ClassLink | Identity \& Access MaI $\newline$ Christ the King $\newline$ https://www.ixl.com/m= $4$ h/algebra $-1$ /factor-polynomials $\newline$ My IXL $\newline$ Algebra $1>$ X. $9$ Factor polynomials TAH $\newline$ Factor completely. $\newline$ $4 f^{2}+7 f+3$ $\newline$ Submit

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Q. ClassLink | Identity \& Access MaI

\newline

Christ the King

\newline

https://www.ixl.com/m=

4

h/algebra

-1

/factor-polynomials

\newline

My IXL

\newline

Algebra

1>

9

Factor polynomials TAH

\newline

Factor completely.

\newline

4 f^{2}+7 f+3

\newline

Submit

Identify Common Factor: Look for a common factor in all terms of the polynomial $4f^2 + 7f + 3$ . Check if there is a greatest common factor (GCF) that can be factored out. In this case, the terms $4f^2$ , $7f$ , and $3$ do not have a common factor other than $1$ .
Attempt Trinomial Factoring: Since there is no common factor, we will attempt to factor the trinomial into two binomials. $\newline$ The general form of factoring a trinomial is $(af + b)(cf + d)$ , where the product of $ac$ equals the coefficient of $f^2$ (which is $4$ in this case), and the product of $bd$ equals the constant term (which is $3$ in this case), and the sum of $ad + bc$ equals the coefficient of $f$ (which is $7$ in this case).
Find Suitable Numbers: Find two numbers that multiply to $4 \times 3 = 12$ and add up to $7$ . The numbers that satisfy these conditions are $3$ and $4$ .
Write Four-Term Expression: Write the trinomial as a four-term expression using the numbers found in Step $3$ . $\newline$ $4f^2 + 4f + 3f + 3$
Factor by Grouping: Group the terms into two pairs and factor by grouping. $\newline$ $(4f^2 + 4f) + (3f + 3)$ $\newline$ Factor out the common factors from each group. $\newline$ $4f(f + 1) + 3(f + 1)$
Factor Common Binomial: Factor out the common binomial factor $(f + 1)$ . $\newline$ $(4f + 3)(f + 1)$
Verify Factored Form: Check the factored form by multiplying the binomials to see if we get the original polynomial. $\newline$ $(4f + 3)(f + 1) = 4f^2 + 4f + 3f + 3 = 4f^2 + 7f + 3$ $\newline$ The factored form matches the original polynomial, so the factoring is correct.