Given the polynomial 8x3 + 6x2 − 32x − 24, what is the value of the constant 'k' in the factored form?

8x3 + 6x2 − 32x − 24 = 2(x + k)(x − k)(4x + 3)

Question

Given the polynomial 8x3 + 6x2 − 32x − 24, what is the value of the constant 'k' in the factored form?

8x3 + 6x2 − 32x − 24 = 2(x + k)(x − k)(4x + 3)

Phantomdex · Answer

2(x + k)(x - k)(4x + 3):
2(x + k)(x - k)(4x + 3)=2[(x^2 - k^2)(4x + 3)]
= 2[x^2(4x + 3) - k^2 (4x + 3)
= 2[4x^3 + 3x^2 - 4k^2x - 3k^2]

Phantomdex · Answer

4x 3 =8x 3⟹4=8
k^2=1⟹k=±1
−3k^2 = −24 ⟹ k^2 = 8 ⟹ k = ± (sqrt)8 = ±2 (sqrt)2
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So, the value of the constant 'k' in the factored form is k=±1.

Phantomdex · Answer

I believe anyways.

D14610 · Answer

@phantomdex wrote:

4x 3 =8x 3⟹4=8 k^2=1⟹k=±1 −3k^2 = −24 ⟹ k^2 = 8 ⟹ k = ± (sqrt)8 = ±2 (sqrt)2 So, the value of the constant 'k' in the factored form is k=±1.

checks out, thanks :D

Phantomdex · Answer

Yippee!