factor the following: 9x²-66x+21
9x²-66x+21
always look for common factors first, thus resulting i smaller numbers
= 3(3x^2 - 22 + 7)
= 3(3x - 1)(x - 7)
To factor the quadratic expression 9x² - 66x + 21, we need to look for two binomials with the form (ax + b)(cx + d) that multiply together to give us the original expression.
First, let's look at the coefficient of the x² term, which is 9. This means that our binomials will have an x term of the form (3x)(3x) or (9x)(x).
Next, we need to look at the constant term, which is 21. We need to find two numbers that when multiplied together equal 21, and when added or subtracted, give us the coefficient of the x term, which is -66.
The possible factor pairs of 21 are (1, 21) and (3, 7).
Since we have a negative coefficient for the x term, we will use the factor pair that gives us a negative sum.
The combination that satisfies this condition is 3 and 7, which when multiplied together is 21 and when subtracted gives us -66.
So, we can factor the expression as:
9x² - 66x + 21 = (3x - 3)(3x - 7)
Therefore, the factored form of 9x² - 66x + 21 is (3x - 3)(3x - 7).