Question

A x squared b x c. an x is drawn with a c in the top half and b in the bottom half. factor x2 – 8x 15. which pair of numbers has a product of ac and a sum of b? what is the factored form of the trinomial?

Answer 1

The pair of numbers have a product of 'ac' and a sum of 'b' are -5 and -3. and, the factored form of the trinomial is (x-5)(x-3).

What is a quadratic equation?

A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers.

It is written in the form of ax²+bx+c.

As we know about the quadratic equation, also the equation that is given to us is in the form of ax²+bx+c, therefore, if we compare the given equation, we will get the following values.

a = 1, b = -8, and c = 15.

Now, in order to find the pair of numbers that has a product equal to ac, and the sum equal to b. We will have to factorize the given equation. Therefore,

$x^2 -8x+15=0\\x^2-5x-3x+15=0\\x(x-5)-3(x-5)=0\\(x-5)(x-3)=0$

Thus, pair of numbers has a product of 'ac' and a sum of 'b' are -5 and -3. and, the factored form of the trinomial is (x-5)(x-3).

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