Resolve each of the following quadratic trinomial into factor: 3 … - Vidyadip

Question

Resolve each of the following quadratic trinomial into factor:
$3 x^2+10 x+3$

✓

Answer

The given expression is $3 x^2+10 x+3$
(Co-efficient of $x^2=3$, co-efficient of $x=10$ and the constant term $=3$ )
We will split the co-efficient of $x$ into two number parts such that their sum is -3 and their product equals to the product of the co-efficient of $x^2$ and constant term, i.e., $3 \times 3=9$
Now,
$9+1=9 \text { And } 9 \times 1=9$
Replacing the middle term 10 x by $9 x + x$, we have:
$3 x^2+10 x+3=3 x^2+9 x+x+3$
$=\left(3 x^2+9 x\right)+(x+3)$
$=3 x(x+3)+1(x+3)$
$=(x+3)(3 x+1)$

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