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

Further explanation

The Problem:

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

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

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 - 12m + 2m - 8= 3m(m - 4) + 2(m - 4)This becomes (3m + 2)(m - 4)

3m² - 10m - 8 = ?

3 x (-8) = -24-24 = 2 x (-12), because 2 + (-12) = -103m² - 10m - 8 = "(3m + 2)(3m - 12)"This becomes (3m + 2)(m - 4)

Notes:

is a quadratic equation in standard form.

x is a variable  a, b, and c are real number coefficients the only c is called a constant (no variables)

Methods of solving quadratic equations include:

Factoring and using the zero product property: Using the square root property: Completing the square: Using the quadratic formula: Learn moreFactoring methods A word problem of a quadratic equation What are the coordinates of the vertex of the graph?

City A

Step-by-step explanation:

200 + 45 = 245

100 + 20 = 120

120 + 110 = 230

50 + 55 = 110

City A has the greatest tendency.