Question

7. (i) x³ + 6x² + 12x + 16 factorisation
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Answer 1

Required Answer:-

Given to factorise:

• x³ + 6x² + 12x + 16

Solution:

Given,

x³ + 6x² + 12x + 16

= x³ + 4x² + 2x² + 8x + 4x + 16

Now, we will group each term,

= x²(x + 4) + 2x(x + 4) + 4(x + 4)

Now, we will take (x + 4) as common

= (x + 4)(x² + 2x + 4)

Now, we will check if x² + 2x + 4 can be factorised or not.

a = 1, b = 2 and c = 4

So, b² - 4ac

= 2² - 4 × 4

= 4 - 16

= -12 which is negative.

So, x² + 2x + 4 cannot be factorised.

Hence, the factorised form is (x + 4)(x² + 2x + 4)

Answer:

• The factorised form is (x + 4)(x² + 2x + 4)

Answer 2

Answer:

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