0240. Let i(p) = 7*k(p) + 5*t(p). Determine b so that i(b) = 0.
-505
Factor 2*j + 5030*j**2 + 3*j + 5030*j**2 + 66 - 10061*j**2.
-(j - 11)*(j + 6)
Determine o, given that 26*o - 74*o - 15843805*o**2 + 96*o**4 + 4*o**3 + 15843665*o**2 = 0.
-1, -3/8, 0, 4/3
Let d be 236/6 + (-82485)/2115. Factor 1/3*k**4 + 0*k + 0*k**3 - d*k**2 + 0.
k**2*(k - 1)*(k + 1)/3
Factor 1/3*j**3 + 0*j + j**2 - 4/3.
(j - 1)*(j + 2)**2/3
Let z = -5813/51 + 343/3. Let d = -156 + 158. Find n such that z*n**d + 2/17*n - 2/17*n**3 - 6/17*n**4 + 0 = 0.
-1, -1/3, 0, 1
Suppose -4*b - 80 = r, -3*r + 3*b + 2*b = 206. Let n be 4 - 3 - 117/r. Find s, given that n + 3*s + 3/8*s**2 = 0.
-7, -1
Let n = -37168/3 + 12390. Let z(h) be the first derivative of 0*h + 1/6*h**4 + 32 + n*h**3 + 2/3*h**2. Factor z(x).
2*x*(x + 1)*(x + 2)/3
Let h(r) = -3*r**2 + 110*r + 48. Let i be h(37). Let y be 4 + 2*i/(-3) + 4. Factor 4/3*s + y*s**2 + 2/3.
2*(s + 1)**2/3
Let y = 85/77 + -688/693. Let s(u) be the second derivative of -y*u**3 - 2/3*u**2 + 1/18*u**4 + 10*u + 0. Factor s(p).
2*(p - 2)*(p + 1)/3
Determine d so that 550 + 222/11*d**2 - 570*d - 2/11*d**3 = 0.
1, 55
Let f be (-12)/(-15)*(-45)/(-18). Determine j, given that 11*j + 4*j**3 + 21*j - 20*j**f - 1 - 32 + 17 = 0.
1, 2
Suppose -19824 = -171*y + 129*y. Let h = y - 470. Suppose 0 - 21/2*r + 3/2*r**h = 0. Calculate r.
0, 7
Let d(h) be the third derivative of -h**6/600 + 37*h**5/100 + 19*h**4/5 + 46*h**3/3 + 2250*h**2. Factor d(p).
-(p - 115)*(p + 2)**2/5
Let r = 22210/11 + -2019. Let h(y) be the third derivative of 0 + 1/330*y**5 + 0*y + r*y**3 - 1/33*y**4 + 20*y**2. Factor h(j).
2*(j - 3)*(j - 1)/11
Let t = -355 - -452. Factor t*n + 149*n - 168*n + 4*n**3 - 42*n**2 - 2*n**3 - 38.
2*(n - 19)*(n - 1)**2
Let p(d) be the third derivative of d**5/15 - 95*d**4/12 - 47*d**3/3 - 257*d**2. Let i be p(48). Factor 0*a - 3/7*a**i + 12/7.
-3*(a - 2)*(a + 2)/7
Suppose 0 = -2*h + 5*v + 41, 55 = h + 2*h - v. Suppose h = -4*t + 158. Factor 41*y**3 - 2*y**2 - 9*y**2 - 42*y**3 - 25 - t*y.
-(y + 1)*(y + 5)**2
Let j be (-4)/2 - (-1 - 1). Suppose m + 20 = -4*m, j = -k + 5*m + 42. Factor k*s**3 - 14*s**3 - 12*s**3.
-4*s**3
Let q(i) = i**4 - 476*i**3 - 468*i**2 + 476*i + 479. Let k(n) = -12*n**4 + 4761*n**3 + 4680*n**2 - 4761*n - 4794. Let h(x) = -2*k(x) - 21*q(x). Factor h(b).
3*(b - 1)*(b + 1)**2*(b + 157)
Factor 22/7*t**2 + 2/7*t**3 - 344/7*t + 320/7.
2*(t - 8)*(t - 1)*(t + 20)/7
Let o be 6928/8050 + 6/(-21). Let x = o - 2/575. Determine d, given that 0 - 6/7*d + 2/7*d**3 - x*d**2 = 0.
-1, 0, 3
Suppose 0 = -809*h + 3640 + 9444 + 2287. Let p = -40 - -44. Factor 14*r + 4*r**4 + 1/2*r**5 + 25/2*r**3 + p + h*r**2.
(r + 1)**2*(r + 2)**3/2
Let k be 0/(18/(-9) + 0). Suppose 7*n - 17*n + 30 = k. Find u, given that 0*u**2 + 1/4*u**n + 1/2 - 3/4*u = 0.
-2, 1
Let k(n) be the third derivative of n**7/210 + 7*n**6/120 + 11*n**5/60 + 5*n**4/24 - 25*n**2 + 146. Let k(c) = 0. What is c?
-5, -1, 0
Let g(f) be the second derivative of f**5/20 + 19*f**4/12 + 40*f**3/3 - 50*f**2 + 985*f - 1. What is h in g(h) = 0?
-10, 1
Suppose -61*i = -60*i - 2. What is z in 53*z**3 - 124*z**4 + 42*z**3 + 20*z**i + 99*z**4 = 0?
-1/5, 0, 4
Let l(m) be the third derivative of -m**6/144 + 1039*m**5/180 - 13468*m**4/9 - 21632*m**3/9 + 4*m**2 + 160. Factor l(t).
-(t - 208)**2*(5*t + 2)/6
Let f(x) = -15*x**4 + 245*x**3 - 24*x**2 - 148*x. Let i(j) = 9*j**4 - 163*j**3 + 12*j**2 + 99*j. Let k(d) = 5*f(d) + 8*i(d). Factor k(y).
-y*(y + 1)*(y + 26)*(3*y - 2)
Factor -2/3*c**3 - 80/3*c + 0 - 44/3*c**2.
-2*c*(c + 2)*(c + 20)/3
Let c = -156 + 158. Suppose 256 - 48*q + 1189*q**2 - 1185*q**c - 16*q = 0. What is q?
8
Let y(q) be the first derivative of -q**4/16 + 5*q**3/4 + q**2/8 - 15*q/4 - 1928. Factor y(p).
-(p - 15)*(p - 1)*(p + 1)/4
Factor 67*j**2 - 160 + 65*j**2 - 209*j**2 + 56*j + 73*j**2.
-4*(j - 10)*(j - 4)
Let w(k) be the second derivative of k**7/210 + k**6/30 + k**5/20 - k**4/12 - k**3/5 - k + 3395. What is r in w(r) = 0?
-3, -2, -1, 0, 1
Let l(p) = 6*p**3 - 142*p**2 - 715*p - 734. Let w(q) = -3*q**3 + 73*q**2 + 358*q + 368. Let b(z) = 2*l(z) + 5*w(z). Factor b(x).
-3*(x - 31)*(x + 2)**2
Let i(r) be the second derivative of -3*r**5/20 - 3*r**4/2 + 18*r**3 + 324*r**2 - 515*r. Factor i(y).
-3*(y - 6)*(y + 6)**2
Let t(a) be the first derivative of -2*a**7/1365 - 17*a**6/2340 - a**5/78 - a**4/156 - 40*a**3/3 + 32. Let m(l) be the third derivative of t(l). Factor m(p).
-2*(p + 1)**2*(8*p + 1)/13
Let h(w) = -4*w - 16. Let g be h(-9). Let p be ((-12)/g)/((-9)/12)*5. Let -974*o**4 + 15*o**2 + o + 15*o**3 + p*o + 979*o**4 = 0. What is o?
-1, 0
Let n(i) = -49*i + 5. Let p be n(7). Let v = -336 - p. Let f + 0 - 5/2*f**4 + 9/2*f**3 - 7/2*f**v + 1/2*f**5 = 0. What is f?
0, 1, 2
Let r(o) be the second derivative of o**8/36960 - o**7/2310 + o**6/440 - o**5/165 + 59*o**4/12 + 5*o - 1. Let m(t) be the third derivative of r(t). Factor m(l).
2*(l - 4)*(l - 1)**2/11
Let q(i) be the third derivative of -i**6/600 - 3*i**5/25 - 11*i**4/40 + 7*i**3/3 + 240*i**2. Factor q(s).
-(s - 1)*(s + 2)*(s + 35)/5
Let i(t) be the first derivative of 1/3*t**4 - 8/3*t**2 + 2/3*t**3 - 2/15*t**5 + 8/3*t + 78. Suppose i(y) = 0. Calculate y.
-2, 1, 2
Let g(m) = m**2 + 315*m + 314. Let f(q) = 312*q + 312. Let k(r) = 4*f(r) - 3*g(r). Factor k(p).
-3*(p - 102)*(p + 1)
Let 140/9*l - 2/9*l**2 + 142/9 = 0. What is l?
-1, 71
Let f(u) be the second derivative of u**4/60 - 64*u**3/5 - 467*u + 7. Factor f(s).
s*(s - 384)/5
Suppose 716 = 15*w - 964. Suppose 42*a - w = 14*a. Factor 8/7*u**3 + 2/7*u**a - 4/7*u**2 - 24/7*u + 18/7.
2*(u - 1)**2*(u + 3)**2/7
Let q be 2*2/12 - 38*(-55)/1254. Factor -17/7 - 1/7*t**q + 18/7*t.
-(t - 17)*(t - 1)/7
Let o(p) be the first derivative of 4*p**3/3 - 2*p**2 - 1088*p + 1852. Factor o(f).
4*(f - 17)*(f + 16)
Find f, given that 4528*f**3 + 464128*f + 1053696 + 212800/3*f**2 + 128*f**4 + 4/3*f**5 = 0.
-28, -6
Suppose 56*l = 54 - 54. Let k(j) be the third derivative of 0*j + 4*j**2 + 1/32*j**4 + 1/240*j**5 + 0*j**3 + l. Factor k(v).
v*(v + 3)/4
Let o(b) = 3088*b + 40148. Let s be o(-13). What is g in -19/10*g**2 - 6/5 + 14/5*g + 1/5*g**3 + 1/10*g**s = 0?
-6, 1, 2
Let 980*m + 1024*m - 2074*m + 5*m**3 + 279 - 35*m**2 - 39 = 0. Calculate m.
-3, 2, 8
Let p(u) be the second derivative of -17 - 2/39*u**3 - 1/78*u**4 - 2*u + 0*u**2. Let p(g) = 0. What is g?
-2, 0
Let l(o) be the third derivative of o**3 + 0 + 1/6*o**5 + 1/60*o**6 - o**2 + 7/12*o**4 + 0*o. Solve l(a) = 0 for a.
-3, -1
Let x be -8*(-25)/90 - (-200)/(-900). Factor 4/3*z**3 - 1/3*z**5 - z - 2/3 + 0*z**4 + 2/3*z**x.
-(z - 2)*(z - 1)*(z + 1)**3/3
Let b = -72 + 77. Suppose 0 = 3*t - 4*g + 6, b*t - 2*t - 18 = -4*g. Suppose -9*a**3 - 2 - 4*a**5 + 2 + 7*a**5 - 6*a**t = 0. What is a?
-1, 0, 2
Let 2*z**3 - 801*z**2 - 1418*z**2 + 3512172*z - 1266723368 - z**3 - 1027*z**2 = 0. What is z?
1082
Let q = 11770/3 + -3375. Let l = -548 + q. Determine g so that 0*g - 4/3*g**2 - l*g**3 + 0 = 0.
-4, 0
Find h such that -8/5*h - 4/5*h**2 + 4/5*h**3 + 8/5 + 1/10*h**4 - 1/10*h**5 = 0.
-2, 1, 2
Let c be ((-5)/(-4))/(9 + 105/(-12)). Suppose 3*h + l = -0*l + 12, 4*l = c*h - 3. Factor 0 - 1/5*z**2 + 0*z + 1/5*z**h.
z**2*(z - 1)/5
Let i(b) = 25*b - 409. Let r be i(-35). Let c be 21 - r/(-48) - (-1 + -6). Factor -2*o**2 + c*o**3 + 0 + o - 1/4*o**4.
-o*(o - 2)**2*(o - 1)/4
Let z(f) be the first derivative of 242/9*f**3 - 70 - 2/3*f**2 - 5/2*f**4 - 32*f. What is r in z(r) = 0?
-3/5, 2/3, 8
Let l(y) = 7*y. Let o be l(4). Suppose -10*a + o = -3*a. Find c such that 4*c**4 - 3*c**3 + a*c**4 - 4*c**5 - c**3 = 0.
0, 1
Let i(p) = 4*p**3 + 648*p**2 + 1278*p + 638. Let k(x) = -16*x**3 - 2594*x**2 - 5113*x - 2553. Let w(s) = 9*i(s) + 2*k(s). Factor w(q).
4*(q + 1)**2*(q + 159)
Let 414/5*g - 78/5*g**3 - 117/5*g**4 + 339/5*g**2 + 6/5*g**5 + 24 = 0. What is g?
-1, -1/2, 2, 20
Let p(o) be the third derivative of -2*o**5/5 - 517*o**4/8 + 525*o**3/2 + 2*o**2 + 495. Find l such that p(l) = 0.
-525/8, 1
Let v(w) = 7*w**3 + 43*w**2 - 352*w + 350. Let k(i) = -8*i**3 - 45*i**2 + 352*i - 355. Let z(t) = 6*k(t) + 7*v(t). Factor z(y).
(y - 8)*(y - 1)*(y + 40)
Let a(y) = -2*y**3 - 32*y**2 + 40*y + 3. Let l(t) = -5*t**3 - 95*t**2 + 120*t + 10. Suppose -150 = 2*u - 17*u. Let x(i) = u*a(i) - 3*l(i). Factor x(n).
-5*n*(n - 1)