Question

Factor completely: 21x3 + 35x2 + 9x + 15 ...?

Answer 1

The complete factored form of given polynomial
`21x^3+35x^2+9x+15` is
`(7x^2+3)(3x+5)`

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)`

Answer 2

21 x³ + 35 x² + 9 x + 15 =
= 7 x² ( 3 x + 5 ) + 3 ( 3 x + 5 ) =
= ( 3 x + 5 ) ( 7 x² + 3 )
That`s all. Thank you.