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5. Trent factors 4x^2+13x+3 He determines that his integers must add to 13 and multiply to 12. He sets up his factors as shown below Determine his mistake and correctly factor the polynomial. (x+12)(x+1)

Pergunta

5. Trent factors 4x^2+13x+3 He determines that his integers must add to 13 and multiply to 12. He sets up his
factors as shown below Determine his mistake and correctly factor the polynomial.
(x+12)(x+1)

5. Trent factors 4x^2+13x+3 He determines that his integers must add to 13 and multiply to 12. He sets up his factors as shown below Determine his mistake and correctly factor the polynomial. (x+12)(x+1)

Solução

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HenriqueProfissional · Tutor por 6 anos

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The correct factorization of the polynomial is .

Explicação

## Step 1
The problem involves factoring a quadratic polynomial. The quadratic polynomial given is . The factors of this polynomial should add up to 13 (the coefficient of the x term) and multiply to 3 (the constant term).

## Step 2
Trent's mistake lies in his incorrect identification of the factors. He incorrectly identified the factors as (x+12) and (x+1), which add up to 13 and multiply to 12, not 3.

## Step 3
To correctly factor the polynomial, we need to find two numbers that add up to 13 and multiply to 3. The correct factors are 1 and 3, because 1+3 equals 13 and 1*3 equals 3.

## Step 4
Therefore, the correct factorization of the polynomial is .
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