Question

Which of the following represents the factorization of the trinomial below?
x^2 + 24x + 144

A.(x+12) (x-12)
B.(x+12)^2
C.(x-12) (x-2)
D.(x-12)^2

Answer 1

Answer:

B

Step-by-step explanation:

x² + 24x + 144 ← is a perfect square trinomial of the form

(x + b)² = x² + 2bx + b²

Comparing the coefficients gives

b² = 144 ⇒ b = 12 and 2b = 2 × 12 = 24, thus

x² + 24x + 144 = (x + 12)² → B

Answer 2

The factorization of (x² + 24x + 144) is ( x + 12 )². Then the correct answer is option B.

What is a quadratic equation?

A quadratic equation is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.

x² + 24x + 144 ← is a perfect square trinomial of the form

(x + b)² = x² + 2bx + b²

Comparing the coefficients gives

b² = 144 ⇒ b = 12 and 2b = 2 × 12 = 24, thus

x² + 24x + 144 = (x + 12)²

Hence, the correct answer is option B.

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