Explain How do you find factors of the polynomial

Mathematics

1 answer:

balandron [24]3 years ago

4 0

Answer:

Step-by-step explanation:

"For a polynomial, no matter how many terms it has, always check for a greatest common factor (GCF) first. Literally, the greatest common factor is the biggest expression that will go into all of the terms. Using the GCF is like doing the distributive property backward.

If the equation is a trinomial — it has three terms — you can use the FOIL method for multiplying binomials backward.

If it’s a binomial, look for difference of squares, difference of cubes, or sum of cubes.

Finally, after the polynomial is fully factored, you can use the zero product property to solve the equation."

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Rewrite the function by completing the square (vertex form)<br><br> f(x)=x^2+16x-46

insens350 [35]

Answer:

$\large\boxed{f(x)=(x+8)^2-110}$

Step-by-step explanation:

$\text{The vertex form of equation}\ y=ax^2+bx+c:\\\\y=a(x-h)^2+k\\\\\text{We have the equation:}\\f(x)=x^2+16x-46=x^2+2(x)(8)-46=x^2+2(x)(8)+8^2-8^2-46\\\\\text{use}\ (a+b)^2=a^2+2ab+b^2\to x^2+2(x)(8)+8^2=(x+8)^2\\\\f(x)=(x+8)^2-64-46=(x+8)^2-110$