Question

Solution for the Trinomial Square

x 2+10x+25.
Options:

A) x+5^2
B) x+5(x + 5)
C) x−5^2
D) x−5(x - 5)

Answer 1

The trinomial square x²+10x+25 is a perfect square and can be factored into (x+5)², hence the answer is Option A: x+5².

Step-by-step explanation:

The solution for the trinomial square of the equation x²+10x+25 can be found by factoring. The equation is a perfect square trinomial, and it can be factored into (x+5)². This is because it fits the form of a perfect square trinomial, which is a² + 2ab + b² = (a+b)². Here's how we can factor the trinomial:

• Identify the square of the first term: x² is the square of x.
• Identify the square of the last term: 25 is the square of 5.
• Since the middle term is positive (10x), and it equals to 2 times the product of the square roots of the first and last terms (2*x*5 = 10x), we have a perfect square trinomial.
• Thus, the factored form is (x+5)(x+5) or (x+5)².

The correct answer is Option A: x+5².