Answer :
To factor the expression [tex]\(-40 + 28x^3\)[/tex] completely, follow these steps:
1. Identify the greatest common factor (GCF):
Look for the largest number that divides both terms of the expression evenly. Here, the coefficients of the terms are [tex]\(-40\)[/tex] and [tex]\(28\)[/tex]. The greatest common factor of 40 and 28 is 4.
2. Factor out the GCF:
Divide each term by the GCF and factor it out of the expression:
[tex]\[
-40 + 28x^3 = 4(-10) + 4(7x^3)
\][/tex]
So, the expression becomes:
[tex]\[
4(-10 + 7x^3)
\][/tex]
3. Check the remaining expression for further factorization:
Now, look at [tex]\(-10 + 7x^3\)[/tex] to see if it can be factored further. In this case, it cannot be factored any further using simple methods as it doesn’t have any common factors or recognizable patterns such as difference of squares or cubes, or trinomial squares.
Thus, the fully factored expression is:
[tex]\[
4(7x^3 - 10)
\][/tex]
1. Identify the greatest common factor (GCF):
Look for the largest number that divides both terms of the expression evenly. Here, the coefficients of the terms are [tex]\(-40\)[/tex] and [tex]\(28\)[/tex]. The greatest common factor of 40 and 28 is 4.
2. Factor out the GCF:
Divide each term by the GCF and factor it out of the expression:
[tex]\[
-40 + 28x^3 = 4(-10) + 4(7x^3)
\][/tex]
So, the expression becomes:
[tex]\[
4(-10 + 7x^3)
\][/tex]
3. Check the remaining expression for further factorization:
Now, look at [tex]\(-10 + 7x^3\)[/tex] to see if it can be factored further. In this case, it cannot be factored any further using simple methods as it doesn’t have any common factors or recognizable patterns such as difference of squares or cubes, or trinomial squares.
Thus, the fully factored expression is:
[tex]\[
4(7x^3 - 10)
\][/tex]
