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2 years ago

Which is a factor of x2 – 9x + 14? x – 9 x – 2 x + 5 x + 7

Mathematics

2 answers:

Nadya [2.5K]2 years ago

7 0

Answer:

The binomial: (x-2) (second option of the list) is a factor of the given trinomial

Step-by-step explanation:

You are looking for two binomial factors of the form; (x+a) and (x+b), with values "a" and "b" such that:

Their product "a times b" results in: "+14" (the numerical term in the initial trinomial $x^2-9x+14$ ,

and their combining "a+b" results in "-9" (the coefficient in the middle term of the trinomial)

Such number "a" and "b" are: "-2" and "-7".

We can see by multiplying the binomials formed with these numbers:

(x-2) and (x-7) that their product indeed renders the original trinomial:

$(x-2) (x-7)= x^2-7x-2x+14=x^2-9x+14$

therefore, the binomials (x-2) and (x-7) are factors of the given trinomial.

The only one shown among the four possible options is then: (x-2)

agasfer [191]2 years ago

3 0

Answer:

x-2

Step-by-step explanation:

Let's factor x2−9x+14

x2−9x+14

The middle number is -9 and the last number is 14.

Factoring means we want something like

(x+_)(x+_)

Which numbers go in the blanks?

We need two numbers that...

Add together to get -9

Multiply together to get 14

Can you think of the two numbers?

Try -2 and -7:

-2+-7 = -9

-2*-7 = 14

Fill in the blanks in

(x+_)(x+_)

with -2 and -7 to get...

(x-2)(x-7)

Answer:

(x−2)(x−7)

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General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality

Algebra I

Coordinates (x, y)
Functions
Function Notation
Terms/Coefficients
Anything to the 0th power is 1
Exponential Rule [Rewrite]: $\displaystyle b^{-m} = \frac{1}{b^m}$
Exponential Rule [Root Rewrite]: $\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}$

Calculus

Derivatives

Derivative Notation

Derivative of a constant is 0

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Derivative Rule [Chain Rule]: $\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)$

Step-by-step explanation:

Step 1: Define

$\displaystyle y = \sqrt{x - 3}$

$\displaystyle y' = \frac{1}{2}$

Step 2: Differentiate

[Function] Rewrite [Exponential Rule - Root Rewrite]: $\displaystyle y = (x - 3)^{\frac{1}{2}}$
Chain Rule: $\displaystyle y' = \frac{d}{dx}[(x - 3)^{\frac{1}{2}}] \cdot \frac{d}{dx}[x - 3]$
Basic Power Rule: $\displaystyle y' = \frac{1}{2}(x - 3)^{\frac{1}{2} - 1} \cdot (1 \cdot x^{1 - 1} - 0)$
Simplify: $\displaystyle y' = \frac{1}{2}(x - 3)^{-\frac{1}{2}} \cdot 1$
Multiply: $\displaystyle y' = \frac{1}{2}(x - 3)^{-\frac{1}{2}}$
[Derivative] Rewrite [Exponential Rule - Rewrite]: $\displaystyle y' = \frac{1}{2(x - 3)^{\frac{1}{2}}}$
[Derivative] Rewrite [Exponential Rule - Root Rewrite]: $\displaystyle y' = \frac{1}{2\sqrt{x - 3}}$

Step 3: Solve

Find coordinates

x-coordinate

Substitute in y' [Derivative]: $\displaystyle \frac{1}{2} = \frac{1}{2\sqrt{x - 3}}$
[Multiplication Property of Equality] Multiply 2 on both sides: $\displaystyle 1 = \frac{1}{\sqrt{x - 3}}$
[Multiplication Property of Equality] Multiply √(x - 3) on both sides: $\displaystyle \sqrt{x - 3} = 1$
[Equality Property] Square both sides: $\displaystyle x - 3 = 1$
[Addition Property of Equality] Add 3 on both sides: $\displaystyle x = 4$