Question

Please solve the following polynomial functions for the variable as defined.

Answer 1

1:

x=2,3

2:

x≈−0.60700729

Answer:

Polynomials are expressions with one or more terms with a non-zero coefficient. A polynomial can have more than one term. In the polynomial, each expression in it is called a term.

Solution given:

1:x²-5x+6

let

f(x)=x²-5x+6

It is polynomial in one variable x

According to definition of variable

f(x)=0

substituting value of f(x)

x²-5x+6=0

Doing middle term factorisation

6=3*2*1

remember that in front of constant term is positive sigh

so we need to add factor of 6 to get 5

I.e. 3+2=5

substituting (3+2) in place of 5

x²-(3+2)x+6=0

x²-3x-2x+6=0

taking common from each two term

x(x-3)-2(x-3)=0

again taking common

(x-3)(x-2)=0

either

x-3=0

x=3

or

x-2=0

x=2

2:

4x³-3x²+2

let

f(x)=4x³-3x²+2

It is polynomial in one variable x.

According to definition of variable

f(x)=0

we cannot solve it by factoring so solving by graph

Graph is in attachment.

The solution is the x-value of the point of intersection.

x≈−0.60700729

Answer 2

Answer:

1. x = 2, 3

2. x = -0.607007

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

1. Brackets
2. Parenthesis
3. Exponents
4. Multiplication
5. Division
6. Addition
7. Subtraction

• Left to Right

Algebra I

• Terms/Coefficients
• Factoring
• Solving by graphing

Step-by-step explanation:

1.

Step 1: Define

x² - 5x + 6

Step 2: Solve for x

1. Factor:                                                                                                               (x - 2)(x - 3) = 0
2. Solve:                                                                                                                x = 2, 3

2.

Step 1: Define

Identify

4x³ - 3x² + 2

Step 2: Graph

See Attachment

Step 3: Solve for x

Where the graph crosses the x-axis would be the solution to the polynomial.

x = -0.607