Polynomials Class 9th
Download as PPTX, PDF0 likes353 views
The remainder theorem states that if a polynomial p(x) is divided by the linear polynomial x - a, the remainder is equal to p(a). The proof involves writing p(x) as the product of (x - a) and a quotient polynomial q(x), plus a remainder r(x). Since the degree of r(x) must be less than the degree of x - a, which is 1, r(x) must be a constant. Therefore, the remainder is equal to the value of p(x) when x is substituted with a.
Polynomials Class 9th
- 1. polynomials
- 2. Remainder theorem • Let p(x) be any polynomial of degree greater than or equal to one and let a be any real number . If p(x) is divide by the linear polynomial x-a then the remainder is p(a) • Proof • Let p(X) be any polynomial with degree greater than or equal to suppose • P(X) is divide by x-a the quotient is q(x) and the remainder is r(x) i.e., • P(x)=(x-a)q(x)+r(x) • The degree of x-a is 1 and the degree of r(x) is less than the degree of x-a the degree of r (x)=0 this means that r(x) is constant, say r.. • P(x)=(x-a)q(x)+r
- 3. Splitting the middle terms • Let its factor be (p x + q) and (r x + s) then • Ax2 +b x+ c=(p x +q)( r x + s)=pr x2+(p s+ q r ) x + q s • The coefficients of x2 a=pr • The coefficients of x b=p s +q rwe get c = gs •