Answer:
We can factorize the polynomial using method of grouping terms.
Step-by-step explanation:
Consider the given polynomial \(3x^3 + 5x + 6x^2 + 10\)
We have to find the factoring method that can be considered to solve the given polynomial.
Consider the given polynomial \(3x^3 + 5x + 6x^2 + 10\)
Since, the polynomial involves 4 terms,
So we can factorize the polynomial using grouping terms,
First rearranging in standard form in decreasing order of degrees of x.
\(3x^3 + 6x^2 + 5x + 10\)
Grouping two terms together, we get,
\(=\left(3x^3+6x^2\right)+\left(5x+10\right)\)
Now taking \(3x^2\) common from first two and 5 from last two , we have,
\(=3x^2\left(x+2\right)+5\left(x+2\right)\)
Now, taking (x+2) common, we have,
\(=\left(x+2\right)\left(3x^2+5\right)\)
\(3x^3 + 5x + 6x^2 + 10=\left(x+2\right)\left(3x^2+5\right)\)
Thus, We can factorize the polynomial using method of grouping terms.
