a. The value of n that makes the polynomial a perfect square trinomial is n = 9/4
b. The trinomial expresssed as the square of a binomial is (y - 3/2)²
What is a trinomial?
A trinomial is a mathematical expression that contains three terms.
What is a perfect square trinomial?
A perfect square trinomial is a polynomial of the form (a + b)²
a. How to find the value of n that makes the polynomial a perfect square trinomial?
Since we have the polynomial y² - 3y + n. We want to express it as a perfect square trinomial.
To be a perfect square trinomial, y² - 3y + n = (y - a)² = y² - 2ay + a²
Comapring both expressions, -2a = -3 and n = a²
So, a = 3/2 and n = a²
= (3/2)²
= 9/4
So, y² - 3y + n = y² - 3y + 9/4
Thus, the value of n that makes the polynomial a perfect square trinomial is n = 9/4
b. How to express the trinomial as a the square of a binomial?
Since we have the trinomial y² - 3y + 9/4
Expressing it a a binomial, we have
y² - 3y + 9/4 = y² - 3y + (3/2)²
= (y - 3/2)²
So, the trinomial expresssed as the square of a binomial is (y - 3/2)²
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