Question

Question 10 of 25

The polynomial (x-2) is a factor of the polynomial 5x² - 6x +4.
O A. True
OB. False

Answer 1

B. False

Explanation:

5x² - 6x + 4 | 5 × 4 = 20

Can't factor it normally

√b² - 4ac

-b ± ---------------

2a

√(-6)² - 4(5)(4)

-(-6) ± ---------------

2(5)

√36 - 80

6 ± ---------------

10

6 ± √-44

---------------

10

6 ± √-4 × 11

---------------

10

6 ± 2i√11

---------------

10

The answer is actually

3 ± i√11

---------------

5

I hope this helps!

Answer 2

B. False

Explanation:

You want to know if (x -2) is a factor of 5x² -6x +4.

Remainder

There are a couple of ways you can determine whether (x -2) is a factor. One is to look at the polynomial value at x=2:

5x² -6x +4 = (5x -6)x +4 = (5(2) -6)(2) +4 = 4(2) +4 = 12

The value is not 0, so (x -2) is not a factor.

Other factor

Another way to tell is to determine what the other factor would be.

The product of roots is the ratio c/a = 4/5 in the polynomial. If 2 is a root, then (4/5)/2 = 2/5 is the other root. That would mean the factorization of the polynomial is ...

(5x -2)(x -2) = 5x² -12x +4 . . . . . . not the same polynomial

The polynomial 5x² -6x +4 does not have a factor (x -2).

Graph

The graph of the polynomial has no x-intercepts, so (x -2) cannot be a factor.