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