Question

v^(2)-10v+25 can be factorised to give an expression of the form (v+a)^(2), where a is an integer. Work out the value of a.

Answer 1

The value of a in the factorized expression v²-10v+25 = (v+a)² is -5.

Step-by-step explanation:

To factorize the expression v²-10v+25 into the form (v+a)², we need to find the value of a. Since the expression is already in the form of a perfect square trinomial, we can directly identify a as half of the coefficient of v, which is -10. Therefore, the value of a is -5.

Answer 2

The given expression v² - 10v + 25 can be factorized as (v + a)², where a is -5.

Step-by-step explanation:

To understand why, let's expand the expression (v + a)² and compare it with the given expression:

(v+a)² = (v + (- 5)) (v + (- 5))

= (v - 5) (v - 5)

= v² - 10v + 25

Here, the expansion of the squared binomial (v - 5)² results in the same expression as given, v² - 10v + 25. This confirms that the factorization of the original expression is indeed (v - 5)², and a in the expression (v+a)² is -5.

The process of factorization involves identifying a perfect square trinomial. In this case, v² - 10v + 25 recognized as the square of v - 5, where the constant term is the square of half the coefficient of the linear term. The factorization is a helpful algebraic technique that simplifies expressions and provides insight into the structure of the original polynomial.