l(-1). Let p be 8/3 + q/(-27). Determine n, given that 5*n**4 + 4*n + 8*n**3 - p*n**4 - 5*n**4 - 10*n**2 = 0.
0, 1, 2
Let k = 584 + -587. Let t be k + (-465)/(-18)*34/255. Factor t*w**3 + 2/9*w - 5/9*w**2 - 1/9*w**4 + 0.
-w*(w - 2)*(w - 1)**2/9
Let d = -69 - -109. Let k(y) = y**2 - 4*y - 13. Let r(g) = 2. Let j(u) = d*r(u) + 5*k(u). Factor j(m).
5*(m - 3)*(m - 1)
Let g = 496109/9 + -55123. Factor 2/9*b**2 + 0 + 2/9*b - 2/9*b**3 - g*b**4.
-2*b*(b - 1)*(b + 1)**2/9
Let a = -471747/7 + 67191. Let u = a + 202. Factor -u*f**3 + 0*f**4 + 2/7*f**5 + 2/7*f + 0*f**2 + 0.
2*f*(f - 1)**2*(f + 1)**2/7
Let k be 2/(-3*2/(-9)). Let r be 27 + -5 + 3 - (-4 - -1). Find w such that -2*w**3 + r*w**2 + 168 - 168 - 2*w**k = 0.
0, 7
Let g(m) be the second derivative of 10*m**3 + 25*m + 2 - 4*m**2 + 17/3*m**4. Find r, given that g(r) = 0.
-1, 2/17
Let q be (2/22)/((-30)/(-33)). Let x(j) be the second derivative of -1/3*j**3 + 1/3*j**4 + 0*j**2 - q*j**5 + 5*j + 0. What is s in x(s) = 0?
0, 1
Suppose -7*b - 2 = -x - 6*b, -5*x + b + 2 = 0. Let h(z) be the third derivative of 1/210*z**5 + 10*z**2 + 0*z + 0*z**3 - 1/84*z**4 + x. Factor h(k).
2*k*(k - 1)/7
Let j(b) be the second derivative of -b**5/20 + 8*b**4/3 - 205*b**3/6 - 43*b**2/2 + 452*b. Let o be j(23). Factor 0 + 4/7*h**2 - 12/7*h - 4/7*h**4 + 12/7*h**o.
-4*h*(h - 3)*(h - 1)*(h + 1)/7
Suppose 0*q = -4*l - q, -5*q = -3*l + 18 + 28. Suppose 16/7*n**l - 4/7*n**3 - 16/7*n + 0 = 0. What is n?
0, 2
Let g(l) = l**3 + 21*l**2 - 24*l + 16. Let v be g(-22). Determine k, given that 57 + 199 - 59*k**2 + v*k**2 - 32*k = 0.
16
Suppose 3*w + 18 = 2*d, -13*d + 4 = -9*d + 2*w. Factor -h**2 + 4*h**d - h**2 - 5*h**2 - h**3 + 13*h**2.
3*h**2*(h + 2)
Let v(o) be the second derivative of o**4/3 + 80*o**3/3 + 408*o**2 + 166*o - 1. Let v(b) = 0. Calculate b.
-34, -6
Let y = -187357/2 + 93679. Factor -1/4*f**3 + f**2 - 5/4*f + y.
-(f - 2)*(f - 1)**2/4
Let v(p) be the third derivative of p**5/20 - 471*p**4 + 1774728*p**3 + 3349*p**2. Factor v(n).
3*(n - 1884)**2
Let y(q) be the first derivative of -q**3 - 21/2*q**2 - 31 + 0*q. Factor y(h).
-3*h*(h + 7)
Let g(d) be the second derivative of d**4/42 - 4*d**3/3 - 128*d**2/7 - 813*d - 2. Factor g(x).
2*(x - 32)*(x + 4)/7
Let s(y) be the first derivative of -10609*y**3/33 + 824*y**2/11 - 64*y/11 + 5780. Determine h, given that s(h) = 0.
8/103
Let j(t) be the first derivative of 1/5*t**4 + 2/5*t**3 + 0*t**2 + 0*t - 149 + 1/50*t**5. Factor j(x).
x**2*(x + 2)*(x + 6)/10
Let u(m) = -24*m**2 - 1076*m + 1488. Let w(k) = 20*k**2 + 1084*k - 1488. Let f(z) = 2*u(z) + 3*w(z). Suppose f(y) = 0. What is y?
-93, 4/3
Suppose 38*p + 1595 = -533. Let j be (-4)/14 + p/(-98). Solve 192/7*c**2 - 32/7*c**3 - 512/7*c + 512/7 + j*c**4 = 0 for c.
4
Suppose 0 = -4*a + 6 + 14. Find j such that -4*j**4 + 2*j**a - 12 + 4*j**5 - 40*j + 32*j**3 - 24*j**2 + 40*j**4 + 2*j**5 = 0.
-3, -1, -1/2, 1
Let q(x) be the second derivative of x**4/60 - 13*x**3/30 - 7*x**2/5 - 96*x + 8. Suppose q(a) = 0. What is a?
-1, 14
What is a in -73*a + 0 + 3/2*a**2 = 0?
0, 146/3
Let z(b) = -3 + 1 + 1 - b**3. Let t(n) = -12*n**3 + 15*n**2 - 7*n - 2. Suppose -6 = -11*s + 8*s, -v + 2*s = 7. Let g(f) = v*z(f) + t(f). Factor g(o).
-(o - 1)*(3*o - 1)**2
Suppose -2288*b - 1055*b = -473*b + 809*b - 956540. Solve b*s**2 + 0 - 1352/5*s + 36/5*s**4 - 384/5*s**3 = 0.
0, 2, 13/3
Factor 2/17*n**2 - 3188/17*n + 3186/17.
2*(n - 1593)*(n - 1)/17
Suppose 17*n - 38 = 18*n. Let q = n + 40. Solve -49*p - 2 + 10*p + 7*p**q + 20*p + 14*p = 0.
-2/7, 1
Let r(h) be the second derivative of h**7/28 - 17*h**6/10 + 189*h**5/40 + 17*h**4/4 - 16*h**3 + 2*h - 2136. Solve r(t) = 0 for t.
-1, 0, 1, 2, 32
Let j(q) = -12*q**4 + 24*q**3 - 60*q**2 - 32*q + 64. Let s(i) = -i**4 - i**3. Let o(g) = j(g) - 8*s(g). Factor o(d).
-4*(d - 4)**2*(d - 1)*(d + 1)
Suppose -14660*r + 14705*r - 44 = 46. Suppose -50/9 + 20/9*n - 2/9*n**r = 0. What is n?
5
Factor 4107 + 3/4*h**3 - 441/4*h**2 + 3996*h.
3*(h - 74)**2*(h + 1)/4
Let x = -3715117/2 - -1857559. Determine m so that -x*m + 2/3 - 13/6*m**2 + 1/6*m**3 + 3/2*m**4 + 1/3*m**5 = 0.
-4, -1, 1/2, 1
Let w = -688 + 552. Let o = w - -138. Factor -5/4*y**3 - 3/4*y**4 + 3/4*y**o + 1/4*y**5 + 0 + y.
y*(y - 4)*(y - 1)*(y + 1)**2/4
Let t be 147/(-343) - 190/(-84). Determine x, given that t*x**3 + 0 + 2*x**2 + 2/3*x + 1/2*x**4 = 0.
-2, -1, -2/3, 0
Suppose 16*y = 26*y + 3*y. Let u(v) be the third derivative of -14*v**2 + y*v + 1/12*v**3 + 1/40*v**5 + 0 - 1/16*v**4 - 1/240*v**6. Factor u(p).
-(p - 1)**3/2
Let y(d) = 25*d**3 + 12*d**2 - 102*d - 40. Let b(c) = 25*c**3 + 13*c**2 - 77 - 39*c + 37 - 96*c + 32*c. Let g(l) = 2*b(l) - 3*y(l). Factor g(q).
-5*(q - 2)*(q + 2)*(5*q + 2)
Let a(u) be the first derivative of 54*u + 1/12*u**4 + 20/9*u**3 + 39/2*u**2 + 231. What is w in a(w) = 0?
-9, -2
Let t(a) be the second derivative of -a**4/18 - 13*a**3/3 - 380*a**2/3 + 7*a - 42. Factor t(p).
-2*(p + 19)*(p + 20)/3
Suppose -1454/15*f - 2/15*f**4 - 224/5 - 38/5*f**3 - 298/5*f**2 = 0. What is f?
-48, -7, -1
Find x such that 16*x**3 - 1312*x**2 + 8*x + 654*x**2 - 4*x**4 + 638*x**2 = 0.
0, 1, 2
Let s(k) be the first derivative of k**3/6 + 49*k**2/2 - 1443*k/2 + 7845. Factor s(a).
(a - 13)*(a + 111)/2
Let i be (-948)/(-632)*(-2)/(-15) - (-19)/5. Factor 3*k**3 + 0 + 0*k - 18/7*k**2 - 3/7*k**i.
-3*k**2*(k - 6)*(k - 1)/7
Factor 55*o**3 - 3 - 72*o**5 - 35*o**3 + 15*o**4 + 3*o**2 + 67*o**5 - 83*o**2 + 83.
-5*(o - 2)**3*(o + 1)*(o + 2)
Let s be (-13)/(-3) - (3 + 24/(-9)). Suppose 16 = 5*l - s. Find n, given that -l - 6 + 40*n**2 - 25*n**5 + 0*n + 0 - 110*n**3 + 15*n + 90*n**4 = 0.
-2/5, 1
Let c(f) be the third derivative of 0*f + 0*f**4 + 0*f**3 + 0*f**5 + 210 - 1/160*f**6 + 1/280*f**7 - f**2. Factor c(q).
3*q**3*(q - 1)/4
Let t be 35/(-14)*2 + (-946)/(-135) + -2. Let w(h) be the second derivative of -11*h - 1/27*h**3 + 0 - t*h**6 + 1/90*h**5 + 1/54*h**4 + 0*h**2. Factor w(x).
-2*x*(x - 1)**2*(x + 1)/9
Let n = 5728/71 + -14273/213. Find v such that 1/3*v**2 + n*v + 40/3 = 0.
-40, -1
Solve 750 - 1405*b**2 + 3670*b**2 + 3740*b - 1485*b + 5*b**4 + 765*b**3 = 0.
-150, -1
Let n(r) be the second derivative of -r**4/4 + 35*r**3/2 - 10*r + 81. Factor n(q).
-3*q*(q - 35)
Let s(r) = -7*r**4 - 73*r**3 - 197*r**2 - 191*r - 64. Let y(l) = 48*l**4 + 510*l**3 + 1377*l**2 + 1335*l + 447. Let z(b) = -27*s(b) - 4*y(b). Factor z(n).
-3*(n + 1)**3*(n + 20)
Let w(d) be the first derivative of -d**4/12 + 44*d**3/3 - 377*d**2/6 - 430*d + 5954. Factor w(p).
-(p - 129)*(p - 5)*(p + 2)/3
Suppose -27313 = 53*z - 27419. Determine b, given that -20/9*b**z - 20/9*b**3 - 2/9*b**5 - 10/9*b - 2/9 - 10/9*b**4 = 0.
-1
Suppose 0 = 83*c - 85*c + 8. Suppose -3*o - 10 = -5*m, -c*o - 4*m + 10 = m. Factor 0 - 8/3*u**3 + 0*u**2 + 4/3*u**5 - 4/3*u**4 + o*u.
4*u**3*(u - 2)*(u + 1)/3
Let n(x) be the third derivative of x**7/945 - 7*x**6/540 + 17*x**5/270 - 17*x**4/108 + 2*x**3/9 + 571*x**2. Factor n(m).
2*(m - 3)*(m - 2)*(m - 1)**2/9
Suppose 5*c + 12*o - 7*o + 15 = 0, -3*c + o + 11 = 0. Factor -c*k**2 + 60*k**3 + 7 - 7 - 8*k - 59*k**3.
k*(k - 4)*(k + 2)
Suppose -7*d - t = -4*d - 27, -2*d - 2*t = -18. Let v be 172/(-36) + d - 4. Let v*p**2 - 4/9*p - 2/3 = 0. What is p?
-1, 3
Let m = 19368 - 96806/5. Factor 289/5 + m*l + 1/5*l**2.
(l + 17)**2/5
Let n(v) be the second derivative of v**8/36960 - v**7/6930 + v**6/3960 - 15*v**4/2 - 68*v + 2. Let r(m) be the third derivative of n(m). Factor r(b).
2*b*(b - 1)**2/11
Let b(h) be the second derivative of h + 0*h**5 + 0*h**3 - 12 + 1/4*h**4 + 0*h**2 - 1/10*h**6. Find k such that b(k) = 0.
-1, 0, 1
Let k(p) = 5*p - 262. Let t(i) = -4*i + 261. Let m(v) = -7*k(v) - 6*t(v). Let s be m(24). Factor 2/5*b**3 - 2/5*b + b**2 + 0 - b**s.
-b*(b - 1)*(b + 1)*(5*b - 2)/5
Let i = -47 - -174. Suppose 128*f - i*f + 1 = -3*y, -5*y = 5*f + 5. Determine k so that y + k**3 + 1/2*k**4 - k - 1/2*k**2 = 0.
-2, -1, 0, 1
Let o = -349685 - -349685. Let 5/2*w**2 + 1/4*w**5 + o + 3/2*w**4 + 3*w**3 + 3/4*w = 0. Calculate w.
-3, -1, 0
Let c(a) be the first derivative of 3*a**4/8 - 25*a**3 + 561*a**2 - 4356*a - 1252. Factor c(f).
3*(f - 22)**2*(f - 6)/2
Let t = 237 - 363. Let h be ((-21)/t)/((-5)/(-60)). Suppose -1/2 + i - 1/2*i**h = 0. What is i?
1
Determine t so that 1/2*t**4 + 5/2*t**3 - 1/2*t**5 - 2 - 1/2*t*