MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Factorisation by Common Factors

simplify : ...

Question

simplify : $a^{3} - 12 a - 16$

Open in App

Solution

Let $f (a) = a^{3} - 12 a - 16$
$f (- 2) = {(- 2)}^{3} - 12 (- 2) - 16 = 0$
Thus,
$(a + 2)$ is a factor of $a^{3} - 12 a - 16$ .
Now dividing $f (a)$ by $(a + 2)$ , we get
$(a^{3} - 12 a - 16) \div (a + 2) = a^{2} - 2 a - 8$
Now,
$a^{2} - 2 a - 8$
$= a^{2} - 4 a + 2 a - 8$
$= (a - 4) (a + 2)$
Therefore,
$a^{3} - 12 a - 16 = (a + 2) (a - 4) (a + 2)$
$\Rightarrow a^{3} - 12 a - 16 = {(a + 2)}^{2} (a - 4)$

Suggest Corrections

thumbs-up

0

Similar questions

(12 a - 36) \div 6

\frac{a^{2} - 16}{a^{3} - 8} \times \frac{2 a^{2} - 3 a - 2}{2 a^{2} + 9 a + 4} \div \frac{3 a^{2} - 11 a - 4}{a^{2} + 2 a + 4}

a^{3} \times a^{3} \times 5 a^{4}

4 a^{2} + 12 a + 9 - m^{2} + 2 m n - n^{2}

(a^{3} - 2 a^{2} + 4 a - 5) - (- a^{3} - 8 a + 2 a^{2} + 5)

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Method of Common Factors

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Factorisation by Common Factors

Standard VIII Mathematics

Join BYJU'S Learning Program

CrossIcon