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Prove that (2x + 1) is a factor of 6x³ + 13x² + 17x + 6 . give answer ​

User Shahriyar
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Explanation:

any polynomial is factored by terms of its zeros (the terms of the x- values creating a 0-y-value as result).

y = (x - a)(x - b)(x - c)...

means that for x = a or b or c or ..., y = 0

and (x - a), (x - b), (x - c), ... are all the factors of the y-expression

so,

2x + 1 = 0

2x = -1

x = -1/2

so, for x = -1/2 our term (2x + 1) = 0.

if now the whole expression is 0 for x = -1/2, then (2x + 1) is a factor :

6×(-1/2)³ + 13×(-1/2)² + 17×(-1/2) + 6 =

= -6×1/8 + 13×1/4 - 17×/1/2 + 6 =

= -6/8 + 13/4 - 17/2 + 6 = -3/4 + 13/4 - 17/2 + 6 =

= 10/4 - 17/2 + 6 = 5/2 - 17/2 + 6 = -12/2 + 6 =

= -6 + 6 = 0

that is why (2x + 1) is indeed a factor of

6x³ + 13x² + 17x + 6

User Freezy Ize
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