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Select the correct answer.

Which expression is equivalent to the given expression?

[tex]\[ 2x^2 - 14x + 24 \][/tex]

A. [tex]\((2x-12)(x-2)\)[/tex]

B. [tex]\(2(x-3)(x-4)\)[/tex]

C. [tex]\(2(x-8)(x+3)\)[/tex]

D. [tex]\(2(x-5)(x-2)\)[/tex]

Sagot :

GinnyAnsweridn
To solve the problem of finding an equivalent expression to [tex]\( 2x^2 - 14x + 24 \)[/tex], we need to factorize the quadratic expression. Here is a step-by-step explanation of how we arrived at the correct factorization:

1. Identify and write down the quadratic expression:
[tex]\[ 2x^2 - 14x + 24 \][/tex]

2. Factor out the greatest common factor (GCF) if there is one:
In this case, the GCF is 2.
[tex]\[ 2(x^2 - 7x + 12) \][/tex]

3. Factor the quadratic expression inside the parentheses [tex]\(x^2 - 7x + 12\)[/tex]:
To factor this, we need to find two numbers that multiply to give the constant term [tex]\(+12\)[/tex] and add to give the middle coefficient [tex]\(-7\)[/tex]. These two numbers are [tex]\(-3\)[/tex] and [tex]\(-4\)[/tex].

4. Rewrite the quadratic expression using these factors:
[tex]\[ x^2 - 7x + 12 = (x - 3)(x - 4) \][/tex]

5. Combine this with the GCF:
[tex]\[ 2(x - 3)(x - 4) \][/tex]

Therefore, the factored form of [tex]\(2x^2 - 14x + 24\)[/tex] is:
[tex]\[ 2(x - 3)(x - 4) \][/tex]

Looking at the given multiple-choice options, we can see that the correct answer is:

B. [tex]\[ 2(x-3)(x-4) \][/tex]
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