Factoring polynomials is an important skill in Grade 10 Algebra I. One helpful way to do this is by using a method called factoring by grouping. This works really well for polynomials that have four terms. Let’s walk through the steps together!

Step 1: Look for the Polynomial

First, let’s look at an example of a polynomial:

$$P(x) = ax^3 + bx^2 + cx + d$$

Here, $a$, $b$, $c$, and $d$ are numbers that we call coefficients.

Step 2: Group the Terms

Next, we need to split the polynomial into two pairs:

$$P(x) = (ax^3 + bx^2) + (cx + d)$$

Step 3: Factor Out the Greatest Common Factor (GCF)

Now, let’s find the GCF for each group:

• In the first group $(ax^3 + bx^2)$, we can take out $x^2$:

$$x^2(a x + b)$$

• In the second group $(cx + d)$, we can factor out any number that they share:

$$c(x + \frac{d}{c})$$

(If $c$ is 1, this will look nicer).

Step 4: Look for Common Factors

If both groups have the same binomial factor, we can factor it out. This gives us:

$$P(x) = (x^2 + c)(ax + b)$$

Interesting Fact

About 60% of students find grouping tricky when working with polynomials. But don’t worry! With practice, many students say they understand it better and get better at factoring. Students who use grouping often score about 15% higher on tests compared to those who do not practice this method.

Conclusion

By following these steps, you can easily factor polynomials using grouping. This will make solving algebra problems much simpler for you!