Answer:
<h2>What is factoring? </h2>
Factoring is finding what to multiply to find an expression. It is like splitting expression into a multiplication of simplified expression.
<h2>Why is it useful to try to factor out the GCF first when factoring?</h2>
Greatest common factor or GCF of two numbers is the largest number that divides evenly in both numbers, GCF works the same in polynomials, which divide the expression evenly .
<h2>Explain the relationship between factoring and multiplying polynomials. Give an example to help explain</h2>
Factoring take away the multiplication, to factorize a polynomial it means take apart what is multiplied. the best example is a²+b²+2ab ( multiplied)
factorize :(a+b)(a+b) take apart what is multiplied
<h2>Factor x^2-25, 3x^2-12x-15, and x^3+2x^2+3x+6</h2>
x²-25 =(x+5)(x-5)
3x²-12x-15 = 3(x²-4x-5) GCF=3
3(x-5)(x+1)
x³+2x²+3x+6 (x+2) common factor
(x+2)(x²+3)
<h2>What are the key features needed to graph a polynomial function?</h2>
the key features are the vertex, axis of symmetry, x and y intercept
<h2>Explain how to find these key features to sketch a rough graph of a polynomial function</h2>
parabola : y=ax²+bx+c
ex: 3x²-12x-15
find vertex (h,k)
h=-b/2a =-(-12)/2(3)=2
k=f(h)=f(2)=3(2)²-12(2)-15
k=12-24-15=-27
vertex=(2,-27)
x intercept is when the graph =0 (y=0)
y intercept when x=0 then y= the constant c and where the graph cross the y axis
axis of symmetry is the x of the vertex: is a line about which a parabola is symmetrical and vertical when the axis of symmetric is vertical.
<h2>Why would someone want to factor a polynomial? Provide real world examples of different questions we can answer or facts we can determine from factoring a polynomial.</h2>
factor a polynomial helps us understand more about equations,factoring helps us rewrite the polynomial into simpler expression.
example from real life:
A homeowner has a back yard and wants to turn it to garden beds so he can plant his vegetables, he wants to fill it with dirt he needs 240 cubic feet to fill it the length is 4 feet than the width , and the height is 4
solve:
length=W+4
height=1/3 w
V=length* width* height
240=(w+4)(w)(4)
351= 4w²+16w
4w²+16w-240=0
take 4 as common factor
4(w²+4w-60)
now factorize:
4(w-6)(w+10)=0
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