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Kalahira
Answer: (3x^2 + 1) (4x – 3)
 12x^3 – 9x^2 + 4x – 3 in factored terms;
3x^2 is a common factor in 12x^3 and 9x^2
 Pulling out 3x^2, we have 3x^2 (4x – 3) + 4x – 3
 Splitting the expression into 2 groups (3x^2 (4x – 3) and 4x – 3)
4x – 3 is a common factor in both groups
 Factorizing 4x – 3, we have 3x^2 (4x – 3) + 1 (4x – 3)
Therefore, in factored form, the equation becomes (3x^2 + 1) (4x – 3)

The given expression [tex]12x^3 - 9x^2 + 4x - 3[/tex] in factored terms will be[tex](3x^2 + 1) (4x - 3).[/tex]

What is factorization?

Factorization is expressing a mathematical quantity in terms of multiples of smaller units of similar quantities.

For an integer, factorization is decomposition of that integer in terms of smaller integers which when multiplied with each other give back that considered number.

Those composing integers are called factors of that considered integers.

The given expression;

[tex]12x^3 - 9x^2 + 4x - 3[/tex]

[tex]3x^2[/tex]is a common factor in [tex]12x^3 and 9x^2[/tex]

By taking common term out [tex]3x^2[/tex], we have

[tex]3x^2 (4x - 3) + 4x -3[/tex]

By Splitting the expression into 2 groups, we get

( [tex]3x^2[/tex] (4x – 3) and 4x – 3)

4x – 3 is a common factor in both groups

Factorizing 4x – 3, we get

[tex]3x^2 (4x - 3) + 1 (4x - 3)[/tex]

Therefore, the equation becomes [tex](3x^2 + 1) (4x - 3).[/tex] in factored form.

Learn more about prime factorization here:

https://brainly.com/question/10454590

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