Question

4
which expression is a factor of (7x^2 - 9x + 14x - 18)?
(a) (x - 2)
(b) (x + 9)
(c) (7x - 9)
(d) (7x + 2)

Explanation:

Step1: Combine like terms

First, combine the middle terms in the quadratic expression: \(7x^{2}-9x + 14x-18=7x^{2}+5x - 18\) (Wait, actually, a better way is to factor by grouping. Let's redo that. Group the first two and last two terms: \((7x^{2}-9x)+(14x - 18)\))

Step2: Factor out common terms from each group

From the first group \(7x^{2}-9x\), we can factor out \(x\) to get \(x(7x - 9)\). From the second group \(14x-18\), we can factor out \(2\) to get \(2(7x - 9)\)

Step3: Factor out the common binomial factor

Now we have \(x(7x - 9)+2(7x - 9)\). We can factor out \((7x - 9)\) to get \((x + 2)(7x - 9)\)

So the factors of \(7x^{2}-9x + 14x-18\) are \((x + 2)\) and \((7x - 9)\)

Answer:

C. \(7x - 9\)