Factor completely what does that mean
25a2 - 30a + 9
It means look for monomial factors that give 25a^2 - 30a + 9
when they are multiplied together.
(5y -3)*(5y -3) = (5y -3)^2 will work
(5a-3)(5a-3)
does this work?
Sorry, I substituted y for a.
Another senior moment
Factoring a polynomial means to express it as a product of its factors. In other words, we want to rewrite the polynomial without any common factors or any terms that can be further simplified.
To factor the quadratic polynomial 25a^2 - 30a + 9, we can follow these steps:
Step 1: Look for any common factors in all three terms of the polynomial. In this case, we observe that all three terms have a common factor of 5. Factoring out 5 gives us:
5(5a^2 - 6a + 9/5)
Step 2: Now, our focus is on factoring the expression inside the parentheses (5a^2 - 6a + 9/5). Since it is a quadratic polynomial, we need to find two binomials that multiply together to give us this expression.
Step 3: Let's try factoring the quadratic expression using the ac-method. First, multiply the leading coefficient (5) by the constant term (9/5), which gives us 45/5 = 9.
Step 4: Next, we need to find two numbers that multiply to give 9 and add up to the coefficient of the linear term (-6). The numbers -3 and -3 satisfy these conditions because (-3)(-3) = 9 and -3 + (-3) = -6.
Step 5: Now, we can rewrite the linear term (-6a) using the two numbers we found: (-3a) + (-3a).
Step 6: Substituting these results back into the original expression, we have:
5[5a^2 + (-3a) + (-3a) + 9/5]
Step 7: Group the terms and factor by grouping:
5[(5a^2 - 3a) + (-3a + 9/5)]
Step 8: Factor out a common term from each group:
5[a(5a - 3) - (3a - 9/5)]
Step 9: Simplify further if needed.
5[(5a - 3)(a - 3/5)]
Therefore, the completely factored form of the given quadratic polynomial is:
5(5a - 3)(a - 3/5)