Question

question 12 of 25
what is the factorization of the trinomial below?
$2x^2 + 13x + 15$

a. $(2x + 3)(x + 5)$
b. $(2x + 15)(x + 1)$
c. $(2x + 1)(x + 15)$
d. $(2x + 5)(x + 3)$

Explanation:

Step1: Expand Option A

To check if \((2x + 3)(x + 5)\) is the factorization, we use the distributive property (FOIL method).
First, multiply the First terms: \(2x\times x = 2x^{2}\).
Then, the Outer terms: \(2x\times5 = 10x\).
Next, the Inner terms: \(3\times x = 3x\).
Finally, the Last terms: \(3\times5 = 15\).
Now, combine like terms: \(2x^{2}+10x + 3x+15=2x^{2}+13x + 15\), which matches the given trinomial.

We can also check other options for completeness:

Step2: Expand Option B

For \((2x + 15)(x + 1)\), using FOIL:
First: \(2x\times x=2x^{2}\), Outer: \(2x\times1 = 2x\), Inner: \(15\times x = 15x\), Last: \(15\times1 = 15\).
Combining like terms: \(2x^{2}+2x + 15x+15=2x^{2}+17x + 15
eq2x^{2}+13x + 15\).

Step3: Expand Option C

For \((2x + 1)(x + 15)\), using FOIL:
First: \(2x\times x = 2x^{2}\), Outer: \(2x\times15 = 30x\), Inner: \(1\times x = x\), Last: \(1\times15 = 15\).
Combining like terms: \(2x^{2}+30x + x+15=2x^{2}+31x + 15
eq2x^{2}+13x + 15\).

Step4: Expand Option D

For \((2x + 5)(x + 3)\), using FOIL:
First: \(2x\times x = 2x^{2}\), Outer: \(2x\times3 = 6x\), Inner: \(5\times x = 5x\), Last: \(5\times3 = 15\).
Combining like terms: \(2x^{2}+6x + 5x+15=2x^{2}+11x + 15
eq2x^{2}+13x + 15\).

Answer:

A. \((2x + 3)(x + 5)\)