Question

Diamond factor and factor by grouping to factored form a(x-r1)(x-r2)6x2-13x-5

Answer 1

Hello there. To solve this question, we'll have to remember some properties about factorisation.

Given the expression:

$6x^2-13x-5$

We want to find it in the form:

$a(x-r_1)(x-r_2)$

Using:

a) Diamond factor

To start, we draw the diagram

In the top, we put the product between the leading and linear coefficients, that is, 6 and -5.

In the bottom, we put the middle coefficient of the expression.

In fact, we have to look for values that have the same product as a and c and a sum equals to b.

==

Solving it by grouping factor

Let's rewrite 6x² - 13x - 5 as:

6x² - 15x + 2x - 5

Notice the factor 6x² - 15x can also be factored

3x * (2x - 5) + 2x - 5

Now, we factor the term 2x - 5

(3x + 1)(2x - 5)

This is the factored form of this expression.