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  • Factorize the following :- (i) 9x^{2} - 12x + 3 (ii) 9x^{2} - 12x + 4

Factorize the following :-

(i) 9x^{2} - 12x + 3

(ii) 9x^{2} - 12x + 4

Answers (1)

(i)(x-1)(9x-3)

Given, 9x^{2} - 12x + 3

To factorize ax2 + bx + c, we have to distribute “bx” into “px” and “qx” such that

p + q = b and p.q = a.c

The given equation can be written as:          

9x^{2}-9x-3x+3                                             {-9 - 3 = -12, (-9) (-3) = (9) (3)}
\\=\left (9x^{2}-9x \right )-\left (3x-3 \right )\\ =9x(x-1)-3(x-1)\\ =(x-1)(9x-3)           

(ii)(3x-2)(3x-2)

Given, 9x^{2} - 12x + 4

To factorize ax2 + bx + c, we have to distribute “bx” into “px” and “qx” such that

p + q = b and p.q = a.c

The given equation can be written as:          

9x^{2}-6x-6x+4                                             {-6 - 6 = -12, (-6) (-6) = (9) (4)}
\\=\left (9x^{2}-6x \right )-\left (6x-4 \right )\\ =3x(3x-2)-2(3x-2)\\ =(3x-2)(3x-2)

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