Mathematics, 30.01.2020 18:02 timothymoles

2p2 -15p + 25 =

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

Answers: 1

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Answer from: townykid96

(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: $\boxed{ \ a(p + q) + b(p + q) \rightleftharpoons (a + b)(p + q) \ }$

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:

$\boxed{ \ ax^2 + bx + c = 0, \ \ \ \ \ a \neq 0 \ }$ 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: $\boxed{ \ x^2 = a, \ then \ x = \pm \sqrt{a} \ }$ Completing the square: $\boxed{ \ x^2 + bx + \bigg({\frac{b}{2}} \bigg)^2 = \bigg( x + \frac{b}{2} \bigg)^2 \ }$ Using the quadratic formula: $\boxed{ \ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \ }$ Learn moreFactoring methods A word problem of a quadratic equation What are the coordinates of the vertex of the graph?
2p2 -15p + 25 = (p - 5)(2p - 5) (p - 5)(2p + 5) (p + 5)(2p - 5) (2p - 15)(p + 5)

2p2 -15p + 25 = (p - 5)(2p - 5) (p - 5)(2p + 5) (p + 5)(2p - 5) (2p - 15)(p + 5)

Answer from: Quest

The academic affairs council is the highest expert body processing academic affairs, as stipulated by the university statutes. specialist aaro häkkinen (educational policy) took part in the council’s meeting. the agenda of the meeting included bachelors’ feedback, the timing of pedagogical studies, the grant system for tuition fees, the standardisation of administrative practices for internships and the situation of foreign-language and multilingual master’s programmes.

Answer from: Quest

im pretty sure its

(8,15)

step-by-step explanation:

Use the substitution method to solve the system of equations.choose the correct ordered pair.y=5x+7x

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2p2 -15p + 25 =

(p - 5)(2p - 5)
(p - 5)(2p + 5)
(p + 5)(2p - 5)
(2p -...

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