Complete the factorization of the perfect square trinomial below by filling in the missing… — Armed Services Vocational Aptitude Battery (ASVAB)

Complete the factorization of the perfect square trinomial below by filling in the missing number.

Cevap:

x^2 + 14x + 49 = (x + 【7】)^2

A perfect square trinomial takes the general form

x^2 + 2bx + b^2 = (x + b)^2

. In the given expression

x^2 + 14x + 49

, the constant term is

49

, which is

7^2

. The middle term is

14x

, which is equal to

2 \times 7 \times x

. Therefore, the expression factors directly as

(x + 7)^2

, meaning the missing number in the blank is 7.

Recognize the polynomial form

The expression

x^2 + 14x + 49

matches the structure of a perfect square trinomial:

a^2 + 2ab + b^2

The first term is a perfect square (

x^2

), and the last term is a perfect square (

49 = 7^2

Verify the middle term

Checking the middle term:

2 \times x \times 7 = 14x

. This matches the middle term of the given expression.

Confirming the middle term proves the expression can be factored exactly as

(a + b)^2

Determine the missing value

The expression factors as

(x + 7)^2

Using the formula

(a + b)^2 = a^2 + 2ab + b^2

where

a = x

and

b = 7

Factoring perfect square trinomials

Soru