Question

Factorise x^2-5x-24 by using the factor theorem.

Answer 1

Question:

Factorise x²-5x-24 by using the factor theorem

Answer:

(x-8)(x+3)

Step-by-step explanation:

Here,

coefficient of the leading term is 1 and the constant term is -24.

A zero of the polynomial p(x) will be a factor of the number -24.By inspection, we find that the number 8 is a divisor of -24 and also we have ,

p(8)=(8)²-5(8)-24

⇒64-40-24=0

8 is a zero of the polynomial p(x).

Then (x-8) is a factor of the polynomial. We can express

x²-5x-24=(x²-8x)+(3x-24)

             =x(x-8)+3(x-8)

             =(x-8)(x+3)

Hope it helps :-)

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