Factor completely. 48-24 x+3x^(2)=

Identify common factor: Identify the common factor in the given quadratic expression. The expression is 48 - 24x + 3x^2. We can see that each term is divisible by 3.Factor out greatest common factor: Factor out the greatest common factor from the expression. The greatest common factor is 3. So we factor it out: 3(16 - 8x + x^2)Recognize perfect square trinomial: Recognize the quadratic expression inside the parentheses as a perfect square trinomial. The expression inside the parentheses is 16 - 8x + x^2, which can be written as (4 - x)^2 because (4 - x)(4 - x) = 16 - 8x + x^2.Write factored form: Write the factored form of the expression. The factored form of the original expression is 3(4 - x)^2.

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Math Problems

Algebra 1

Factor quadratics: special cases

Full solution

Q. Factor completely.

\newline

48-24x+3x^{2}=

Identify common factor: Identify the common factor in the given quadratic expression. $\newline$ The expression is $48 - 24x + 3x^2$ . We can see that each term is divisible by $3$ .
Factor out greatest common factor: Factor out the greatest common factor from the expression. $\newline$ The greatest common factor is $3$ . So we factor it out: $\newline$ $3(16 - 8x + x^2)$
Recognize perfect square trinomial: Recognize the quadratic expression inside the parentheses as a perfect square trinomial. $\newline$ The expression inside the parentheses is $16 - 8x + x^2$ , which can be written as $(4 - x)^2$ because $(4 - x)(4 - x) = 16 - 8x + x^2$ .
Write factored form: Write the factored form of the expression. $\newline$ The factored form of the original expression is $3(4 - x)^2$ .