Answer:
The complete factored form of given polynomial \(21x^3+35x^2+9x+15\) is \((7x^2+3)(3x+5)\)
Step-by-step explanation:
Given polynomial \(21x^3+35x^2+9x+15\)
We have to factorize the given polynomial completely.
Consider the given polynomial \(21x^3+35x^2+9x+15\)
We will solve it by grouping of terms,
Grouping is collecting terms having some factors common
Taking \(7x^2\) common from first two term and 3 from last two terms , we have,
\(21x^3+35x^2+9x+15\)
\(\Rightarrow 7x^2(3x+5)+3(3x+5)\)
Now taking (3x +5) common from both terms , we have,
\(\Rightarrow (7x^2+3)(3x+5)\)
Thus, the complete factored form of given polynomial \(21x^3+35x^2+9x+15\) is \((7x^2+3)(3x+5)\)
