College

The expression below is the factorization of which of the following trinomials?

[tex](2x + 7)(x + 5)[/tex]

A. [tex]2x^2 + 2x + 35[/tex]

B. [tex]2x^2 + 17x + 35[/tex]

C. [tex]2x^2 + 10x + 35[/tex]

D. [tex]2x^2 + 12x + 35[/tex]

Answer :

Sure, let's solve the factorization step-by-step!

We need to find out which trinomial corresponds to the factorized expression [tex]\((2x + 7)(x + 5)\)[/tex]. Here’s how we do it:

1. Use the distributive property (FOIL method) to expand [tex]\((2x + 7)(x + 5)\)[/tex]:

[tex]\[
(2x + 7)(x + 5) = (2x \cdot x) + (2x \cdot 5) + (7 \cdot x) + (7 \cdot 5)
\][/tex]

2. Multiply each term:

[tex]\[
2x \cdot x = 2x^2
\][/tex]

[tex]\[
2x \cdot 5 = 10x
\][/tex]

[tex]\[
7 \cdot x = 7x
\][/tex]

[tex]\[
7 \cdot 5 = 35
\][/tex]

3. Add all these terms together:

[tex]\[
2x^2 + 10x + 7x + 35
\][/tex]

4. Combine like terms:

[tex]\[
2x^2 + (10x + 7x) + 35 = 2x^2 + 17x + 35
\][/tex]

So, the expanded trinomial is [tex]\(2x^2 + 17x + 35\)[/tex].

Now, let's match our result with the given options:

A. [tex]\(2x^2 + 2x + 35\)[/tex]

B. [tex]\(2x^2 + 17x + 35\)[/tex]

C. [tex]\(2x^2 + 10x + 35\)[/tex]

D. [tex]\(2x^2 + 12x + 35\)[/tex]

Clearly, option B ([tex]\(2x^2 + 17x + 35\)[/tex]) matches the expanded trinomial.

Therefore, the correct answer is:
[tex]\[
\boxed{B}
\][/tex]

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