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25 votes
Factor the trinomial6x² + 17x + 12

User Nihilarian
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1 Answer

19 votes
19 votes

Answer: The factor of the above function is (2x + 3) (3x + 4)

We are given the below function


6x^2\text{ + 17x + 12}

This function can be factor using factorization method

The co-efficient of x^2 = 6

Multiply 6 by 12 to get the constant of the function

12 x 6 = 72

Next, find the factors of 72

Factors of 72 : 1 and 72, 2 and 36, 6 and 12, 9 and 8, 3 and 24

The only factor that will give us 17 when add and give us 72 when multiply is 8 and 9

The new equation becomes


\begin{gathered} 6x^2\text{ + 17x + 12} \\ 6x^2\text{ + 8x + 9x + 12} \\ \text{Factor out 2}x \\ 2x(3x\text{ + 4) + 3(3x + 4)} \\ (2x\text{ + 3) (3x + 4)} \end{gathered}

The factor of the above function is (2x + 3) (3x + 4)

User AlexGuti
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