2p2 -15p + 25 =

(p - 5)(2p - 5)
(p - 5)(2p + 5)
(p + 5)(2p - 5)
(2p - 15)(p + 5)

(p - 5)(2p - 5), in the first option

The Problem:

Which are the factors of 2p² - 15p + 25 = ?

The Process:

The problem we have this time is how to solve factoring a quadratic equation.

First Way

2p² - 15p + 25 = 2p² - 10p - 5p + 25

                       = 2p(p - 5) - 5(p - 5)

                       = (2p - 5)(p - 5) or (p - 5)(2p - 5)

Recall this:

Second Way

Allow me to introduce the "temporary quadratic" method. This is a unique way! Look carefully below.

2p² - 15p + 25 ⇒ multiply 2 as the coefficient of the p² term with 25 as a constant.

2 x 25 = 50.

Then, find two factors of 50 which if added are -15 as the coefficients of the term p.

We get the following: - 5 x - 10 = 50, i.e., -5 and -10.

Both are positioned in factor brackets. Simultaneously we place the term of 2p in both brackets as a sum operation with both factors. This is properly the uniqueness of this method!

2p² - 15p + 25 = "(2p - 10)(2p - 5)"

Because we call it the "temporary quadratic" method, simplify the factors in parentheses if it can still be done.

Thus, we get 2p² - 15p + 25 = (p - 5)(2p - 5), i.e. the two terms of (2p - 10) divided by 2.

Third Way

Let us check one by one of the answer options available.

(p - 5)(2p - 5)  = p(2p - 5) - 5(2p - 5)

                      = 2p² - 5p - 10p + 25

                      = 2p² - 15p + 25 (yes, this is correct)

(p - 5)(2p + 5)  = p(2p - 5) - 5(2p + 5)

                      = 2p² - 5p - 10p - 25

                      = 2p² - 15p - 25

(p + 5)(2p - 5)  = p(2p - 5) + 5(2p - 5)

                      = 2p² - 5p + 10p + 25

                      = 2p² + 5p + 25

(2p - 15)(p + 5) = 2p(p + 5) - 15(p + 5)

                      = 2p² + 10p - 15p - 75

                      = 2p² - 5p - 75

_ _ _ _ _ _ _ _ _ _

Take a look at this example:

3m² - 10m - 8 = ?

3m² - 10m - 8 = ?

Notes:

is a quadratic equation in standard form.

Methods of solving quadratic equations include:

step- i d k and i d c : )

you: : 0

bye

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.