On a test, Leo is asked to completely factor the polynomial 3x3 – 3x + 5x2 – 5. He uses double grouping to get (x2 – 1)(3x + 5). Has he factored the polynomial completely? Explain.

Question

snowflake0531 · Answer

$$3x^3+5x^2-3x-5 = (x^2-1)(3x+5)$$ and you're trying to figure out whether or not it's fully factored

Hint: look at the $x^2-1$ and use the $a^2-b^2 = (a-b)(a+b)$ formula to expand it/factor it fully

jhonyy9 · Answer

so like a simple idea when the sum of free part of the terms equal zero from this result that this polynomial can divide by (x-1)

jhonyy9 · Answer

in this above wrote way we have

+3 +5 -3-5 = +8-8 = 0