Question

trinomial: $5x^2 - 13x + 6$

Explanation:

Step1: Identify the trinomial

We have the trinomial \(5x^2 - 13x + 6\) (assuming the middle term is \(-13x\) as the image shows \(5x^2-13x + 6\)). We will factor it using the AC method. For a quadratic \(ax^2+bx + c\), we find two numbers that multiply to \(a\times c\) and add up to \(b\). Here, \(a = 5\), \(b=- 13\), \(c = 6\). So \(a\times c=5\times6 = 30\). We need two numbers that multiply to \(30\) and add up to \(-13\). The numbers are \(-10\) and \(-3\) since \((-10)\times(-3)=30\) and \(-10+(-3)=-13\).

Step2: Rewrite the middle term

Rewrite the trinomial by splitting the middle term:
\(5x^2-10x-3x + 6\)

Step3: Group the terms

Group the first two terms and the last two terms:
\((5x^2-10x)+(-3x + 6)\)

Step4: Factor out the GCF from each group

Factor out \(5x\) from the first group and \(-3\) from the second group:
\(5x(x - 2)-3(x - 2)\)

Step5: Factor out the common binomial factor

Now, we can factor out \((x - 2)\) from both terms:
\((5x - 3)(x - 2)\)

Answer:

The factored form of the trinomial \(5x^2-13x + 6\) is \((5x - 3)(x - 2)\)