How do you factor the expression $5 x^{2} + 16 x + 3$ $5x^2+16x+3$ ?

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Answer 1 · 2016-04-06T12:47:10

$(5 x + 1) (x + 3)$ $color(green)( (5x + 1 ) ( x + 3)$ is the factorised form of the expression.

$5 x^{2} + 16 x + 3$ $5x^2 + 16x +3$

We can Split the Middle Term of this expression to factorise it.

In this technique, if we have to factorise an expression like $a x^{2} + b x + c$ $ax^2 + bx + c$ , we need to think of 2 numbers such that:

$N_{1} \cdot N_{2} = a \cdot c = 5 \cdot 3 = 15$ $N_1*N_2 = a*c = 5 * 3 = 15$

AND

$N_{1} + N_{2} = b = 16$ $N_1 +N_2 = b = 16$

After trying out a few numbers we get $N_{1} = 15$ $N_1 = 15$ and $N_{2} = 1$ $N_2 =1$

$15 \cdot 1 = 15$ $15* 1 = 15$ , and $15 + 1 = 16$ $15 + 1= 16$

$5 x^{2} + 16 x + 3 = 5 x^{2} + 15 x + 1 x + 3$ $5x^2 + color(blue)( 16x) +3 = 5x^2 + color(blue)(15x + 1x) +3$

$= 5 x (x + 3) + 1 (x + 3)$ $= 5x ( x + 3) + 1 ( x + 3)$

$(x + 3)$ $(x+3)$ is a common factor to each of the terms

$(5 x + 1) (x + 3)$ $color(green)( (5x + 1 ) ( x + 3)$ is the factorised form of the expression.

How do you factor the expression 5x2+16x+35x^2+16x+3?