Factorisation Test

Result

Factorisation Test - 3

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Weekly Quiz Competition

Question 1
1 / -0

If (x² + x + 4) (x² - x + 4) = p² - q², then what is the value of p?

A
(x² + x)

B
(x + 4)

C
(x² + 4)

D
(x² - x)

Solution

(x² + x + 4) (x² - x + 4)
= [(x² + 4) + x] [(x² + 4) - x]

= (x² + 4)² - x²[Using (a + b)(a - b) = a²- b²]

Now, (x² + 4)² - x² = p² - q²
∴ p = (x² + 4)
Question 2
1 / -0

Which of the following options is the same as (x + 2)² – 6(x + 2) + 9?

A
(x + 5)(x – 1)

B
(x – 5)(x + 1)

C
(x – 1)(x – 1)

D
(x + 1)(x – 1)

Solution

(x + 2)² - 6(x + 2) + 9

Put x + 2 = a .........(1)
a² - 6a + 9
= a² - 3a - 3a + 9

= a(a - 3) - 3(a - 3)
= (a - 3)²

Put the value of 'a' from (1).
= [(x + 2) - 3]²
= [x + 2 - 3]² = (x - 1)² = (x - 1)(x - 1)