(x-1).jpeg "(x-6)(x-1)")
Factoring and Expanding (x-6)(x-1)
This expression represents the product of two binomials: (x-6) and (x-1). We can work with this expression in two ways: expanding it to get a polynomial, or factoring a polynomial to get this expression.
Expanding (x-6)(x-1)
To expand this expression, we can use the FOIL method:
- First: Multiply the first terms of each binomial: x * x = x²
- Outer: Multiply the outer terms of the binomials: x * -1 = -x
- Inner: Multiply the inner terms of the binomials: -6 * x = -6x
- Last: Multiply the last terms of each binomial: -6 * -1 = 6
Now, combine the terms: x² - x - 6x + 6
Finally, simplify by combining like terms: x² - 7x + 6
Therefore, the expanded form of (x-6)(x-1) is x² - 7x + 6.
Factoring x² - 7x + 6
If we are given the polynomial x² - 7x + 6, we can factor it into the product of two binomials.
Here's how:
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Find two numbers that multiply to give the constant term (6) and add up to the coefficient of the x term (-7).
These numbers are -6 and -1.
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Write the factored form using these numbers.
(x - 6)(x - 1)
Therefore, the factored form of x² - 7x + 6 is (x - 6)(x - 1).
Summary
- Expanding (x-6)(x-1) results in the polynomial x² - 7x + 6.
- Factoring x² - 7x + 6 gives us the expression (x - 6)(x - 1).