6316. Factor c(p).
2*(p - 49)*(p - 11)*(p - 2)
Suppose 0*h - h = 4*k - 25, -5 = -k. Suppose 3*a + 25 = h*y, a + 7 = 4*y - 3*y. Factor -106*q**y - 4*q**3 + 4*q + 106*q**2.
-4*q*(q - 1)*(q + 1)
Let v = 4516925/423462 + 1/141154. Let s be -2*(-2 - 8/(-6)). Determine g, given that 64/3 - v*g + s*g**2 = 0.
4
Let h(w) = 4*w**3 + w**2 - w + 1. Let t be h(1). Suppose 9*j = -6*j + 16*j - 2. Factor 38*k + j*k + 6 + 66*k**2 + t*k.
3*(2*k + 1)*(11*k + 2)
Factor -985/2*t**3 - 64350*t**2 + 5749920 - 5/4*t**4 - 2744280*t.
-5*(t - 2)*(t + 132)**3/4
Let r(d) be the third derivative of -47/140*d**6 + 122*d**2 - 1/7*d**3 + 1/7*d**5 + 0*d + 9/56*d**4 - 5/112*d**8 + 51/245*d**7 + 0. Find v, given that r(v) = 0.
-2/7, 1/5, 1
Suppose 27 = 3*y + 99*u - 102*u, -32 = -2*y + 4*u. Factor -7 + 31/3*w - 4/3*w**y.
-(w - 7)*(4*w - 3)/3
Let f(r) be the first derivative of -r**5/110 + r**4/6 + 14*r**3/33 - 24*r**2/11 + 60*r - 95. Let b(t) be the first derivative of f(t). Solve b(l) = 0.
-2, 1, 12
Let v(m) be the second derivative of -5*m**6/12 + 11*m**5/4 - 5*m**4/8 - 55*m**3/6 + 10*m**2 + 125*m - 6. Let v(d) = 0. Calculate d.
-1, 2/5, 1, 4
Let u = 73716989/453 + -162731. Let w = -1/151 - u. Suppose -w - 4/3*r**2 - 5/3*r = 0. What is r?
-1, -1/4
Let x be 4/((-4)/(-3)) - 0. Let w be x/((-6)/(-2)*(-5)/(-15)). Factor 138 - w*i**2 + 133 - 6*i - 262.
-3*(i - 1)*(i + 3)
Let n(t) = -t + 1. Let f(y) = 2*y**2 - 580*y - 594. Let p(d) = f(d) + 6*n(d). Solve p(c) = 0 for c.
-1, 294
Let y(v) be the third derivative of -13*v**2 + 1/245*v**7 + 1/7*v**4 - 11/210*v**5 - 4/21*v**3 - 1/1176*v**8 + 0*v + 1/420*v**6 + 0. Find q such that y(q) = 0.
-2, 1, 2
Let f = 1195 - 1189. Let s(u) be the third derivative of 0 - 1/4*u**5 - 5/12*u**f - 1/14*u**7 - 7*u**2 + 0*u + 0*u**4 + 0*u**3. Factor s(x).
-5*x**2*(x + 3)*(3*x + 1)
Let h(l) be the second derivative of -45*l**3 - 122*l + 0 + 0*l**2 - 5/12*l**4. Factor h(b).
-5*b*(b + 54)
Suppose 1304/3*d + 430/3*d**2 - 2/3*d**3 + 872/3 = 0. What is d?
-2, -1, 218
Let m(n) be the third derivative of -n**6/96 + 2957*n**5/240 - 1033*n**4/24 + 295*n**3/6 + 6993*n**2. Determine s so that m(s) = 0.
2/5, 1, 590
Let u be (-1684)/6*((-1270)/316 + 4). Let z = u + 1/237. Determine h so that -8/3 - 12*h - z*h**2 = 0.
-2, -1/4
Let j(v) = -v**3 - 37*v**2 + 84*v + 234. Let k be j(-39). Let l(c) be the second derivative of -18*c + 1/66*c**4 - 1/11*c**3 + k + 2/11*c**2. Factor l(n).
2*(n - 2)*(n - 1)/11
Let p(y) = 3*y**2 + 13*y + 60. Let i(n) = -7*n**2 - 25*n - 128. Let q(f) = -2*i(f) - 5*p(f). What is z in q(z) = 0?
-11, -4
Suppose -2*s + 2 = -2*c, 3*s + 407 = 4*c + 408. Let d(y) be the first derivative of 2/15*y**2 - 2/45*y**s - 2/15*y + 11. Factor d(f).
-2*(f - 1)**2/15
Suppose 1312/7*l - 64/7 + 688/7*l**3 - 1860/7*l**2 - 76/7*l**4 = 0. Calculate l.
1/19, 1, 4
Suppose 2*j - 2680 = -4*c, -5 = -10*c + 11*c. Let l be (-2)/(-3) - (-9)/(j/140). Factor 0*t - l*t**3 + 0*t**2 + 32/5*t**4 - 14/5*t**5 + 0.
-2*t**3*(t - 2)*(7*t - 2)/5
Let n(p) = 3*p**2 - 6*p + 5. Let o be n(5). Factor 5*g**2 + 33 - 90*g + o*g + 9 + 33.
5*(g - 5)*(g - 3)
Let t(h) = 5*h - 6. Let f(g) = 6*g - 6. Let c(r) = 4*f(r) - 5*t(r). Let x be c(2). Factor x + 5*b**2 + 8*b - 8*b**3 + 10*b**3 - b**3.
(b + 1)*(b + 2)**2
Let f(p) be the third derivative of -p**5/75 - 9*p**4/20 - 46*p**3/15 + 1538*p**2. Factor f(z).
-2*(z + 2)*(2*z + 23)/5
Let n(g) be the third derivative of -65/48*g**4 - 3/4*g**6 - 52*g**2 + 0 - 5/12*g**3 + 0*g - 2*g**5. Solve n(w) = 0 for w.
-1, -1/6
Let a(l) be the second derivative of 87*l**5/20 + 89*l**4/4 + 32*l**3 + 6*l**2 + 380*l - 1. Find d, given that a(d) = 0.
-2, -1, -2/29
Let a(p) be the first derivative of p**5 + 15*p**4 - 160*p**3/3 - 120*p**2 + 560*p + 3905. Factor a(l).
5*(l - 2)**2*(l + 2)*(l + 14)
Let f(l) = -l**5 + 148*l**4 + 3603*l**3 + 27494*l**2 - 31250*l + 3. Let y(g) = -g**5 + g**3 - 2*g**2 + 1. Let u(z) = f(z) - 3*y(z). What is q in u(q) = 0?
-25, 0, 1
Suppose -2*d + 3*h - 288 = -6*d, 0 = d - 4*h - 72. Suppose 0 = 15*v + 9*v - d. Solve 0 + 4*l**2 - 8/3*l - 4/3*l**v = 0 for l.
0, 1, 2
Find t, given that -106/9*t - 100/9*t**2 - 8/3 + 16/9*t**3 + 28/9*t**4 - 2/3*t**5 = 0.
-1, -1/3, 3, 4
Let h(f) = -f**3 - 19*f**2 - 90*f + 2. Let l be h(-9). Let a(z) be the first derivative of 1/9*z**3 + 48*z - 4*z**l - 10. Find k such that a(k) = 0.
12
Factor 0 - 83232/11*u - 816/11*u**2 - 2/11*u**3.
-2*u*(u + 204)**2/11
Let r(h) be the first derivative of -2/17*h**3 + 4/17*h + 1/17*h**4 - 3/17*h**2 - 54. Factor r(g).
2*(g - 2)*(g + 1)*(2*g - 1)/17
Let l = 260 + -258. Find w such that -61 + 212*w + 53*w**2 - 26*w**l + 41*w**2 + 85 = 0.
-3, -2/17
Let h(w) be the first derivative of -11/3*w**3 + 0*w - 5/12*w**4 + 0*w**2 - 1/900*w**6 - 1/30*w**5 - 18. Let f(q) be the third derivative of h(q). Factor f(b).
-2*(b + 5)**2/5
Let s(z) be the second derivative of z**7/7 + 17*z**6/15 - 9*z**5/10 - 17*z**4/6 + 2*z**3 + 1862*z - 2. Suppose s(n) = 0. Calculate n.
-6, -1, 0, 1/3, 1
Let x(g) be the second derivative of -g**4/60 - 13*g**3/30 + 189*g**2/5 - g - 3563. Factor x(z).
-(z - 14)*(z + 27)/5
Factor 0*n - 99*n - 570 + 4710*n**2 - 4707*n**2.
3*(n - 38)*(n + 5)
Let j(i) be the third derivative of i**6/360 + i**5/48 + i**4/16 + 18*i**3 + 2*i**2 + i. Let q(a) be the first derivative of j(a). Find b, given that q(b) = 0.
-3/2, -1
Let d(k) be the first derivative of 0*k**2 + 26 + 1/10*k**4 - 2/75*k**5 + 0*k - 4/45*k**3. Determine y, given that d(y) = 0.
0, 1, 2
Let l = -4556 - -4558. Let a(w) be the third derivative of 1/4*w**4 - 2/3*w**3 + 1/16*w**5 + 0*w + 0 - 16*w**l - 5/96*w**6. Factor a(x).
-(x + 1)*(5*x - 4)**2/4
Suppose 4*p + 3*l = 1, -8*p = -3*p - 5*l - 10. Let q(k) = -2*k**2 + 8*k + 12. Let d(f) = -1. Let o(i) = p*q(i) + 2*d(i). Let o(h) = 0. What is h?
-1, 5
Let m be 31 - (12/(-3) + -4). Let 96*n**3 - 2*n + 36 - 5*n - 11*n - m = 0. What is n?
-1/4, 1/2
Let i(b) be the third derivative of b**5/105 + 40*b**4/21 + 296*b**3/7 + b**2 + 3257*b. Factor i(u).
4*(u + 6)*(u + 74)/7
Let i(g) = -108*g**3 - 388*g**2 - 520*g - 184. Let h(k) = -31*k**3 - 111*k**2 - 149*k - 53. Let n(c) = 24*h(c) - 7*i(c). Factor n(z).
4*(z + 2)**2*(3*z + 1)
Solve -3*v + 217 + 349 - 566 - 151*v**2 = 0 for v.
-3/151, 0
Factor -497*x + 14*x**2 + 936*x - 8 - 8 - 4 - 473*x + 4*x**3.
2*(x - 2)*(x + 5)*(2*x + 1)
What is a in -34/3*a**3 + 704/3 - 2/3*a**4 - 44*a**2 + 64/3*a = 0?
-11, -4, 2
Let t = -60 + 172. Let v = -110 + t. Determine l so that 4*l**3 + 16*l + 11*l**v + 8*l**2 + l**2 = 0.
-4, -1, 0
Suppose 10*f + 64 = -6*f. Let c(t) = -8*t**2 + 12*t - 18. Let p(v) = -10*v**2 + 12*v - 18. Let x(h) = f*c(h) + 3*p(h). Determine u so that x(u) = 0.
3
Let c(b) be the second derivative of b**5/25 + 542*b**4/15 - 362*b**3/5 - 155*b - 3. Let c(g) = 0. Calculate g.
-543, 0, 1
Find p, given that -1/2*p**2 - 63/2 + 12*p = 0.
3, 21
Let k = 1034 + -633. Let y = k + -397. Solve 0*n - 26/5*n**y + 0 + 8/5*n**2 - 2*n**5 - 8/5*n**3 = 0 for n.
-2, -1, 0, 2/5
Let h(s) = 2*s**2 - 126*s - 976. Let d be h(-7). Factor 14 + d*v + 2/7*v**2.
2*(v + 7)**2/7
Let a(h) = 40*h**4 - 143*h**3 + 75*h**2 + 6*h. Let u(g) = 275*g**4 - 1000*g**3 + 525*g**2 + 40*g. Let o(s) = 20*a(s) - 3*u(s). Factor o(q).
-5*q**2*(q - 5)*(5*q - 3)
Find q such that -72/5 + 2/5*q**3 - 8/5*q**2 - 82/5*q = 0.
-4, -1, 9
Let y be (-4)/(-8)*(-12)/33 - 10052/(-1078). Let c(l) be the first derivative of 4/21*l**3 + y*l - 1 - 16/7*l**2. Determine a so that c(a) = 0.
4
Let c(x) be the second derivative of x**4/6 + 29*x**3/3 + 154*x**2 + 87*x - 2. Factor c(v).
2*(v + 7)*(v + 22)
Solve 298/19*b - 28/19 + 2*b**3 - 308/19*b**2 = 0 for b.
2/19, 1, 7
Let z(n) = -n**3 - n**2 + 4*n + 2. Let t(i) = -5*i**3 - 17*i**2 + 46*i + 8. Let r(m) = -5*t(m) + 20*z(m). Find y such that r(y) = 0.
-15, 0, 2
Let z be (4/(-6))/((-30)/(-9) + -4). Let v(m) = m**2 + 5*m - 6. Let w be v(z). What is y in 0 + 10*y + w*y**2 - 5/2*y**3 = 0?
-2, 0, 2
Let n(k) be the second derivative of -1/6*k**4 + 0 - 7/3*k**3 + 84*k - 6*k**2. Factor n(w).
-2*(w + 1)*(w + 6)
Let m = -16974 + 16978. Let y(t) be the first derivative of -2*t**2 - 4/5*t**5 + 11 - m*t**3 - 3*t**4 + 0*t. Factor y(s).
-4*s*(s + 1)**3
Suppose -60/11 + 34/11*u - 2/11*u**2 = 0. Calculate u.
2, 15
Let o be 2/(-8) - 3/36*-39. Factor -57*y**2 + 106 + 516*y - 48*y**2 + 5*y**o - 60