Questions: Factor the polynomial completely using the grouping method. 21x-4+18x^2 21x-4+18x^2=

Transcript text: Factor the polynomial completely using the grouping method. \[ \begin{array}{l} 21 x-4+18 x^{2} \\ 21 x-4+18 x^{2}= \end{array} \]

Solution

Solution Steps

To factor the polynomial \( 21x - 4 + 18x^2 \) completely using the grouping method, we need to rearrange the terms and group them in pairs that can be factored easily.

Rearrange the polynomial in standard form: \( 18x^2 + 21x - 4 \).
Group the terms in pairs: \( (18x^2 + 21x) + (-4) \).
Factor out the greatest common factor (GCF) from each group.
Look for a common binomial factor.

Step 1: Rearranging the Polynomial

We start with the polynomial \( 21x - 4 + 18x^2 \). Rearranging it in standard form gives us: \[ 18x^2 + 21x - 4 \]

Step 2: Grouping the Terms

Next, we group the polynomial into two parts: \[ (18x^2 + 21x) + (-4) \]

Step 3: Factoring Each Group

Now, we factor out the greatest common factor (GCF) from each group: \[ 3x(6x + 7) - 4 \]

Step 4: Finding Common Factors

We can rewrite the expression as: \[ 3x(6x + 7) - 4(1) \] This does not yield a common binomial factor directly, so we can factor the entire polynomial as: \[ (3x + 4)(6x - 1) \]