Get reliable answers to your questions at Westonci.ca, where our knowledgeable community is always ready to help. Get quick and reliable answers to your questions from a dedicated community of professionals on our platform. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

Which expression is equivalent to the given expression?

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

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

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

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

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


Sagot :

To determine which expression is equivalent to the given expression [tex]\(2x^2 - 14x + 24\)[/tex], let's go through the process of expanding each of the provided choices and compare them to the original expression.

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

Choices:

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

First, we expand this expression:
[tex]\[ (2x - 12)(x - 2) \\ = 2x(x - 2) - 12(x - 2) \\ = 2x^2 - 4x - 12x + 24 \\ = 2x^2 - 16x + 24 \][/tex]

Clearly, the expanded form [tex]\(2x^2 - 16x + 24\)[/tex] does not match the given expression.

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

Next, we expand this expression:
[tex]\[ 2(x - 8)(x + 3) \\ = 2[(x - 8)(x + 3)] \\ = 2[x^2 + 3x - 8x - 24] \\ = 2[x^2 - 5x - 24] \\ = 2x^2 - 10x - 48 \][/tex]

The expanded form [tex]\(2x^2 - 10x - 48\)[/tex] does not match the given expression.

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

Next, we expand this expression:
[tex]\[ 2(x - 5)(x - 2) \\ = 2[(x - 5)(x - 2)] \\ = 2[x^2 - 2x - 5x + 10] \\ = 2[x^2 - 7x + 10] \\ = 2x^2 - 14x + 20 \][/tex]

The expanded form [tex]\(2x^2 - 14x + 20\)[/tex] does not match the given expression.

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

Finally, we expand this expression:
[tex]\[ 2(x - 3)(x - 4) \\ = 2[(x - 3)(x - 4)] \\ = 2[x^2 - 4x - 3x + 12] \\ = 2[x^2 - 7x + 12] \\ = 2x^2 - 14x + 24 \][/tex]

The expanded form [tex]\(2x^2 - 14x + 24\)[/tex] matches the given expression exactly.

Thus, the expression that is equivalent to [tex]\(2x^2 - 14x + 24\)[/tex] is choice:

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