Week 5 – Solving Quadratic Equations

In the fifth week of Pre-Calculus 11 we began the Quadratics unit. This week we reviewed factoring polynomials and learned a few new strategies about factoring.

What is Factoring? Factoring is taking an expression and breaking it up into pieces so that you can multiply those pieces together to get the original number. For example, the number 9 can be factored to $9*1$ or $3*3$ . To factor polynomials it’s helpful to think about the acronym CDPEU.

C- Is there anything COMMON within the terms?

Ex. $7x^3+14x$

$7x(x^2+2)$

In the expression above, the greatest common factor is $7x$ because $7x$ can factor into both of the terms.

D- Is there a DIFFERENCE of squares? A difference of squares requires the expression to be a binomial, the terms have to be subtracting (difference) and both of the terms have to be perfect squares.

Ex. $100x^2-4$

$(10x+2)(10x-2)$

P- Does the expression have the right PATTERN? To factor a trinomial the expression has to have the correct pattern by having $x^2$ , x, and a number.

Ex. $3+y-x$

The expression above cannot be factored because it does not have the pattern $x^2$ , x, and a number. It also does not have any common terms.

Ex. $x^2+7x+12$

$1*12=12$ $1+12=13$

$2*6=12$ $2+6=8$

$3*4=12$ $3+4=7$

$(x+4)(x+3)$

The trinomial above can be simplified because it has the pattern we are looking for. To find out what numbers I needed to use I listed all of the factors of 12. After listing the factors of 12 I figured out which one of the factors adds up to the middle term (7).

E– Is the expression EASY to factor? To determine the complexity of an expression you have to check if the $x^2$ has a coefficient. If the $x^2$ does not have a coefficient then it is an easy expression to factor.

Ex. $x^2-12x+20$

$-1*-20=20$ $-1+-20=-21$

$-2*-10=20$ $-2+-10=-12$

$-4*-5=20$ $-4+-5=-9$

$(x-10)(x-2)$

U- Is the expression UGLY to factor? A trinomial that’s difficult to factor is when the $x^2$ has a coefficient.

Ex. $2x^2-9x+4$

$(2x-1)(x-4)$

To factor the expression above I multiplied the first and the last term together. After multiplying the two terms together I got $8x^2$ , then I began to list all the factors of $8x^2$ . After figuring out the factors of $8x^2$ I chose the two factors that add up to -9x. Lastly, I placed the two factors in the chart above and found the GCF of the terms that were horizontal and vertical from each other.

M	T	W	T	F	S	S
			1	2	3	4
5	6	7	8	9	10	11
12	13	14	15	16	17	18
19	20	21	22	23	24	25
26	27	28	29	30	31

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