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Factors of the expression 3 x^{2}+7 x+2 is/are

Option: 1

(3x + 2)


Option: 2

(2x + 3)


Option: 3

(x + 1)


Option: 4

(x + 2)


Answers (1)

best_answer

First Consider First and Last term,

mn=3\quad\text{and}\quad pq=2

 mn=3=1\times3\quad\text{and}\quad pq=2=1\times2

Begin by writing the factors of the first term, 3x^2, as follows:

3 x^{2}+7 x+2=(x \quad {\color{Red} ?})(3 x \quad {\color{Red} ?})

The middle and last term are both positive; therefore, the factors of 2 are chosen as positive numbers. In this case, the only choice is in which grouping to place these factors.

{\color{DarkGreen} (x+1)(3 x+2)} \quad \text { or } \quad{\color{DarkBlue} (x+2)(3 x+1)}

Determine which grouping is correct by multiplying each expression.

\begin{aligned} (x+1)(3 x+2) &=3 x^{2}+2 x+3 x+2 \\ &=3 x^{2}+5 x+2 \quad {\color{DarkRed} \text{False}} \\ (x+2)(3 x+1) &=3 x^{2}+x+6 x+2 \\ &=3 x^{2}+7 x+2 \quad{\color{DarkGreen} \text{True}} \end{aligned}

Notice that these products differ only in their middle terms. Also, notice that the middle term is the sum of the inner and outer products.

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Gaurav

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