Question

(Due soon) Check each factorization to find the polynomial that does not have its GCF correctly factored out.

Choose the correct answer below.


12x^(2)+8x=4x(3x+2)

15x^(2)+12x+9=3(5x^(3)+4x+3)

4x^(4)+12x^(3)+18x^(2)=2x^(2)(2x^(2)+6x+9)

16x^(5)+24x^(2)=4x^(2)(4x^(3)+6)

Answer 1

Option d

Explanation:

Given options are ,

• 12x² + 8x = 4x( 3x + 2)

Firstly find the GCF of 12x² and 8x .

The GCF of 12 and 8 is 4 , whereas the GCF of x² and x is x , So

→ GCF(12x² , 8x) = 4*x = 4x

Therefore the GCF is correctly factored out from the polynomial .

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• 15x² + 12x + 9 = 3(5x² + 4x +3)

Here GCF of 15x² , 12x and 9 , will be ;

GCF of 15,12 and 9 is 3 whereas of x² , x and 1 is 1

→ GCF = 3*1 = 3

Therefore the GCF is correctly factored out from the polynomial .

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• 4x⁴+ 12x³ +18x² = 2x²(2x² + 6x + 9 )

Here GCF of 4 , 12 and 18 is 2 and that of x⁴ , x³ and x² is x² . So ,

→ GCF = 2*x² = 2x²

Therefore the GCF is correctly factored out from the polynomial .

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• 16x^5 + 24x² = 4x²( 4x³ + 6 )

Here GCF of 16 and 24 is 8 and that of x^5 and x² is x² . So ,

→ GCF = 8*x² = 8x²

But they have factored out 4x² .

Therefore the GCF is " not " correctly factored out from the polynomial .

Option d is correct .