How to determine if a factor is a factor of a polynomial using factor theorem

👉 Learn about and how to apply the remainder and factor theorem. The remainder theorem states that f(a) is the remainder when the polynomial f(x) is divided by x - a. Thus, given a polynomial, f(x), which is to be divided by a linear binomial of form x - a, the remainder of the division is given by f(a).

The factor theorem is a special case of the remainder theorem which states that if f(a) = 0, then x - a is a factor of the polynomial f(x). Thus, given a polynomial, f(x), to see if a linear binomial of form x - a is a factor of the polynomial, we solve for f(a). If f(a) = 0, then x - a is a factor, and x - a is not a factor otherwise.

These two theorems help us understand how we better understand the relationship between a polynomial function, its factors, and the remainder. Using the theorem also can save us time from determining if we have a factor or zero of a polynomial without having to use division.

Organized Videos:
✅Remainder and Factor Theorem
✅Remainder and Factor Theorem | Learn About
✅How to apply the Remainder and Factor Theorem

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[ashcasper]

This was so much easier than doing what my teacher was trying to get us to do

[brainnn]

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[randomlygenius-BeCool]

Thanks, you explained me the topic that my teacher couldn't teach me for an hour 😢😊

[shaniai]

thank you so much this was much easier to understand 😀

[yourstruly.adelynne]

my teacher needs to take notes from this, i don’t understand his way of teaching 🙄

[blazezing]

3x-4;
how to get the answer of that if it is not like X-1 or x+1?

[ultragamerz]

This is very hard and ununderstandable

[katsaurusrex]

but isn’t it a little exhausting to sub in numbers to an expression and if it equals zero then you have the factor...like let’s say i look at an expression and think hmmm let me try 4 like i’m just picking out any numbers and if by subbing in 4 i get zero then i have my factor but if it doesn’t i have to then try another number. is there not a more efficient way of finding out factor

[Chelsea-yjhb]

So basically it is a factor if the remainder is zero

[notsodope]

If x+3 =0 then can't we divide the Polynomial through 0, as the value of the divisor x+3 is 0 hence we get the value of it . If we can divide it, then your answer is undefined . If you are not supposed to explain this, then reply the explanation of x+3=0.

[rlkrazy]

dues the god damn goat my teacher is so damn bad at teaching and would never go through this much effort

[CheekBustah]

wait why did he plug in a positive 3 instead of a negative?

[ScarySkyPuppy]

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