Question

factor the polynomial. drag the expressions into the box if they are part of the factored form of the polynomial.
48 - 3k²

Explanation:

Step1: Factor out the GCF

First, find the greatest common factor (GCF) of \(48\) and \(3k^2\). The GCF of \(48\) and \(3\) is \(3\). So we factor out \(3\) from the polynomial:
\(48 - 3k^2=3(16 - k^2)\)

Step2: Apply difference of squares

Notice that \(16 - k^2\) is a difference of squares, which can be factored using the formula \(a^2 - b^2=(a + b)(a - b)\). Here, \(a = 4\) and \(b = k\) because \(16 = 4^2\) and \(k^2=k^2\). So we factor \(16 - k^2\):
\(16 - k^2=(4 + k)(4 - k)\)

Step3: Combine the factors

Substitute the factored form of \(16 - k^2\) back into the expression from Step 1:
\(3(16 - k^2)=3(4 + k)(4 - k)\)

Answer:

The factored form of \(48 - 3k^2\) is \(3(4 + k)(4 - k)\), so the expressions that are part of the factored form are \(3\), \(4 + k\), and \(4 - k\).