The factor of the polynomial expression 4x^3 – 12x^2 + 4x by using GCF method is 4x(x^2 - 3x + 1).
The factors of a given number are those numbers that are divisible by the given number without a remainder.
By using the GCF method in an algebraic, i.e. the factors of the algebraic equation will be dependent on the greatest common factor.
From the given information, we are to factorize the following expression by using the GCF method as follows.
1.
4x^3 – 12x^2 + 4x
Here; the common expression in all the three variables is 4x. So, we have:
= 4x(x^2 - 3x + 1)
Option A is correct
2.
9x^4 + 4x^3 - 27x^2 + 12x
The common expression here is (x); So,
= x(9x^3 +4x^2 - 27x + 12)
Option B is correct
3.
x^2 - 3x + 4
This polynomial expression cannot be factored.
Option F is correct.
4.
17x^5 + 51x^2 - 34
= 17(x^5 + 3x^2 - 2)
Option D is correct.
The factorization of a quadratic equation (polynomial expression) in the form (ax^2 + bx + c) by grouping results into two factors that if multiplied together result back into the original equation.
Given that:
5.
x^2 – 2x + 1
Factors are two numbers that if the multiplied result in (ac) and if added it gives us (b)
By grouping, the polynomial expression is:
= (x - 1)(x - 1)
Option A is correct
6.
x^2 + 2x - 15
= (x + 5) (x - 3)
Option C is correct
7.
x^2 – 3x – 18
=(x + 3)(x - 6)
Option B is correct
8.
8x^2 + 47x + 28
= This polynomial expression cannot be factored in as it contains rational numbers.
Option A is correct.
Learn more about factors of polynomial expressions here:
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