B^2+ 8b + 12 = (b + 6) (?) find the other binomial which will complete the factorization

Step-by-step explanation:

here we gonna use a rule:

if x1 and x2 are rooots of the quadratic equation: ax² + bx + c = 0

then x1 + x2 = -b/a

b^2+ 8b + 12 = (b - b1) (b - b2)

This prove that “b1 = -6” is a root of the quadratic equation b^2+ 8b + 12 = 0

since, the sum of roots b1 + b2 = -8/1 = -8 then b2 = -8 - b1 = -8 - (-6) = -2

then

b^2+ 8b + 12 = (b - (-6)) (b - (-2))

                     = (b + 6) (b+ 2).

:)

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

answer: x=3 and y=4

step-by-step explanation: