Factorize and then divide $5 x^{3} + 16 x^{2} + 12 x$ by $(x + 2)$ . Find the value of $5 x^{3} + 16 x^{2} + 12 x$ for $x = 3.$ [4 MARKS]

Open in App

Solution

Factorisation: 2 Marks
Division: 1 Mark
Substitution: 1 Mark

$5 x^{3} + 16 x^{2} + 12 x$

$= 5 x^{3} + 10 x^{2} + 6 x^{2} + 12 x$

$= 5 x^{2} (x + 2) + 6 x (x + 2)$

$= (5 x^{2} + 6 x) (x + 2)$

Dividing above expression by (x+2) gives $5 x^{2} + 6 x$

x = 3

$5 x^{3} + 16 x^{2} + 12 x$

$= 5 (3)^{3} + 16 (3)^{2} + 12 (3)$

$= 315$

Suggest Corrections

Similar questions

5 x^{3} + 16 x^{2} + 12 x

x = 3

Factorise $x^{2} - 12 x - 45$ and find its value for $x = 3.$ [3 MARKS]

44 (x^{4} - 5 x^{3} - 24 x^{2})

11 x (x - 8)

\frac{9 x^{2} + 12 x + 4}{4 x^{2} - 27 x - 7} \div \frac{12 x^{2} + 5 x - 2}{16 x^{2} - 1} .

Join BYJU'S Learning Program