As the title suggests, is there an easy

Cole Gardner

Cole Gardner

Answered question

2022-03-17

As the title suggests, is there an easy way to see that (x2+5x+4)(x2+5x+6)48=(x2+5x+12)(x2+5x2) that doesn't require expanding in full? Is there a trick?

Answer & Explanation

obduciramwz6

obduciramwz6

Beginner2022-03-18Added 8 answers

(x2+5x+51)(x2+5x+5+1)48
=(x2+5x+5)272
diesel817637dsf

diesel817637dsf

Beginner2022-03-19Added 13 answers

Step 1
If x2+5x+12=0 then
(x2+5x+4)(x2+5x+6)48=(8)(6)48=0.
Step 2
If x2+5x2=0 then
(x2+5x+4)(x2+5x+6)48=6848=0.
Therefore LHS and RHS have the same zeroes. Since RHS has no double roots and both sides are polynomials of degree 4, we conclude LHS = RHS.

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