Question

Which of the following represents the factorization of the trunk oak below?

x^2 - 14x + 48

Answer 1

Answer: C

Explanation:

To factorize the equation x^2 - 14x + 48, we need to find two binomial factors that, when multiplied together, result in the given quadratic expression.

To factorize the quadratic equation, we look for two numbers that multiply to give the constant term (48) and add up to give the coefficient of the linear term (-14). In this case, the numbers are -6 and -8 since (-6) * (-8) = 48 and (-6) + (-8) = -14.

Now, we can rewrite the quadratic expression as follows:

x^2 - 14x + 48 = (x - 6)(x - 8)

Therefore, the factored form of the equation x^2 - 14x + 48 is (x - 6)(x - 8).

Answer 2

C. (x - 6)(x - 8)

Explanation:

To factorize the expression x^2 - 14x + 48, we need to find two binomial factors whose product is equal to the given expression. We are looking for two numbers that multiply to give 48 and add up to -14.

The possible factor pairs of 48 are:

1 * 48

2 * 24

3 * 16

4 * 12

6 * 8

Among these pairs, the only pair whose sum is -14 is 6 and 8.

So, the factorization of the expression x^2 - 14x + 48 is:

(x - 6)(x - 8)