Question

Factorise 8x²-20x-12​

Answer 1

Solution

4(−3)(2+1)

Hope it helps you

Answer 2

$\large\sf\underline{Given\::}$

• $\sf\:8x^{2}-20x-12$

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$\large\sf\underline{To\::}$

• Factorise the given expression

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$\large\sf\underline{Solution\::}$

$\sf\:8x^{2}-20x-12$

• Let's simplify the expression by taking common

I have taken 4 as common.

$\sf\implies\:4(2x^{2}-5x-3)$

$\sf\implies\:2x^{2}-5x-3$

• Now let's break the middle term.

In order to factorise $\sf\:2x^{2}-5x-3$ we have to find numbers p and q such that, ${\sf{{\green{p±q\:=\:5}}}}$ and ${\sf{{\green{p \times q\:=\:(3 \times 2) = 6}}}}$ .

When p = 6 and q = 1

${\sf{{\pink{p-q\:=\:5\:\to\:6-1=5}}}}$

${\sf{{\pink{p \times q\:= 6\:\to\:6 \times 1=6}}}}$

So middle term of $\sf\:2x^{2}-5x-3$ :

$\sf\implies\:2x^{2}-(6-1)x-3$

$\sf\implies\:2x^{2}-6x+x-3$

• Taking 2x common from first term and 1 from second term

$\sf\implies\:2x(x-3)+1(x-3)$

$\large{\mathfrak\red{\implies\:(2x+1)(x-3)}}$

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‎ $\large\sf\underline{Verifying\::}$

We know,

Factorise means to express the given expression into its product form.

So let's see what happens when I multiply my factorised value !?

$\sf\:(2x+1)(x-3)$

$\sf\implies\:(2x+1) \times (x-3)$

$\sf\implies\:2x(x-3) + 1(x-3)$

$\sf\implies\:2x^{2}-6x + x-3$

$\sf\implies\:2x^{2}-5 x-3$

So cleary it gives me the expression which I have solved by middle term breaking.

Hence it is verified !

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!! Hope it helps !!