Which of the following is the correct factorization of the polynomial below?

2x2 - 16x+ 32

O A. (2x+4)(x+2)

O B. 2(x+2)(x+8)

O c. 2(x-4)2

O D. The polynomial is irreducible.

Skip to content# Which of the following is the correct factorization of the polynomial below? 2×2 – 16x+ 32 O A. (2x+4)(x+2) O B. 2(x+2)(x+8)

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Which of the following is the correct factorization of the polynomial below?

2x2 - 16x+ 32

O A. (2x+4)(x+2)

O B. 2(x+2)(x+8)

O c. 2(x-4)2

O D. The polynomial is irreducible.

Here given a quadratic polynomial

we have to factorize it

2x²-8x+8

take 2 as common

2(x²-4x+4)

Here x²-4x+4 can also be written as

(x-2)²= x²-2×2×x +(2)²

(x-3

2)²= x²-4x+4

Hence ,

2(x-2)² is our answer

Option C is the correct option

B

Step-by-step explanation:

I think the answer is B.

The polynomial is irreducible

Step-by-step explanation:

There is nothing we can subtract between x3-12

For example: you are trying to find the polynomial of x4-6

Options:

A. (x+4)(x-6)

B. (x+1+3)(x-6)

C. None the polynomial is irreducible.

You would chose C because there is no subtraction sign in between the parentheses. If you would choose a right answer, you would rewrite it as:

(x+4)-(6)

Answer option C

27x³+64y³

it's written as

(3x)³ +(4y)³

Now by using identify

a³+b³=(a+b)(a²-ab+b²)

(3x)³+(4y)³= (3x+4y){(3x)² - 3x*4y+(4y)²}

→ (3x+4y)( 9x²-12xy+16y²)

So required answer is option C

(21xy +15x )+ (35ry +25r)

3x(7y+5)+ 5r(7y+5)

(3x+5r)(7y+5)

Please rate

the correct option is

(B) [tex](4x+3)(16x^2-12x+9).[/tex]

Step-by-step explanation: We are given to select the correct factorization of the following polynomial :

[tex]P=64x^3+27.[/tex]

We will be using the following factorization formula :

[tex]a^3+b^3=(a+b)(a^2-ab+b^2).[/tex]

Therefore, the factorization of the given polynomial is as follows :

[tex]P\\\\=64x^3+27\\\\=(4x)^3+3^3\\\\=(4x+3)((4x)^2-4x\times3+3^2)\\\\=(4x+3)(16x^2-12x+9).[/tex]

Thus, the required factored form is [tex](4x+3)(16x^2-12x+9).[/tex]

Option (B) is CORRECT.

C. 2(x-4)^2

Step-by-step explanation:

To factorize 2x^2-16x+32

We have to take it step by step and know if it's factorizable then if it is we will look for the answer.

2x^2-16x+32 = 2x² -16x +(2x²)(32)

2x^2-16x+32= 2x² -16x +64x²

I'll ask myself what do i multiply to give me +64x² and add to get -16x.

It's simple.

The answer is -8x

-8x *-8x = 64x²

-8x+-8x = -16x

2x^2-16x+32= 2x² -16x +32

2x^2-16x+32=2x²-8x-8x+32

2x^2-16x+32= 2x(x-4)-8(x-4)

2x^2-16x+32=(2x-8)(x-4)

2x^2-16x+32=2(x-4)(x-4)

2x^2-16x+32=2(x-4)²

64x^3 + 27 is a sum of cubes: (4x)^3 + 3^3, for which the factors are (4x + 3)(16x^2 - 12x + 9)

correct answer is B.(2x+3y)(4x^2-6xy+9y^2)

8x^3 + 27y^3

(2x)^3+(3y)^3

(2x+3y)(4x^2-6xy+9y^2) <answer