Question

Q8. Factorise : i) 2x2 + 3x + 1 and
ii) 3x2 + 2x − 1 .​

Answer 1

Answer:

$i) \: {2x}^{2} + 3x + 1$

${2x}^{2} + (2 + 1)x + 1$

${2x}^{2} + 2x + x + 1$

$2x(x + 1) + 1(x + 1)$

$(x + 1)(2x + 1)$

$ans. \: \: (x + 1)(2x + 1)$

$ii) \: {3x}^{2} + 2x - 1$

${3x}^{2} + (3 - 1)x - 1$

${3x}^{2} + 3x - x - 1$

$3x(x + 1) - 1(x + 1)$

$(x + 1)(3x - 1)$

$ans. \: \: (x + 1)(3x - 1)$

Hope it helps.

Answer 2

Answer

(2x +1) (x+1)

Step-by-step explanation:

We can Split the Middle Term of this expression to factorise it

In this technique, if we have to factorise an expression like ax² +bx + c ,we need to think of 2 numbers such that:

N1 . N2 = a .c =2 . 1 = 2 and

N1 + N2 = b = 3

After trying out a few numbers we get N1 = 2 and N2 = 1

2 . 1 = 2 , and 2 + 1 = 3

2x² + 3x + 1 = 2x² + 2x + x + 1

2x ( x + 1 ) + 1 ( x + 1)

(2x+1)(x+1)