[Week 5]- Factoring Polynomial Expressions

[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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