Questions: Completely factor the polynomial, if possible. 12-12 x+3 x^2

Completely factor the polynomial, if possible.
12-12 x+3 x^2

Transcript text: Completely factor the polynomial, if possible. \[ 12-12 x+3 x^{2} \]

Solution

Solution Steps

To factor the polynomial \(12 - 12x + 3x^2\), we first look for a common factor in all the terms. Then, we can attempt to factor the resulting quadratic expression, if possible, using methods such as factoring by grouping or applying the quadratic formula.

Step 1: Identify the Polynomial

We start with the polynomial \(3x^2 - 12x + 12\).

Step 2: Factor Out the Greatest Common Factor

The greatest common factor (GCF) of the terms in the polynomial is \(3\). We factor this out: \[ 3(x^2 - 4x + 4) \]

Step 3: Factor the Quadratic Expression

Next, we focus on the quadratic expression \(x^2 - 4x + 4\). This can be factored as: \[ (x - 2)^2 \] Thus, we can rewrite the polynomial as: \[ 3(x - 2)^2 \]

Final Answer

The completely factored form of the polynomial is: \[ \boxed{3(x - 2)^2} \]

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

Answered

Fifty-four wild bears were anesthetized, and then their weights and chest sizes were measured and listed in a data set. Results are shown in the accompanying display. Is there sufficient evidence to support the claim that there is a linear correlation between the weights of bears and their chest sizes? When measuring an anesthetized bear, is it easier to measure chest size than weight? If so, does it appear that a measured chest size can be used to predict the weight? Use a significance level of α=0.05. Determine the null and alternative hypotheses. H0: p=□ H1: ρ> Identify the correlation coefficient, r. r= □ Identify the critical value(s). A. There are two critical values at r= ± □ B. There is one critical value at r= □ Is there sufficient evidence to support the claim that there is a linear correlation between the weights of bears and their chest sizes? Choose the correct answer below and, if necessary, fill in the answer box within your choice. A. Yes, because the correlation coefficient □ falls outside the critical value(s). B. No, because the correlation coefficient □ falls outside the critical value(s). C. No, because the correlation coefficient □ falls between the critical values. D. Yes, because the correlation coefficient □ falls between the critical values. E. The answer cannot be determined from the given information. When measuring an anesthetized bear, is it easier to measure chest size than weight? If so, does it appear that a measured chest size can be used to predict the weight? A. Yes, it is easier to measure a chest size than a weight because measuring weight would require lifting the bear onto the scale. The chest size could not be used to predict weight because there is not a linear correlation between the two. B. Yes, it is easier to measure a chest size than a weight because measuring weight would require lifting the bear onto the scale. The chest size could be used to predict weight because there is a linear correlation between the two. C. No, it is easier to measure weight than chest size because the chest is not a flat surface. D. Yes, it is easier to measure a chest size than a weight because measuring weight would require lifting the bear onto the scale. The chest size could not be used to predict weight because there is too much variance in the weight of the bears.

< Previous Next >

Thank you for your feedback.

Copied!