Answered

Simplify [tex]$(x+4)\left(x^2-6x+3\right)$[/tex].

A. [tex]$x^3-2x^2-21x+12$[/tex]
B. [tex][tex]$x^3-14x^2+3x+12$[/tex][/tex]
C. [tex]$x^3-10x^2-27x+12$[/tex]
D. [tex]$x^3-6x^2-17x+12$[/tex]



Answer :

GinnyAnswer
Sure, let's simplify the expression [tex]\((x + 4)\left(x^2 - 6x + 3\right)\)[/tex] step-by-step.

First, let's distribute [tex]\((x + 4)\)[/tex] across each term in the polynomial [tex]\((x^2 - 6x + 3)\)[/tex]:

[tex]\[ (x + 4)\left(x^2 - 6x + 3\right) = (x + 4) \cdot x^2 + (x + 4) \cdot (-6x) + (x + 4) \cdot 3 \][/tex]

Now, we distribute each term separately.

1. Distribute [tex]\(x^2\)[/tex]:

[tex]\[ (x + 4) \cdot x^2 = x \cdot x^2 + 4 \cdot x^2 = x^3 + 4x^2 \][/tex]

2. Distribute [tex]\(-6x\)[/tex]:

[tex]\[ (x + 4) \cdot (-6x) = x \cdot (-6x) + 4 \cdot (-6x) = -6x^2 - 24x \][/tex]

3. Distribute [tex]\(3\)[/tex]:

[tex]\[ (x + 4) \cdot 3 = x \cdot 3 + 4 \cdot 3 = 3x + 12 \][/tex]

Now, combine all these results together:

[tex]\[ x^3 + 4x^2 - 6x^2 - 24x + 3x + 12 \][/tex]

Next, combine like terms:

- For [tex]\(x^2\)[/tex] terms: [tex]\(4x^2 - 6x^2 = -2x^2\)[/tex]
- For [tex]\(x\)[/tex] terms: [tex]\(-24x + 3x = -21x\)[/tex]
- The constant term is [tex]\(12\)[/tex]

So, the simplified expression is:

[tex]\[ x^3 - 2x^2 - 21x + 12 \][/tex]

Thus, the correct answer is:

[tex]\[ x^3 - 2x^2 - 21x + 12 \][/tex]

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