Factor +14x + 40 by completing the square. Half of the linear coefficient is: )² = =² + =+ So we expand the complete square (x + This is our 'helper line' that will help with the main computation. We start the main computation. The polynomial to be factored is: x2 + 14x + 40 We smuggle in the missing term for a complete square: We re-write the first three terms as a x + 14x + +40 complete square and combine the last two terms. We re-write the subtracted number as (x + -ロ a square as we get ready to factor. We factor via the difference of squares theorem. (x+ (2 + +(e + (x + We combine like terms in each factor.
Factor +14x + 40 by completing the square. Half of the linear coefficient is: )² = =² + =+ So we expand the complete square (x + This is our 'helper line' that will help with the main computation. We start the main computation. The polynomial to be factored is: x2 + 14x + 40 We smuggle in the missing term for a complete square: We re-write the first three terms as a x + 14x + +40 complete square and combine the last two terms. We re-write the subtracted number as (x + -ロ a square as we get ready to factor. We factor via the difference of squares theorem. (x+ (2 + +(e + (x + We combine like terms in each factor.
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
Quadratic Funtions
Transcribed Image Text:Factor + 14x + 40 by completing the square.
Half of the linear coefficient is:
So we expand the complete square (x +
D' = =² +
x +
This is our 'helper line' that will help with the main computation.
We start the main computation. The polynomial to be
factored is:
+ 14x + 40
We smuggle in the missing term for a
complete square:
We re-write the first three terms as a
x2 + 14x +
+40
complete square and combine the last
two terms.
We re-write the subtracted number as
(x +
a square as we get ready to factor.
We factor via the difference of squares
theorem.
(x +
)(x +
O-O
(x +
We combine like terms in each factor.
So the final answer is
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