Advanced Functions

[cirquedufreak]

Could Someone please help me...I have no idea what to do for these two promblems

For what values of k does the function f(x) = x3 + 6x2 + kx – 4 give the same remainder when divided by (x-1) and (x + 2)?

Determine the value of k when x3 + kx2 + 2x – 3 is divided by x + 2, and the remainder is 1.

[MAS1]

Originally Posted by cirquedufreak

Could Someone please help me...I have no idea what to do for these two promblems

For what values of k does the function f(x) = x3 + 6x2 + kx – 4 give the same remainder when divided by (x-1) and (x + 2)?

Determine the value of k when x3 + kx2 + 2x – 3 is divided by x + 2, and the remainder is 1.

1. Divide x^3 + 6x^2 + kx - 4 by (x - 1). This gives x^2 + 7x + (k + 7) with a remainder of k + 3. Then divide x^3 + 6x^2 + kx - 4 by (x + 2).This gives x^2 + 4x + (k - 8) with a remainder of 12 - 2k. Then set the two remainders equal to each other.

k + 3 = 12 - 2k
3k = 9
k = 3

2. Divide x^3 + kx^2 + 2x - 3 by x + 2 giving x^2 + (k -2)x + (2 - 2(k - 2)) with a remainder of -3 - 2(2 - 2(k -2)). Then set the remainder equal to 1 and solve for k.

-3 - 2(2 - 2(k - 2)) = 1
-2(2 - 2k + 4) = 4
2 - 2k + 4 = -2
6 - 2k = -2
-2k = -8
k = 4

[jmw106462]

1. Divide x^3 + 6x^2 + kx - 4 by (x - 1). This gives x^2 + 7x + (k + 7) with a remainder of k + 3. Then divide x^3 + 6x^2 + kx - 4 by (x + 2).This gives x^2 + 4x + (k - 8) with a remainder of 12 - 2k. Then set the two remainders equal to each other.

k + 3 = 12 - 2k
3k = 9
k = 3

2. Divide x^3 + kx^2 + 2x - 3 by x + 2 giving x^2 + (k -2)x + (2 - 2(k - 2)) with a remainder of -3 - 2(2 - 2(k -2)). Then set the remainder equal to 1 and solve for k.

-3 - 2(2 - 2(k - 2)) = 1
-2(2 - 2k + 4) = 4
2 - 2k + 4 = -2
6 - 2k = -2
-2k = -8
k = 4

[MAS1]

Originally Posted by jmw106462

1. Divide x^3 + 6x^2 + kx - 4 by (x - 1). This gives x^2 + 7x + (k + 7) with a remainder of k + 3. Then divide x^3 + 6x^2 + kx - 4 by (x + 2).This gives x^2 + 4x + (k - 8) with a remainder of 12 - 2k. Then set the two remainders equal to each other.

k + 3 = 12 - 2k
3k = 9
k = 3

2. Divide x^3 + kx^2 + 2x - 3 by x + 2 giving x^2 + (k -2)x + (2 - 2(k - 2)) with a remainder of -3 - 2(2 - 2(k -2)). Then set the remainder equal to 1 and solve for k.

-3 - 2(2 - 2(k - 2)) = 1
-2(2 - 2k + 4) = 4
2 - 2k + 4 = -2
6 - 2k = -2
-2k = -8
k = 4

Nice job of cutting and pasting!

[jmw106462]

Lol i was seeing if u would catch that you did.*of) Course, The other post i didn't Cut and Paste Thou