[Music] hello makawaomat in this video we will discuss about remainder theorem remainder theorem given a polynomial p of x with of divisor in the form x minus c the remainder denoted by r of the polynomial is given by r is equal to p of c where p of c is obtained by substituting the value indicator c to the polynomial remainder is the number left in dividing two expression whose quotient is not exact for example determine the remainder of x x to the power power plus 4 x cubed minus x squared minus 16x minus 4 when divided by x minus 2. so you under nothing identify your number indicator 910 or your value indicator so r is equal to p of 2 and then after that so papadi positive 2 so that will become 2 to the fourth plus 4 times the quantity of 2 cubed minus 2 squared minus 16 times two minus four and then uh evaluate nothing is isa so two raised to four that is sixteen and two cubed that is uh eight times four k at 32 and 2 squared that is 4 and the negative 16 times 2 that is 32 minus 4 and then simplifying along 16 plus 32 minus 4 minus 32 minus four is equal to eight so a big sub n young remainder so x to the fourth plus four x cubed minus x squared minus 16 x minus four divided by x minus two the remainder is eight next find the remainder when five x squared minus two x plus one is divided by x plus two using the remainder theorem and the synthetic division so using the remainder qrm uh value indicator from the device source so on divisor net is x plus 2 so yum value indicator nothing is negative 2. so subtitles indicator in that tens okay 5 x squared minus 2 x plus 1 so palliative negative 2 human x not n and that is 5 times negative 2 squared minus 2 times negative 2 plus 1 and after that simplify so negative 2 squared that is 4 negative 2 times negative 2 that is positive 4 plus 1 and 5 times 4 that is 20 plus 4 plus n plus 1 that is equal to 25 so a big sub n young remainder capacity divide and see five x squared minus two x plus one k x plus two you are nothing remainder is twenty five so that is using the remainder to your m okay pounding the monkey pug using the synthetic division 25 link processor using the synthetic division connecting and that is five negative two and one then coordinating value indicator not n that is negative two and then positive is a step bring down five and then multiply five to value indicator that is five times negative two the answer is negative ten negative two plus negative tender that is negative twelve negative twelve times negative two that is positive 24 then add 1 plus 24 the answer is 25. so mykitarinaten using the synthetic division 25 the num uh nothing remainder or using the synthetic division or by using the remainder theorem remainder another so find the remainder when p of x is equal to two x to the fourth plus five x cubed plus two x squared minus seven x minus fifteen is divided by two x minus three so using the two method again so first using the remainder theorem identifying value indicator nut and since this is two x minus three sophanog value indicator in the top ready nothing to equate by zero or uh two x minus three can write as two times the quantity of x minus three over two so that will be so you muggling value indicator nothing is three over two so subtitle polynomials so polytechnic x and three over two that will be two times three over two raised to four plus five times three over two cubed plus two times the quantity of three two squared minus seven times three over two minus fifteen and after that simplifying like not n so 3 over 2 to the fourth power that is 81 over 16 okay so that is 3 times 3 times 3 times 3k 81 and this is 2 times 2 times 2 times 2 and again 16 and then 3 over 2 cubed that is 27 over 8 3 over 2 squared that is 9 over 4 and negative 7 times 3 over 2 that is 21 over 2 minus 15. and then uh simplify again 2 times 81 over 16 that is 81 over 8 5 times 27 over 8 that is 135 over 8 plus 2 times 9 over 4 that is 18 over 4 minus 21 over 2 minus 15 that is equal to 6. so tingnan not nothing nothing using the synthetic division so that is 2 5 2 and negative 7 and negative 15 okay negative 7 so na putu lag na di negative so well animal time missing term soy tu la hation bring down two and then multiply two times three over two so two times three over two that is two divided that's 1 times 3 the answer is 3 then add 5 plus 3 8 and then 8 times 3 over 2 or 8 divide 2 4 times 3 the answer is 12. 2 plus 12 6 14 14 times 3 over 2 or 14 uh divide by 2 that's 7 times 3 the answer is 21 negative 7 plus 21 the answer is 14 then 14 times 3 over 2 that is 21 okay so negative 15 plus 21 the answer is six so nothing using the remainder theorem and the synthetic division the answer is the same so parenthesis uh six thank you for watching this video i hope you learned something don't forget to like subscribe and hit the bell button but updated ko for more video tutorial this is your guide in learning your mod lesson your walmart channel