Welcome to Westonci.ca, your ultimate destination for finding answers to a wide range of questions from experts. Join our platform to connect with experts ready to provide precise answers to your questions in various areas. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A 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
We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.
