Westonci.ca offers quick and accurate answers to your questions. Join our community and get the insights you need today. Get expert answers to your questions quickly and accurately from our dedicated community of professionals. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
Sagot :
Answer:
[tex]\frac{1}{4}[/tex] (2x + 11)²
Step-by-step explanation:
given
x²+ 11x + [tex]\frac{121}{4}[/tex]
Convert the coefficients of the x²- term and the x- term to fractions with denominator of 4, that is
1 = [tex]\frac{4}{4}[/tex] and 11 = [tex]\frac{44}{4}[/tex]
Rewrite the expression as
[tex]\frac{4}{4}[/tex] x² + [tex]\frac{44}{4}[/tex] x + [tex]\frac{121}{4}[/tex] ← factor out [tex]\frac{1}{4}[/tex] from each term
= [tex]\frac{1}{4}[/tex] (4x² + 44x + 121 )
factorise 4x² + 44x + 121
Rewrite 4x² as (2x)² and 121 as 11²
= (2x)² + 44x + 11²
Consider the perfect square trinomial
a² + 2ab + b² = (a + b)²
Now check that the middle term 44x is two times the product of the numbers being squared in the first and third terms
2 × 2x × 11 = 44x
Then with a = 2x and b = 11
4x² + 44x + 121 = (2x + 11)²
Finally
x² + 11x + [tex]\frac{121}{4}[/tex] = [tex]\frac{1}{4}[/tex] (2x + 11)²
Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.
