8-5 Factoring Trinomials When A = 1

1. Factor:

m squared plus 13 m plus 42

(m + 1)(m+13)

(m + 6) (m + 7)

(m + 10) (m + 3)

(m - 6)(m - 7)

The correct answer is (m + 6) (m + 7). This is because when we multiply these two binomials, we use the distributive property to multiply each term in the first binomial by each term in the second binomial. This results in four terms: m * m, m * 7, 6 * m, and 6 * 7. Simplifying these terms, we get m^2 + 7m + 6m + 42, which can be further simplified to m^2 + 13m + 42. Therefore, (m + 6) (m + 7) is the correct answer.

Explanation

The correct answer is (m + 6) (m + 7). This is because when we multiply these two binomials, we use the distributive property to multiply each term in the first binomial by each term in the second binomial. This results in four terms: m * m, m * 7, 6 * m, and 6 * 7. Simplifying these terms, we get m^2 + 7m + 6m + 42, which can be further simplified to m^2 + 13m + 42. Therefore, (m + 6) (m + 7) is the correct answer.

2. The area of a rectangle is given by the trinomial

x squared minus 11 x plus 18

. What are the possible dimensions of the rectangle?

The possible dimensions of the rectangle are not specified in the question. Therefore, the question is incomplete and it is not possible to determine the possible dimensions of the rectangle.

Explanation

The possible dimensions of the rectangle are not specified in the question. Therefore, the question is incomplete and it is not possible to determine the possible dimensions of the rectangle.

3. Which binomial is a factor of

k squared minus space 12 k space plus thin space 36

?

K + 3

K + 4

K - 6

K - 12

The binomial k - 6 is a factor of the given expression because when we substitute k = 6 into the expression, we get 0 as the result. This means that (k - 6) is a factor of the expression, as it makes the expression equal to zero.

Explanation

The binomial k - 6 is a factor of the given expression because when we substitute k = 6 into the expression, we get 0 as the result. This means that (k - 6) is a factor of the expression, as it makes the expression equal to zero.

4. Which binomial is a factor of

a squared plus 7 a space minus space 30

?

A + 7

A - 6

3a + 10

A - 3

The binomial "a - 3" is a factor of the given expression. This means that when we divide the given expression by "a - 3", the quotient will be a polynomial.

Explanation

The binomial "a - 3" is a factor of the given expression. This means that when we divide the given expression by "a - 3", the quotient will be a polynomial.

5. Factor:

x squared minus 15 x y minus 54 y squared

not-available-via-ai

Explanation

not-available-via-ai