Question

Divide by factorisation 3x² - 4x - 15 by x - 3​

Answer 1

Answer:

= 3x + 5 is the correct answer

Answer 2

Answer:

• According to the Question :

⇒ (3x² - 4x - 15) ÷ (x - 3)

⇒ [3x² - (9 - 5)x - 15] ÷ (x - 3)

⇒ [3x² - 9x + 5x - 15] ÷ (x - 3)

⇒ [3x(x - 3) + 5(x - 3)] ÷ (x - 3)

⇒ (3x + 5)(x - 3) ÷ (x - 3)

⇒ (3x + 5)

∴ Hence, we will get (3x + 5) as quotient.

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How to do factorisation?

• To factorise a quadratic equation (x² + bx + c) we have to find numbers p and q such that p + q = b and pq = c.
• After finding p and q, we split the middle term in the quadratic as px + qx and get desired factors by grouping the terms.

Here is an Example :

Factorize x² + 6x + 8

To factorize x² + 6x + 8, we find two numbers p and q such that p + q = 6 and pq = 8.

Clearly, 2 + 4 = 6 and 2 × 4 = 8.

We know split the middle term 6x in the given quadratic as (2x + 4x), so that

⇢ x² + 6x + 8

⇢ x² + 2x + 4x + 8

⇢ (x² + 2x) + (4x + 8)

⇢ x(x + 2) + 4(x+ 2)

⇢ (x + 2)(x + 4)