Answer :

Alright, let's break down the process of factorizing the expression [tex]\( 28x + 35x^2 \)[/tex] step-by-step:

1. Identify Common Factors:
First, we notice that both terms, [tex]\( 28x \)[/tex] and [tex]\( 35x^2 \)[/tex], share some common factors. Specifically, they share a common factor of [tex]\( x \)[/tex].

2. Factor Out the Common Variable:
Factor [tex]\( x \)[/tex] out of each term:
[tex]\[
28x + 35x^2 = x(28 + 35x)
\][/tex]

3. Identify Common Numerical Factors:
Next, let's inspect the numerical coefficients [tex]\( 28 \)[/tex] and [tex]\( 35 \)[/tex]. The greatest common divisor (GCD) of [tex]\( 28 \)[/tex] and [tex]\( 35 \)[/tex] is [tex]\( 7 \)[/tex].

4. Factor Out the Numerical Common Factor:
Now we factor out the [tex]\( 7 \)[/tex] from both [tex]\( 28 \)[/tex] and [tex]\( 35 \)[/tex]:
[tex]\[
28 + 35x = 7 \times 4 + 7 \times 5x
\][/tex]

Therefore, we can write:
[tex]\[
28x + 35x^2 = x \left( 7 \times 4 + 7 \times 5x \right)
\][/tex]

5. Combine All Factored Terms:
We can factor out the [tex]\( 7 \)[/tex] from the parentheses:
[tex]\[
x \left( 7 \times (4 + 5x) \right)
\][/tex]

Finally, include all the factors outside the parentheses:
[tex]\[
28x + 35x^2 = 7x (4 + 5x)
\][/tex]

So, the correct factorized form of [tex]\( 28x + 35x^2 \)[/tex] is:

[tex]\[ 7x (4 + 5x) \][/tex]

This step-by-step method helps ensure that we've correctly factorized the original expression.

Thanks for taking the time to read Factorize the following expression a tex 28x 35x 2 tex. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada