[Week 6]-Developing and applying the quadratic formula

What I have learned:

Solving quadratic equations by determining square roots.

Solving by completing the square when a=1.

Solving by completing the square when a≠1.

Solving a problem using a quadratic equation.

Solving a quadratic equation of the form .

Solving a quadratic equation of the form .

Using the quadratic formula to solve a problem.

Ex. Solve equation. Verify the solution.

Take the square root of each side.

X= ±√3

To verify, substitute each root in the given equation .

For x=√3,

=5

For x=-√3,

$ latex L.S.= 2(-√3)^2-1 $

=5

For each root, the left side is equal to the right side, so the solution is verified.

[Week 5]- Factoring Polynomial Expressions

What I have learn:

Determining whether a given binomial is a factor of a given trinominal.

Factoring trinomials with rational coefficients

Factoring using a trinomial pattern.

Factoring using the difference of squares pattern.

Ex. Is d-4 a factor of each trinomial? Justify the answer.

2d^2+6d-56

Use logical reasoning.

If d-4 is a factor, then trinomial can be written as:

(d-4) (ad+b)

2d^2+6d-56 = (d-4) (ad+b) Expand

2d^2+6d-56 = ad^2-(4a+b)d-4b

The d^2 – terms on both sides must be equal.

a=2

-4b= -56,

So b= 9

The trinomial would be: (d-4)(2d+9)

Expand to check the d- term.

(d-4)(2d+9) = 2d^2+6d-56

since this trinomial is equal to the given trinomial, d-4 is a factor of the given trinomial.

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