Question

Factorise the following:

a) x² + 6x + 5
b) x² - 10x + 24
c) x²-x-6
d) x² + 2x-63
Answer
Answer
Answer
Answer

Answer 1

The quadratic expressions are factored by finding two numbers that multiply to ac and add to b. The correct factorizations are: (a) (x + 5)(x + 1), (b) (x - 6)(x - 4), (c) (x - 3)(x + 2), and (d) (x + 9)(x - 7).

Step-by-step explanation:

Factoring Quadratic Expressions

To factorise a quadratic expression of the form ax² + bx + c, we look for two numbers that multiply to give the product, ac, and add to give b. This is applicable to all expressions given in the question:

1. x² + 6x + 5: The numbers 5 and 1 multiply to give 5 and add to give 6. So, the factorisation is (x + 5)(x + 1).

2. x² - 10x + 24: The numbers 6 and 4 multiply to give 24 and add to give -10. So, the factorisation is (x - 6)(x - 4).

3. x² - x - 6: The numbers -3 and 2 multiply to give -6 and add to give -1. So, the factorisation is (x - 3)(x + 2).

4. x² + 2x - 63: The numbers 9 and -7 multiply to give -63 and add to give 2. So, the factorisation is (x + 9)(x - 7).

To check if the factorization is correct, you can multiply the binomials back and see if you get the original quadratic expression. All the provided factorisations are correct, making option (a), (b), (c), and (d) valid. Always eliminate terms wherever possible to simplify the algebra.