0 + 0*v - 1/3*v**5. Factor a(u).
5*u*(u - 3)*(u - 1)
Let j(w) be the first derivative of -w**3/3 - 13*w**2/2 + 140*w + 256. Let t be j(-20). Let 1/6*x**3 + t*x**2 + 0 - 2/3*x = 0. Calculate x.
-2, 0, 2
Let a(o) = -o**3 + 49*o**2 + 286*o + 245. Let c(u) = 48*u**2 + 286*u + 244. Suppose 9*m = 2*m - 14. Let y(h) = m*a(h) + 3*c(h). Factor y(k).
2*(k + 1)*(k + 11)**2
Let z(s) = -41*s**2 - 970*s + 10202. Let w(d) = 1125*d**2 + 26190*d - 275455. Let t(p) = -2*w(p) - 55*z(p). Factor t(g).
5*(g - 10)*(g + 204)
Let j(t) be the first derivative of -2*t**5/15 + 61*t**4/6 - 116*t**3/3 - 4*t**2/3 + 464*t/3 + 2715. Suppose j(w) = 0. Calculate w.
-1, 2, 58
Let m(y) be the third derivative of y**6/40 - 19*y**5/5 + 149*y**4/8 - 37*y**3 - 456*y**2 - y. Find i, given that m(i) = 0.
1, 74
Let o(i) = -11*i**3 - 55*i**2 - 92*i - 45. Let m(h) = -13*h**3 - 55*h**2 - 91*h - 45. Let s(w) = 3*m(w) - 4*o(w). Solve s(a) = 0.
-9, -1
Determine j so that -1/9*j + 4/9*j**4 + 4/9*j**2 - 2/3*j**3 + 0 - 1/9*j**5 = 0.
0, 1
Let j(t) = -t**3 + 25*t**2 + 11*t + 390. Let r be j(26). Suppose 6/5*z**2 + 22/5*z**4 + 0*z - 3/5*z**5 - 5*z**3 + r = 0. What is z?
0, 1/3, 1, 6
Let q(j) = 31*j**2 + 3*j + 4. Let b be q(5). Let y = b + -794. Factor -5/7*x**4 + 8/7*x**2 - 4/7*x + x**3 + y.
-x*(x - 2)*(x + 1)*(5*x - 2)/7
Factor 24/7*r**2 - 60/7 - 3/7*r**3 - 33/7*r.
-3*(r - 5)*(r - 4)*(r + 1)/7
Let m(i) be the first derivative of -8*i**2 + 64*i + 39 + 1/3*i**3. Factor m(j).
(j - 8)**2
Let r(d) be the first derivative of -d**3/9 - 499*d**2/6 - 994*d/3 + 7503. Factor r(y).
-(y + 2)*(y + 497)/3
Suppose -5*s**4 + 13794*s + 360 + 60*s**3 + 1217*s**2 - 13704*s - 1422*s**2 = 0. Calculate s.
-1, 3, 4, 6
Let l(x) be the third derivative of 0*x**3 - 5*x - 1/420*x**6 + 0 + 1/84*x**4 + 0*x**5 + 2*x**2. Factor l(j).
-2*j*(j - 1)*(j + 1)/7
Let b(a) = 3*a**3 - 498*a**2 - 18247*a - 115221. Let t(h) = -2*h**3 + 248*h**2 + 9124*h + 57612. Let o(x) = -8*b(x) - 14*t(x). Suppose o(s) = 0. What is s?
-60, -8
Let v(x) be the second derivative of 2*x**6/105 - 17*x**5/35 + 9*x**4/7 + 30*x**3/7 - 49*x - 96. Let v(r) = 0. What is r?
-1, 0, 3, 15
Suppose 168*u = -72*u + 480. Let m = 10 + -7. Let -8/11*v**u + 2/11*v**m - 12/11 - 2*v = 0. What is v?
-1, 6
Factor -5/2*a**2 + 160/3*a + 335/6.
-5*(a + 1)*(3*a - 67)/6
Let r = 295 - 504. Let n be r/(-55) + (-2)/(-10). Suppose 16*l - 4*l**2 - 20*l + 13 - 9 + n*l**3 = 0. Calculate l.
-1, 1
Suppose 3*g - w - 165 = 0, -g + 18*w = 19*w - 59. Let o be 2/g*(-76)/(-19). Let -1/7 + o*l**3 + 1/7*l**2 - 1/7*l = 0. What is l?
-1, 1
Let y be 2745*((-408)/(-420) + (-4)/7). Let b = y + -1098. Factor 3/4*a**4 + 3/4*a + 9/4*a**3 + 9/4*a**2 + b.
3*a*(a + 1)**3/4
Let v = 339 - 333. Let -61*c**3 + v*c**2 - 2 + 142*c - 72*c - 51*c + 38*c**4 = 0. Calculate c.
-1/2, 2/19, 1
Let n(i) = -2*i**2 - 2*i + 6. Let w be (2/(-6))/((-11)/(-66)). Let p(o) = o**2 + 3*o - 7. Let u(f) = w*p(f) - 3*n(f). Suppose u(k) = 0. What is k?
-1, 1
Let o(j) = -37*j**2 - 697*j + 3352. Let x(c) = 169*c**2 + 2789*c - 13409. Let z(p) = -9*o(p) - 2*x(p). Factor z(u).
-5*(u - 134)*(u - 5)
Suppose 33564*s - 33517*s = 0. Let j(p) = -p**3 - 6*p**2 + p + 8. Let k be j(-6). Find q, given that s + 1/8*q**k - 1/8*q**4 + 1/8*q**3 - 1/8*q = 0.
-1, 0, 1
Let o(k) = k**5 + 3*k + 1. Let l(f) = -7*f**5 + 16*f**4 - 96*f**3 + 256*f**2 - 274*f - 6. Let x(n) = -l(n) - 6*o(n). Factor x(t).
t*(t - 4)**4
Let c(s) be the third derivative of -s**5/20 - 44*s**4 - 350*s**3 + 5986*s**2. Let c(k) = 0. What is k?
-350, -2
Suppose 55*w = 60*w - 15. Factor 5*o**4 + 2*o**3 + 0*o**3 - 36*o**3 - 55*o**2 + 0*o**3 - 16*o**w.
5*o**2*(o - 11)*(o + 1)
Let z = -5653256/9 - -628140. Let b be (8/(-54))/(1/(-6)). Factor -b*x + 0 + z*x**2.
4*x*(x - 2)/9
Let r(o) be the second derivative of o**5/70 - o**4/21 - o**3/3 - 4*o**2/7 + 7752*o. Factor r(w).
2*(w - 4)*(w + 1)**2/7
Let u be ((-162)/(-48))/((-1269)/(-564)). Determine c so that -15/8*c**3 - 3/8*c**4 - 9/8*c**2 + 15/8*c + u = 0.
-4, -1, 1
Suppose -11/3*d**2 - 3*d**3 + 1/3*d**4 + 10/3 + 3*d = 0. What is d?
-1, 1, 10
Let f(q) be the first derivative of -q**3/3 + 61*q**2/2 - 321. Factor f(v).
-v*(v - 61)
Let z = -59 + 63. Suppose -k = z*i - 14, 5*k + 4*i - 7 - 15 = 0. Find p such that 3*p**2 - 13*p - k*p**2 + 3*p + 11*p = 0.
-1, 0
Find c such that -28/15 + 2/15*c - 2/15*c**3 + 28/15*c**2 = 0.
-1, 1, 14
Suppose 7*i = -14*i + 42. Factor 4*g**i + 83 - 12 + 41 - 26*g - 18*g.
4*(g - 7)*(g - 4)
Let a = 1388 - 1374. Let q(z) be the first derivative of 3*z**2 + 6*z - a + 1/2*z**3. Factor q(d).
3*(d + 2)**2/2
Let k be (113/5)/((-224)/(-840)). Let d = k - 285/4. Let 3/2*z**3 - 6 + d*z - 9*z**2 = 0. What is z?
1, 4
Let u(i) be the second derivative of -1/10*i**5 + 141*i - 7*i**2 + 0 + 1/3*i**3 + 7/6*i**4. Factor u(m).
-2*(m - 7)*(m - 1)*(m + 1)
Let d(x) be the second derivative of x**5/4 - 25*x**4 + 510*x**3 - 4320*x**2 - 242*x - 2. Let d(o) = 0. Calculate o.
6, 48
Let g(k) be the third derivative of -49*k**5/12 - 245*k**4 - 830*k**3/3 - 1285*k**2. Factor g(f).
-5*(7*f + 2)*(7*f + 166)
Let r(o) be the third derivative of 0 + 3/80*o**6 + 0*o - 1/6*o**4 - 43*o**2 - 1/40*o**5 + 1/3*o**3. Factor r(g).
(g + 1)*(3*g - 2)**2/2
Suppose -k - 5*w = -29, -3*w + 13 = 2*k - 2*w. Find t such that 131 + 20*t**3 + 131 - 262 + 16*t + k*t**4 + 32*t**2 = 0.
-2, -1, 0
Let s(n) be the third derivative of 0*n + 0 - 95*n**2 - 1/45*n**6 - 1/9*n**5 + 16/9*n**3 + 7/9*n**4. Suppose s(c) = 0. What is c?
-4, -1/2, 2
Let r = -909 + 603. Let i = 309 + r. Factor 0 - 1/3*q**i + 1/6*q**4 + 1/6*q**2 + 0*q.
q**2*(q - 1)**2/6
Let t(v) be the second derivative of v**5/10 - 65*v**4/3 + 257*v**3/3 - 128*v**2 - 2187*v. Factor t(o).
2*(o - 128)*(o - 1)**2
Let -2/15*g**2 + 3604/5*g - 4870806/5 = 0. Calculate g.
2703
Factor 756/19*f - 754/19 - 2/19*f**2.
-2*(f - 377)*(f - 1)/19
Let o(i) be the third derivative of i**5/240 - 31*i**4/96 - 4*i**3/3 + 4*i**2 + 8*i - 10. Factor o(t).
(t - 32)*(t + 1)/4
Let t be (1 - -1) + (-2)/3. Let u be ((-4296)/33831)/((-3)/504). Factor -u - t*l**2 - 32/3*l.
-4*(l + 4)**2/3
Determine y so that 42/5*y**4 - 194/5*y**3 - 102/5*y**2 + 114/5*y - 4 = 0.
-1, 2/7, 1/3, 5
Let t(j) be the first derivative of 9*j**4/4 + 7*j**3/2 - 3*j**2 - 167*j + 204. Let z(d) be the first derivative of t(d). Factor z(s).
3*(s + 1)*(9*s - 2)
Let f = -3/4243 - -34007/89103. Let a(r) be the first derivative of 2/21*r**6 + 0*r**2 - f*r**3 + 5/7*r**4 + 0*r - 16/35*r**5 - 20. Let a(s) = 0. Calculate s.
0, 1, 2
Let y be 1276/(-14297) + 684/3306. Solve -256/17*l + y*l**2 + 8192/17 = 0 for l.
64
Factor 1/6*m**2 - 35/2 - 4/3*m.
(m - 15)*(m + 7)/6
Let t(d) be the first derivative of 1/3*d**3 - 1/6*d**6 + 3/5*d**5 - 3/4*d**4 + 0*d + 20 + 0*d**2. Suppose t(g) = 0. Calculate g.
0, 1
Let v(z) be the first derivative of 3*z**5/10 - 363*z**4/16 + 143*z**3/2 + 705*z**2/8 - 261*z/2 + 329. Determine n, given that v(n) = 0.
-1, 1/2, 3, 58
Let g(b) be the second derivative of b**5/20 - 7*b**4/12 + b**3/2 + 21*b**2/2 + 2*b - 242. Let w be g(6). Factor -1/4*j**w + j**2 - 5/4*j + 1/2.
-(j - 2)*(j - 1)**2/4
Let z(m) be the third derivative of -5*m**3 - 1/360*m**5 + 0 + 1/36*m**4 + 0*m - 1/1080*m**6 + 9*m**2. Let l(r) be the first derivative of z(r). Factor l(t).
-(t - 1)*(t + 2)/3
Let l(d) = 36*d**2 - 10*d - 26*d - 15 - 13 + 64*d**3 - 64*d**4. Let q(w) = 7*w**4 - 7*w**3 - 4*w**2 + 4*w + 3. Let x(b) = 3*l(b) + 28*q(b). Factor x(n).
4*n*(n - 1)**2*(n + 1)
Let b = -28024 - -84098/3. Factor -b*h + 2*h**2 + 8/3.
2*(h - 4)*(3*h - 1)/3
Find t, given that 1239/8*t + 155 - 1/8*t**2 = 0.
-1, 1240
Let g be 2/9 - (8 + (-1176)/54). Factor 27*t + 21*t**2 + g*t**2 - 36*t**2.
-t*(t - 27)
Let y(i) be the third derivative of -i**9/75600 +