Question

1) Factorize: x^2 - 10x +24

Answer 1

We are given with a quadratic equation and we have to factorise it , so let's proceed.

${:\implies \quad \sf x^{2}-10x+24}$

${:\implies \quad \sf x^{2}-6x-4x+24}$

${:\implies \quad \sf x(x-6)-4(x-6)}$

${:\implies \quad \bf \underline{\underline{(x-6)(x-4)}}}$

Used Concepts :-

To factorise a quadratic polynomial ax² + bx + c we have to split it's middle term bx into say mx and nx and it will look like ax² + mx + nx + c ,also we should split it such that it follows the both conditions below :-

• m × n = c × a
• m + n = b

Answer 2

To Factorize:

• $\underline{ \sf {x}^{2} - 10x + 24}$

$~$

Solution:

$\: \: \: \: \sf \longrightarrow {x}^{2} - 10x + 24$

$\: \: \: \: \sf \longrightarrow {x}^{2} - 4x - 6x + 24$

$\: \: \: \: \sf \longrightarrow x(x - 4) - 6(x - 4)$

$\: \: \: \: \sf \longrightarrow (x - 6)(x - 4)$