Question

factorise the following by splitting the middle term 7 under root 2 x square - 10 x - 4 under root 2​

Answer 1

AnswEr:-

Your Answer Is $\bf ( 7 \sqrt{2} - 4)(x - \sqrt{2}).$

ExplanaTion:-

Given Expression:-

• 7$\sqrt{2}$ - 10x - 4$\sqrt{2}$.

And we have to factorize the above term.

So Here,

↦ Cofficient of x² × Constant term,

$\tt = 7 \sqrt{2} \times 4 \sqrt{2}$

$\tt= 7 \times 4 \times 2.$

$\tt = 28 \times 2 = 56.$

Also,

↦ 56 = 2 × 2 × 2 × 7.

And,

↦ (7 × 2) - (2 × 2) = 10 = Middle term.

So lets split the term:-

$\tt\mapsto7 \sqrt{2} {x}^{2} - 10x - 4 \sqrt{2} .$

$\tt = 7 \sqrt{2} {x}^{2} - (14 - 4)x - 4 \sqrt{2} .$

$\tt = 7 \sqrt{2} {x}^{2} - 14x + 4x - 4 \sqrt{2} .$

$\tt = 7 \sqrt{2}x(x - \sqrt{2}) + 4(x - \sqrt{2}) .$

$\tt =( 7 \sqrt{2} - 4)(x - \sqrt{2}).$

...Hence Factorized...