Algebra II Factoring: 16x^4-8x+1,r^2-6r-9s^2+9,u^2-4r^2-3u-

[andyleija]

The instructions are to factor completely. These are the only problems I've had trouble with. I'll show as much work as I can, although I'm sure a lot of it is off.

16x^4 - 8x + 1
(4x^2 - 4x) + (-4x + 1)
(4x^2 + 4x)(4x^2 - 4x)

r^2 - 6r - 9s^2 + 9
(r^2 - 6r) + (-9s^2 + 9)
r(r - 6) + 9(s^2 - 1)

u^2 - 4r^2 - 3u - 6r
(u^2 - 4r^2) + (-3u - 6r)
-1(-u^2 + 4r^2) + 3(-u - 2r)

10w^2 - 14wy - 13w + 21y
(10w^2 - 14wy) + (-13w + 21y)
2w(5w - 7y) + -1(13w - 21y)

2x^2 - 6x +3
cannot be factored

2x^2 + 4x -1
cannot be factored

3x^2 - 42x + 40
cannot be factored

x^2 + 16
cannot be factored

35ac - abd - 7ad + 15bc
(35ac - abd) + (-7ad + 15bc)
a(35c - ad) + -1(7ad - 15bc)

Thanks in advance, I really appreciate it.

 

[skeeter]

The instructions are to factor completely. These are the only problems I've had trouble with. I'll show as much work as I can, although I'm sure a lot of it is off.

16x^4 - 8x + 1 = (4x^2 - 1)(4x^2 + 1) = (2x - 1)(2x + 1)(4x^2 + 1)


r^2 - 6r - 9s^2 + 9 = (r^2 - 6r + 9) - 9s^2 = (r - 3)^2 - 9s^2 = [(r - 3) - 3s][(r - 3) + 3s]


u^2 - 4r^2 - 3u - 6r
(u^2 - 4r^2) + (-3u - 6r) = (u - 2r)(u + 2r) - 3(u + 2r) = (u + 2r)(u - 2r - 3)


10w^2 - 14wy - 13w + 21y check this one ... as it sits, factoring doesn't lead to anything productive


2x^2 - 6x +3
cannot be factored

2x^2 + 4x -1
cannot be factored

3x^2 - 42x + 40
cannot be factored

x^2 + 16
cannot be factored

35ac - abd - 7ad + 15bc check this one ... as it sits, factoring doesn't lead to anything productive

 

[mmm4444bot]

The instructions are to factor completely. I assume you are to factor over the real number system only.

16x^4 - 8x + 1 = (4x^2 - 1)(4x^2 + 1) = (2x - 1)(2x + 1)(4x^2 + 1)

This is not correct.

(2x - 1)(2x + 1)(4x^2 + 1) = 16x^4 - 1

The given expression does not factor.

If the 8x term were to change to 8x^2, then the resulting trinomial would factor as (2x + 1)^2 * (2x - 1)^2


r^2 - 6r - 9s^2 + 9 = (r^2 - 6r + 9) - 9s^2 = (r - 3)^2 - 9s^2 = [(r - 3) - 3s][(r - 3) + 3s]

I agree, but I write it differently.

(r - 3 - 3s)(r - 3 + 3s)

u^2 - 4r^2 - 3u - 6r
(u^2 - 4r^2) + (-3u - 6r) = (u - 2r)(u + 2r) - 3(u + 2r) = (u + 2r)(u - 2r - 3)


10w^2 - 14wy - 13w + 21y check this one ... as it sits, factoring doesn't lead to anything productive

I agree; not much to factor other than w from the middle two terms.

2x^2 - 6x +3
cannot be factored Correct.

2x^2 + 4x -1
cannot be factored Correct.

3x^2 - 42x + 40
cannot be factored Correct.

x^2 + 16
cannot be factored Correct.

35ac - abd - 7ad + 15bc check this one ... as it sits, factoring doesn't lead to anything productive

I agree. We can write a[7(5c - d) - bd] + 15bc, but why would we want to?