Question

problems 5 – 8: factor each of the following that they are not equations. your answers 5.) 2x² - 8x 7.) 2x² + 3x + 1 problems 9-18: solve each of the foll simplifying checklist: terms that can be combine there are no rounded-off there are no fractions or there are no square roots there are no square roots any complex-imaginary

Explanation:

Step1: Factor \(2x^2 - 8x\)

Find the greatest common factor (GCF) of \(2x^2\) and \(-8x\). The GCF of \(2\) and \(8\) is \(2\), and the GCF of \(x^2\) and \(x\) is \(x\), so the GCF is \(2x\).
Divide each term by \(2x\): \(\frac{2x^2}{2x}=x\) and \(\frac{-8x}{2x}=-4\).
So, \(2x^2 - 8x = 2x(x - 4)\).

Step2: Factor \(2x^2 + 3x + 1\)

We use the AC method. For \(ax^2+bx+c\) (here \(a = 2\), \(b = 3\), \(c = 1\)), find two numbers that multiply to \(a\times c=2\times1 = 2\) and add to \(b = 3\). The numbers are \(1\) and \(2\).
Rewrite the middle term: \(2x^2+2x+x + 1\).
Group the terms: \((2x^2+2x)+(x + 1)\).
Factor out the GCF from each group: \(2x(x + 1)+1(x + 1)\).
Factor out \((x + 1)\): \((2x + 1)(x + 1)\).

Answer:

• For \(2x^2 - 8x\), the factored form is \(2x(x - 4)\).
• For \(2x^2 + 3x + 1\), the factored form is \((2x + 1)(x + 1)\).