Answer :
The final completely factored expression for [tex]\(7x^5 - 21x^4 + 14x^3\)[/tex] is: [tex]\[ 7x^3(x - 1)(x - 2) \][/tex]
Factoring the Polynomial [tex]7x^5 - 21x^4 + 14x^3[/tex]
To factor the given polynomial completely, we start by finding the greatest common factor (GCF) of all the terms.
Step 1: Identify the GCF of the coefficients and the variable terms.
The coefficients are 7, 21, and 14. The GCF of these numbers is 7.
The variable terms are [tex]x^5[/tex], [tex]x^4[/tex], and [tex]x^3[/tex].
The GCF is [tex]x^3[/tex].
Step 2: Factor out the GCF from the polynomial.
GCF = [tex]7x^3[/tex]
[tex]7x^5 - 21x^4 + 14x^3 = 7x^3(x^2 - 3x + 2)[/tex]
Step 3: Factor the quadratic expression [tex](x^2 - 3x + 2)[/tex].
[tex](x^2 - 3x + 2)[/tex] can be factored further:
[tex]x^2 - 3x + 2[/tex]
[tex]= (x - 1)(x - 2)[/tex]
Putting it all together, we get:
[tex]7x^5 - 21x^4 + 14x^3[/tex]
[tex]= 7x^3(x - 1)(x - 2)[/tex]
Thus, the completely factored form is [tex]7x^3(x - 1)(x - 2)[/tex].
Correct question:
Factor completely. [tex]\(7x^5 - 21x^4 + 14x^3\)[/tex]
