Question

2. Factorise the following quadratic polynomials by splitting the middle term:
(i) x2 +33x + 6
(ii) x2 - 2x - 12
(iii) x2 +115x + 50
(iv) 32x2 +11x +42
(v) 23x2 + 7x-53
(vi) 5x2+4/5x+3
(vii) 2x2 - 4 12x-5
(viii) 232 +2 14x +7.​

Answer 1

x²+3√3x+6 = (x+2√3)(x+√3)

Explanation:

Given quadratic expression:

x²+3√3x+6

Splitting the middle term, we get

=x²+2√3x+√3x+6

= x²+2√3x+√3x+2×√3×√3

= x(x+2√3)+√3(x+2√3)

= (x+2√3)(x+√3)

Therefore,

x²+3√3x+6 = (x+2√3)(x+√3)