question\nfactor the trinomial:\n$5x^{2}+22x + 8$\nanswer attempt 1 out of 2

Answer

Explanation:

Step1: Multiply coefficients

Multiply the coefficient of $x^{2}$ (which is 5) and the constant term (which is 8). So, $5\times8 = 40$.

Step2: Find factor - pair

Find two numbers that multiply to 40 and add up to the coefficient of $x$ (which is 22). The numbers are 20 and 2 since $20\times2=40$ and $20 + 2=22$.

Step3: Rewrite the middle term

Rewrite the trinomial as $5x^{2}+20x + 2x+8$.

Step4: Group the terms

Group the terms: $(5x^{2}+20x)+(2x + 8)$.

Step5: Factor out GCF from each group

Factor out the greatest - common factor (GCF) from each group. From the first group, the GCF of $5x^{2}$ and $20x$ is $5x$, so $5x^{2}+20x=5x(x + 4)$. From the second group, the GCF of $2x$ and $8$ is 2, so $2x + 8=2(x + 4)$.

Step6: Factor out common binomial

We now have $5x(x + 4)+2(x + 4)$. Factor out the common binomial $(x + 4)$ to get $(5x + 2)(x+4)$.

Answer:

$(5x + 2)(x + 4)$