How do you factor the expressions # -x^2 + 6x + 16#?

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Answer 1 · 2016-09-01T20:36:03

# -(x+8)(x-2)" = "(-x-8)(x-2) " = "(x+8)(2-x)#

They are all correct.

# -x^2 + 6x + 16# The negative at the front is not comfortable!

There are two options:

Option 1

Re-arrange the terms.
In this case it will work because the 16 is positive.

# -x^2 + 6x + 16" = "16+6x -x^2#

Find the factors of 16 (and 1) which subtract to give 6.

#[8 xx 2 =16 and 8-2 = 6]#
There must be more positives.

#16+6x -x^2" = " (8 - x)(2 + x)#

Option 2

Divide -1 out as a common factor.
This has the effect of changing all the signs.

# -x^2 + 6x + 16 " = "-(x^2 - 6x - 16)#

Find the factors of 16 (and 1) which subtract to give 6.

#-(x^2 - 6x - 16) " = "-(x+8)(x-2)#

The answer can be left like this, OR the minus sign can be multiplied into EITHER of the brackets. (NOT BOTH!)