Find the factorization of the polynomial below.64𝑥2+48𝑥+964x 2 +48x+9A.(8x + 3)(8x - 3)B.(8x + 3)(8x + 3)C.(8x + 9)(8x - 9)D.(8x + 9)(8x + 9)

Question

Find the factorization of the polynomial below.

$64x^{2} + 48x + 9$

A. $(8x + 3)(8x - 3)$
B. $(8x + 3)(8x + 3)$
C. $(8x + 9)(8x - 9)$
D. $(8x + 9)(8x + 9)$

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Solution

The given polynomial is 64x^2 + 48x + 9.

We can factorize this polynomial by looking for two numbers that multiply to give 64*9 = 576 (the product of the coefficient of x^2 and the constant term) and add up to give 48 (the coefficient of x).

The numbers that satisfy these conditions are 24 and 24 because 24*24 = 576 and 24 + 24 = 48.

Therefore, we can write the polynomial as 64x^2 + 24x + 24x + 9.

Now, we can factor by grouping:

64x^2 + 24x + 24x + 9 = 8x(8x + 3) + 3(8x + 3)

= (8x + 3)(8x + 3)

So, the factorization of the polynomial 64x^2 + 48x + 9 is (8x + 3)(8x + 3).

Therefore, the correct answer is B. (8x + 3)(8x + 3).

This problem has been solved

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Find the factorization of the polynomial below.64𝑥2+48𝑥+964x 2 +48x+9A.(8x + 3)(8x - 3)B.(8x + 3)(8x + 3)C.(8x + 9)(8x - 9)D.(8x + 9)(8x + 9)

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