Question

Factor completely: 9x^4 + 12x^3 + 21x^2.

3(3x^4 + 4x^3 + 7x^2)
3x(3x^3 + 4x^2 + 7x)
3x^2(3x^2 + 4x + 7)
Prime

I think its A

Answer 1

i think it iz da 3rd one

Answer 2

\(\color{#0cbb34}{\text{Originally Posted by}}\) @Kamyoboi
i think it iz da 3rd one
\(\color{#0cbb34}{\text{End of Quote}}\)
why. explanation-?

Answer 3

mm you want to find the common factor between \(x^4\), \(x^3\) and \(x^2\)

Do you know what value it would be?

Answer 4

x^2

Answer 5

Then find the GCM of 9, 12, and 21

Answer 6

Yeah thats all you needed to really do (you'd need to solve for the factor for each coefficient if you weren't given similar options)

3(3x^4 + 4x^3 + 7x^2)
3x(3x^3 + 4x^2 + 7x)
\(\color{orange}{3x^2}\)(3x^2 + 4x + 7)


You can check it by expanding it

\(\color{orange}{3x^2}(\color{blue}{3x^2} + \color{green}{4x} + \color{red}{7})\)

\((\color{orange}{3x^2}\times\color{blue}{3x^2})=9x^4\)
\((\color{orange}{3x^2}\times\color{green}{4x})=12x^3\)
\((\color{orange}{3x^2}\times\color{red}{7})=21x^2\)

Answer 7

tysm