giannisdagoat
Answered

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Factor [tex]\( 15x^3 - 5x^2 + 6x - 2 \)[/tex] by grouping. What is the resulting expression?

A. [tex]\( (5x^2 + 2)(3x - 1) \)[/tex]
B. [tex]\( (5x^2 - 2)(3x + 1) \)[/tex]
C. [tex]\( (15x^2 + 2)(x - 1) \)[/tex]
D. [tex]\( (15x^2 - 2)(x + 1) \)[/tex]

Sagot :

GinnyAnswer
To factor the polynomial expression [tex]\(15x^3 - 5x^2 + 6x - 2\)[/tex] by grouping, follow these steps:

1. Identify and Group Terms:
Let's group the terms in pairs to make it easier to see any common factors:
[tex]\[ (15x^3 - 5x^2) + (6x - 2) \][/tex]

2. Factor Out the Greatest Common Factor (GCF) from Each Group:
For the first group [tex]\((15x^3 - 5x^2)\)[/tex]:
[tex]\[ 15x^3 - 5x^2 = 5x^2(3x - 1) \][/tex]

For the second group [tex]\((6x - 2)\)[/tex]:
[tex]\[ 6x - 2 = 2(3x - 1) \][/tex]

Now, the expression looks like this:
[tex]\[ 5x^2(3x - 1) + 2(3x - 1) \][/tex]

3. Factor Out the Common Binomial Factor:
Notice that [tex]\((3x - 1)\)[/tex] is a common factor in both terms. We can factor [tex]\((3x - 1)\)[/tex] out:
[tex]\[ (3x - 1)(5x^2 + 2) \][/tex]

4. Conclusion:
The factored form of the given polynomial [tex]\(15x^3 - 5x^2 + 6x - 2\)[/tex] is:
[tex]\[ (3x - 1)(5x^2 + 2) \][/tex]

So, the correct answer is:
[tex]\(\left(5 x^2+2\right)(3 x-1)\)[/tex].
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