Question

One of the factors of 3x3 - 12x is

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Answer 1

Answer:

$3x {}^{3} - 12x = 0 \\ = > 3x(x {}^{2} - 4) = 0 \\ = > 3x = 0 \\ = > x = 0 \\ x {}^{2} - 4 = 0 \\ = > x{}^{2} - 4 = 0 \\ = > x = 2$

Answer 2

One of the factor of polynomial is 3x.

All factors of polynomial are

$\bf \pink{3 {x}^{3} - 12x = 3x(x + 2)(x - 2)}$

Given:

• $3 {x}^{3} - 12x$

To find:

• Find one of the factor of given polynomial.

Solution:

Identity to be used:

$\bf ( {a}^{2} - {b}^{2} ) = (a + b)(a - b)$

Step 1:

Take 3x common from both terms.

$3 {x}^{3} - 12x= 3x( {x}^{2} - 4)$

Thus,

One of the factor of polynomial is 3x.

Step 2:

Rewrite the term in bracket, so that identity can be applied.

$3x( {x}^{2} - {2}^{2} ) = 3x(x + 2)(x - 2)$

Thus,

All factors of polynomial are

$\bf 3 {x}^{3} - 12x = 3x(x + 2)(x - 2)$

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