What is the factorization of the trinomial below?3x2 + 36x + 81A.(x + 2)(x + 27)B.3(x + 2)(x + 9)C.3(x + 3)(x + 9)D.(x + 3)(x + 9)SUBMITarrow_backPREVIOUS

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What is the factorization of the trinomial below?

$3x^2 + 36x + 81$

A. (x + 2)(x + 27)
B. 3(x + 2)(x + 9)
C. 3(x + 3)(x + 9)
D. (x + 3)(x + 9)

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Solution

The factorization of the trinomial 3x^2 + 36x + 81 can be found by looking for two numbers that multiply to 81 (the constant term) and add to 36 (the coefficient of the x term).

The two numbers that satisfy these conditions are 9 and 9, because 9*9 = 81 and 9+9 = 18. However, we need to consider the coefficient of x^2, which is 3. So, we need to multiply these numbers by 3 to get the correct coefficient for x. This gives us 27 and 27, which add up to 54, not 36.

Therefore, we need to find two other numbers that multiply to 27 (93) and add to 12 (36/3). These numbers are 3 and 9, because 39 = 27 and 3+9 = 12.

So, the factorization of the trinomial is 3(x + 3)(x + 9), which corresponds to option C.

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What is the factorization of the trinomial below?3x2 + 36x + 81A.(x + 2)(x + 27)B.3(x + 2)(x + 9)C.3(x + 3)(x + 9)D.(x + 3)(x + 9)SUBMITarrow_backPREVIOUS

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