Question

Factorise following quadratic polynomials using factor theorem :-
$i) \: \: 2 {x}^{2} + 7x + 3 \\ ii) \: \: 4 {x}^{2} - 12x + 9$
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Answer 1

Given

Factorise following quadratic polynomials using factor theorem :-

$i) \: \: 2 {x}^{2} + 7x + 3 \\ ii) \: \: 4 {x}^{2} - 12x + 9$

Solution

By factor theorem

splitting middle term

i) 2x² + 7x + 3

=> 2x² + 6x + x + 3

=> 2x(x+3) + 1(x+3)

=> (x+3)(2x+1)

ii) 4x² - 12x + 9

=> 4x² - 6x - 6x + 9

=> 2x(2x-3) - 3(2x - 3)

=> (2x - 3)(2x - 3)

Alternative method

i) 2x² + 7x + 3

p(x) = 2(x²+7/2x+3)

= x² + 7/2x + 3/2

By trail

p(-3) = (-3)²+7/2 × (-3) + 3/2

= 9 - 21/2 + 3/2 = 0

By factor theorem (x+3) is a factor of 2x²+7x +3

By trail

p(-1/2) = (-1/2)² + 7/2(-1/2) +3/2

= 1/4 - 7/4 + 3/4 = 0

By factor theorem (x+1/2) is a factor of 2x²+7x+3