Question

Louise begins factoring the polynomial, which has four terms.

8x3+24x2+10x+30

2(4x3+12x2+5x+15)

2[4x2(x+3)+5(x+3)]

Which is the completely factored form of her polynomial?

8x2(x + 3)2
2x(4x2 + 5)
2(4x2 + 5) (x + 3)
2(4x2 + 5) (x + 3)2

Answer 1

2 (4x² + 5)(x + 3)  is factored form of 8x³ + 24x² + 10x + 30

Step-by-step explanation:

8x³ + 24x² + 10x + 30

Let take 2 common

= 2(4x³ + 12x² + 5x + 15)

Lets take 4x²  common in first two term & 5 in next two terms

= 2( 4x²(x + 3) + 5(x + 3))

Lets take (x + 3) common

= 2 (x + 3)(4x² + 5)

= 2 (4x² + 5)(x + 3)

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Answer 2

Option 3

The completely factored form of her polynomial is $8x^3+24x^2+10x+30=2(4x^2+5)(x+3)$

Step-by-step explanation:

Given : Louise begins factoring the polynomial, which has four terms.

Step 1 - Write the polynomial,

$8x^3+24x^2+10x+30$

Step 2 - Take 2 common,

$2(4x^3+12x^2+5x+15)$

Step 3 - Take common term inside bracket,

$2[4x^2(x+3)+5(x+3)]$

Step 4 - Take common term out,

$2[(4x^2+5)(x+3)]$

The required factored form of polynomial is $2(4x^2+5)(x+3)$

Therefore, Option 3 is correct.

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