Question

Factor the polynomial completely using the X method. X2 11x 24 An x-method chart shows the product a c at the top of x and b at the bottom of x. Above the chart is the expression x squared 11 x 24. The value of ac is. The value of b is. The equivalent factored form of the polynomial is.

Answer 1

The factored form of the considered polynomial is $(x+3)(x+8)$

How to find the factors of a quadratic expression?

If the given quadratic expression is of the form

$ax^2 + bx + c$

then its factored form is obtained by two numbers alpha( α ) and beta( β) such that:

$b = \alpha + \beta \\ ac =\alpha \times \beta$

Then writing b in terms of alpha and beta would help us getting common factors out.

For the considered polynomial, we've got the quadratic expression as:

$x^2 + 11x + 24$

Comparing this with $ax^2 + bx + c$, we get:

• a = 1 (since $x^2 = 1\times x^2$ )
• b = 11
• c=  24

Therefore, we have : ac = c = 24

Two numbers whose multiplication gives 24 and and whose addition gives 11.

24 = $2 \times 2 \times 2 \times 3$

If we take first three 2s, and 3, then:

$24 = 8 \times 3 = (2 \times 2 \times 2) \times 3\\11 = 8 + 3 = (2 \times 2 \times 2) + 3$

Thus, we need to write 11 in the middle in terms of 8 and 3:

$x^2 + 11x + 24 = x^2 + 8x + 3x + 24 = x(x+8) + 3(x+8) = (x+3)(x+8)$

Thus, the factored form of the considered polynomial is $(x+3)(x+8)$

Learn more about factors of a quadratic equations here:

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