Welcome to Westonci.ca, the Q&A platform where your questions are met with detailed answers from experienced experts. Join our platform to get reliable answers to your questions from a knowledgeable community of experts. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields 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 stopping by. We are committed to providing the best answers for all your questions. See you again soon. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.
