Factorise- Z 2-4 z -12

The first term is, z2 its coefficient is 1 . The middle term is, 4z its coefficient is 4 . The last term, "the constant", is 12 Step 1 : Multiply th ...

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Standard VIII

Mathematics

Introduction to Algebraic Expressions

Factorise, Z ...

Question

Factories $z^{2} - 4 z - 12$

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Solution

Given: $z^{2} - 4 z - 12$
We have to find two numbers such that their product is $- 12 z^{2}$ and their sum is $- 4 z$ .
Such two numbers are $- 6 z$ and $2 z$ .
Using Middle Term Splitting,
$\Rightarrow z^{2} - 6 z + 2 z - 12$
$\Rightarrow z (z - 6) + 2 (z - 6)$
$\Rightarrow (z - 6) (z + 2)$
$∴ z^{2} - 4 z - 12 = (z - 6) (z + 2)$
Hence, the given expression has been factorised.

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Factories z2−4z−12

Given: z2−4z−12We have to find two numbers such that their product is −12z2 and their sum is −4z.Such two numbers are −6z and 2z.Using Middle Term Splitting,⇒z2−6z+2z−12⇒z(z−6)+2(z−6)⇒(z−6)(z+2)∴z2−4z−12=(z−6)(z+2)Hence, the given expression has been factorised.

Factories $z^{2} - 4 z - 12$