List the terms and coefficients. 8x3 – 4x2 + 3
Write using positive exponents only. b–2
Factor completely. 3(x – 2)2 – 3(x – 2) – 6
State which method should be applied as the first step for factoring the polynomial.
To find the terms and coefficients in the expression 8x^3 - 4x^2 + 3, we can identify the terms by looking at the individual parts of the expression. The terms in this expression are:
Term 1: 8x^3 (coefficient: 8, exponent: 3)
Term 2: -4x^2 (coefficient: -4, exponent: 2)
Term 3: 3 (coefficient: 3)
Therefore, the terms in the expression are 8x^3, -4x^2, and 3, and their corresponding coefficients are 8, -4, and 3.
To write the expression b^(-2) using positive exponents only, we can apply the rule that states that any base raised to a negative exponent can be rewritten as the reciprocal of the base raised to the positive exponent. Using this rule, b^(-2) can be rewritten as 1/b^2.
So, b^(-2) using positive exponents only is 1/b^2.
To factor the expression 3(x - 2)^2 - 3(x - 2) - 6 completely, we can start by noticing that we have a common factor of (x - 2) in all terms.
We can factor out (x - 2) from each term:
3(x - 2)^2 - 3(x - 2) - 6 becomes:
(x - 2) ( 3(x - 2) - 3 - 6)
Simplifying further:
(x - 2) (3x - 6 - 3 - 6) = (x - 2) (3x - 15)
Now we have factored the expression completely to (x - 2) (3x - 15).
To determine the method that should be applied as the first step for factoring the polynomial, we need to consider the specific polynomial in question. There are several methods to factor polynomials, including factoring out common factors, factoring by grouping, factoring trinomials, and factoring special products.
The first step for factoring a polynomial depends on the structure of the polynomial. If the polynomial has a common factor among all its terms, factoring out the common factor would be the first step. In other cases, identifying any special patterns or using other methods might be more appropriate as the first step.
Without the specific polynomial being mentioned, it is not possible to determine the exact method that should be applied as the first step for factoring the polynomial.