+234
Given 5x^3+8x^2−7x−6
1) The binomial (x+2) is a factor of the polynomial expression. Describe how you know it is a factor.
2) The binomial (x+1) is NOT a factor of the polynomial expression. Explain how you know it is not a factor.
+128474 5x^3+8x^2−7x−6
If (x + 2) is a factor then -2 must be a root
So...putting -2 into 5x^3+8x^2−7x−6 and evaluating we get
5(-2)^3 + 8(-2)^2 - 7(-2) - 6 =
-40 + 32 + 14 - 6 =
-8 + 8 = 0
We get a 0....this tells us that -2 is a root and ( x - -2) = (x + 2) is a factor
If x + 1 is a factor....then -1 must be a root
So
5(-1)^3 + 8(-1)^2 - 7(-1) - 6 =
-5 + 8 + 7 - 6 =
3 + 1 =
4
This does not produce a 0...so......-1 isn't a root and ( x - - 1) = ( x + 1) isn't a factor !!!
