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)

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.

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This Post Has 10 Comments

  1. 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

  2. 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)

  3. 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

  4.  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.

  5. 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

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