Question

Factorise this please

Answer 1

Expand $(ax+b)(cx+d)$. We have $acx^2+(ad+bc)x+bd$

Since ac=3, let's try a=3, c=1

And since bd=2, let's try b=d=-√2

(Two numbers should be negative, because middle term has negative sign.)

→ ad+bc → -3√2 -√2 → -4√2

∴a=3, b=-√2, c=1, d=-√2

Factorization is opposite of expanding

→ $3x^2-4\sqrt{2}x+2= (3x-\sqrt{2} )(x-\sqrt{2} )$

Hope this helps.