GRADE 7 MATHEMATICS Quarter 2 Week 1 Addition and Subtraction of Polynomials

[Music] hi everyone good day i'm miss marijini gonzalez grade 7 mathematics teacher before we proceed do not forget to like share and hit the subscribe button and notification bell for updates about our videos for our today's lesson we are going to discuss addition and subtraction of polynomials our main objective here is to add and subtract polynomials so polynomials for the information of everybody polynomial is a special kind of algebraic expression where the exponent of a variable is a whole number and polynomial came from the word poly which means many and nomial which means terms the polynomial is in the form of a x to the n where a is any real number x is a variable and n is the non-negative integer this polynomial is a polynomial in one variable n is a degree of ax ax alone it has a degree of 1 and the constant a has a degree of 0. so to understand more clearly about polynomial let us define some important terms in polynomials first we have the word degree degree refers to the highest degree of its term in a polynomial a polynomial is in the standard form if it is written in the descending order from highest to lowest [Music] and we have the so-called coefficient it refers to the integer in front of the letter or variable note that if a variable has no coefficient therefore the coefficient is one so as i've said a while ago a polynomial is in the standard form if its terms are arranged from the term with the highest degree up to the term with the lowest degree [Music] so if the given polynomial is in the standard form we will consider the first term as the leading term and the numerical coefficient of the leading term is called the leading coefficient and the exponent or the sum of the exponents of the variable in the leading term is called the degree of the polynomial so for our example let's have the given polynomial 4x squared minus seven x to the fifth power minus two x cubed plus three x minus ten obviously the given polynomial is not yet in the standard form so we have to look for the highest exponent so what do you think is the highest exponent yes you are correct 5 is the highest exponent and that is the degree so therefore the given polynomial in the standard form will be negative seven x to the fifth power minus two x cubed plus four x squared plus three x minus 10 [Music] and the leading term for that polynomial is negative 7 x to the fifth power and of course the leading coefficient will be negative 7. and as as we said the degree is five so now let's have a warm-up so let us try to write the given polynomial in the standard form negative five x squared plus eight x cubed plus six so what is the highest exponent yes you are correct it's three so therefore we will have now eight x to the third power minus five x squared plus six as the standard form of the given polynomial so this time let us find the leading term so what is the leading term yes you are correct very good 8 x to the third power and the leading coefficient is yes you're right it's eight and the degree of course is no other than three so let's have another example [Music] negative seven x squared plus twelve x minus four again what is the highest exponent yes very good it's two so as you can see and obviously the given polynomial is already in the standard form so therefore the leading term is what yes you're correct negative seven x is squared so therefore the leading coefficient is negative seven and the degree is two very good so now let's proceed to our lesson so we have important thing to remember so first in adding polynomials remember to simply add or combine like terms and like terms are constant or terms with the same variables raised to the same power or powers and to subtract polynomials remember that subtracting is the same as adding the opposite and to find the opposite of a polynomial you must write the opposite of each term in the second polynomial which is considered the subtrahend so again in adding polynomials we simply add like terms just add the coefficient and not the variables and it is more easier to add polynomials using the vertical form [Music] so now let us rewrite the given polynomials first polynomial 2x squared plus x minus 5 plus the second polynomial x squared plus x plus six so as you can see our two polynomials are already aligned so all we have to do now is to combine like terms so two x squared plus x squared will give you three x squared x plus x will give you two x and negative five plus six will give you positive one so therefore the sum of the given polynomials two x squared plus x minus five plus x squared plus x plus six is three x squared plus two x plus one and now we're going to move in subtraction of [Music] polynomials remembering subtracting polynomials again we're going to write the polynomials in vertical form and align like terms [Music] and remember also to change the sign of every term in the second polynomial so in this case we're also going to apply the so-called k c f oops that's not kfc as i've said k c f it means keep change and flip so let's have an example again it is more easier to solve or subtract polynomials in vertical form so quantity of 8x to the fourth minus 3x squared minus 11x minus 3 minus negative 13 x to the fourth minus three x squared plus two x minus seventeen so first step is to keep the first polynomial which is eight x to the fourth minus three x squared minus eleven x minus three second step is to change the minus sign to addition sign so our third step is to flip the sign of each term of the second polynomial so the first term of the second polynomial is negative 13 x to the fourth power so it will become positive 13 x to the fourth power then the second term of the second polynomial is negative 3x squared so it will become positive 3x squared then the third term of the second polynomial is positive 2x so it will become negative 2x and the last term is negative 17 so it will become positive 17 and the final answer is 21 x to the fourth power minus 13 x plus 14. so do you want to have some more okay let's have more examples so for our solution for these two examples [Music] we have for number one do you want to have some more example okay let's have these last two examples for the solution for number one we have thirteen x squared plus nine x plus four plus eight x squared plus seven x minus ten [Music] make sure that the given polynomials are aligned or line up with the same term so for the final answer in number one we have 21x squared plus 16x minus 6. for the solution of the second example 5x squared minus 2x cubed plus 12 minus 2x cubed plus 6s squared minus 3 remember to apply the kcf the keep change and flip so for the solution we're going to keep the first polynomial 5x squared minus 2x cubed plus 12 then change the subtraction to addition and the last one is to flip the sign of each term of the second polynomial so we will have now negative 2 x cubed plus 5x squared plus 12 plus negative 2x cubed minus six x squared plus three so we have now as the final answer negative four x cubed minus x squared plus fifteen so that's all for today children thank you and always remember to add love and subtract hatred again this is miss margin e gonzalez grade 7 mathematics teacher [Music]

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Length: 12min 47sec (767 seconds)

Published: Sun Feb 07 2021