Question

the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer. match each polynomial on the left with its two factors on the right. 8x³ + 1 2x - 1 8x³ - 1 2x + 1 4x² + 4x + 1 4x² + 2x + 1 4x² - 4x - 1 4x² - 2x + 1 clear click and hold an item in one column, then drag it to the matching item in the other column. be sure your cursor is over the target will highlight or the cursor will change. need help? watch this video.

Explanation:

Step1: Recall Sum/Difference of Cubes

The sum of cubes formula is \(a^3 + b^3=(a + b)(a^2 - ab + b^2)\), and the difference of cubes is \(a^3 - b^3=(a - b)(a^2 + ab + b^2)\). For \(8x^3+1\), \(a = 2x\), \(b = 1\) (since \((2x)^3=8x^3\), \(1^3 = 1\)). So \(8x^3 + 1=(2x + 1)(4x^2-2x + 1)\) (using \(a^3 + b^3=(a + b)(a^2 - ab + b^2)\), here \(a^2 - ab + b^2=(2x)^2-(2x)(1)+1^2 = 4x^2-2x + 1\)).

Step2: Factor \(8x^3 - 1\)

For \(8x^3-1\), \(a = 2x\), \(b = 1\) (since \((2x)^3=8x^3\), \(1^3 = 1\)). Using the difference of cubes formula \(a^3 - b^3=(a - b)(a^2 + ab + b^2)\), we get \(8x^3 - 1=(2x - 1)(4x^2+2x + 1)\) (here \(a^2 + ab + b^2=(2x)^2+(2x)(1)+1^2 = 4x^2+2x + 1\)).

Answer:

• \(8x^3 + 1\) matches with \(2x + 1\) and \(4x^2 - 2x + 1\)
• \(8x^3 - 1\) matches with \(2x - 1\) and \(4x^2 + 2x + 1\)