Question

Factor completely 9x4 + 12x3 + 21x2.

3(3x4 + 4x3 + 7x2)
3x(3x3 + 4x2 + 7x)
3x2(3x2 + 4x + 7)
Prime

Answer 1

3x2(3x2 + 4x + 7)

Explanation:

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Answer 2

The factor of
`9 x^(4)+12 x^(3)+21 x^(2) \text { is } 3 x^(2)\left(3 x^(2)+4 x+7\right)`

Solution:

From question given that the equation is

`9 x^(4)+12 x^(3)+21 x^(2)`

We have to find the factors of the given equation.

By taking 3 as a common term in above expression,

`=3\left(3 x^(4)+4 x^(3)+7 x^(2)\right)`

By taking “x” as a common term in above expression, we get equation as

`=3 x\left(3 x^(3)+4 x^(2)+7 x\right)`

Again taking “x” as a common term in above expression, we get

`=3 x^(2)\left(3 x^(2)+4 x+7\right)`

`\left(3 x^(2)+4 x+7\right)` cannot be factorized.(imaginary roots)

Hence factor of
`9 x^(4)+12 x^(3)+21 x^(2) \text { is } 3 x^(2)\left(3 x^(2)+4 x+7\right)`