Math, asked by arshichandarki, 1 year ago

Factorise 3z^3 - 4z^2 - 12z + 16

Answers

Answered by Aɾꜱɦ
15

Answer:

\huge\underline\textsf{Question:- }

\boxed{\sf3z ^{2}  - 4x {}^{2}  - 12x + 16}

\huge\underline\textsf{Explantion:- }

\large\mathtt{z^2(3z-4)-4(3z-4)}

\large\mathtt{(3z-4)(z^2-4)}

\large\underline\textsf{ans.(3z-4)(z+2)(z-2) }

Answered by SteffiPaul
4

Given,

  • 3z^3 - 4z^2 - 12z + 16 is given.

To find,

  • factors of 3z^3 - 4z^2 - 12z + 16

Solution,

The factors of 3z^3 - 4z^2 - 12z + 16 are (3z-4)(z+2)(z-2)  .

We can simply find the factors of 3z^3 - 4z^2 - 12z + 16 by taking out the common terms.

                       =  3z^3 - 4z^2 - 12z + 16

Taking z² common from first two terms and -4 common from last two terms, we get

                       = z^2(3z-4)-4(3z-4)

Now, taking (3z-4) common, we get

                      = (3z-4)(z^2-4)

Using (a²-b²) = (a+b)(a-b), we get

                      = (3z-4)(z+2)(z-2)

Hence, the factors of 3z^3 - 4z^2 - 12z + 16 are (3z-4)(z+2)(z-2).

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