3x4 + 5x2 – 7x + 1 The polynomial above is in standard form. Standard form of a polynomial - means that the degrees of its monomial terms decrease from left to right.:

3x 4 + 5x 2 – 7x + 1 The polynomial above is in standard form. Standard form of a polynomial - means that the degrees of its monomial terms decrease from left to right.

State whether each expression is a polynomial. If it is, identify it.:

State whether each expression is a polynomial. If it is, identify it. 1) 7y - 3x + 4 trinomial 2) 10x 3 yz 2 monomial 3) not a polynomial

Find the degree of x5 – x3y2 + 4:

Find the degree of x 5 – x 3 y 2 + 4 0 2 3 5 10

3) Put in ascending order in terms of y: 12x2y3 - 6x3y2 + 3y - 2x:

3 ) Put in ascending order in terms of y : 12x 2 y 3 - 6x 3 y 2 + 3y - 2x -2x + 3y - 6x 3 y 2 + 12x 2 y 3 Put in ascending order: 5a 3 - 3 + 2a - a 2 -3 + 2a - a 2 + 5a 3

Write in ascending order in terms of y: x4 – x3y2 + 4xy – 2x2y3:

Write in ascending order in terms of y: x 4 – x 3 y 2 + 4xy – 2x 2 y 3 x 4 + 4xy – x 3 y 2 – 2x 2 y 3 – 2x 2 y 3 – x 3 y 2 + 4xy + x 4 x 4 – x 3 y 2 – 2x 2 y 3 + 4xy 4xy – 2x 2 y 3 – x 3 y 2 + x 4

Slide 26:

Remainder Theoram If p(x) a polynomial divided by a divisor g(x) of order 1(ex. x-a) And r(x) be the remainder then we can write P(x)=g(x).q(x) +r(x) P(x)= (x-a).q(x) + r(x) P(a)=r(a) Since g(x) is order of 1 hence r(x) will be order of zero(N.B: the order of remainder is always less than divisor.) Since the order of r(x) is zero hence it is constant. Suppose r(a)= r Therefore p(a)= r

Slide 30:

Q. On dividing the polynomial 4x² - 5x² - 39x² - 46x – 2 by the polynomial g(x) the quotient is x² - 3x – 5 and the remainder is -5x + 8.Find the polynomial g(x). Ans: p(x) = g(x).q(x)+r(x) let p(x) = 4x4 – 5x³ – 39x²– 46x – 2 q(x) = x²– 3x – 5 and r (x) = -5x + 8 now p(x) – r(x) = g(x).q(x) 4x² - 5x² - 39x² - 46x – 2 –(-5x+8)= (x² - 3x – 5 ).g(x) ∴ g(x) = 4x2 + 7x + 2

Slide 31:

Q. If the squared difference of the zeros of the quadratic polynomial x² + px + 45 is equal to 144 , find the value of p. Ans: Let two zeros are α and β where α > β According given condition ( α - β)2 = 144 Let p(x) = x² + px + 45 α + β = − p αβ = 45 now ( α + β)² = (α - β)² + 4 αβ (-P)² = 144 +180=324 Solving this we get p = ± 18

Slide 32:

Q. If α & ß are the zeroes of the polynomial 2x² ─ 4x + 5, then find the value of a. α² + ß² b. 1/ α + 1/ ß c. (α ─ ß)² d. 1/α² + 1/ß² e. α² + ß² Q. Obtain all the zeros of the polynomial p(x) = 3x4 ─ 15x³ + 17x² +5x ─6 if two zeroes are ─1/√3 and 1/√3 Q. If one zero of the polynomial 3x² - 8x +2k+1 is seven times the other, find the zeros and the value of k Q.If two zeros of the polynomial f(x) = x4 - 6x3 - 26x2 + 138x – 35 are 2±√3.Find the other zeros.

Slide 33:

Q. Find all zeroes of f(x) = 3x4+6x³-2x²-10x-5, if two of its zeroes are √ 5/3 and -√5/3. Since √ 5/3 and -√5/3. are zeroes of f(x). Therefore (x- √ 5/3 )(x+-√5/3) = (x²- 5/3) is a factor of f(x). After dividing f(x) by (x²- 5/3), we get

Slide 34:

As (x²+2x+1) = ( x+1)² Therefore for obtaining other zeroes of f(x) ,we put (x+1)² = 0 , Therefore x= -1 and -1 Hence zeroes of f(x) is are √ 5/3 and -√5/3. 1 and -1.

Slide 35:

Alternative Method: Say the other roots are α and β Therefore √ 5/3 -√5/3+α +β=-6/3=-2 α +β=-2……………….(i) Again√ 5/3 (-√5/3).α.β=-5/3 α.β=5/3 Using the algebraic identity α -β=………….… (ii) Solving (i) and (ii) we can find the other two roots

Slide 36:

Find zeros third degree polynomial equation, x³ - 2x² + 2x - 1 = 0 Let P(x) = , x³ - 2x² + 2x – 1 P(1) = (1) 3 - 2(1) 2 + 2(1) - 1 = 0 Since P(1) = 0, x - 1 is the factor of P(x). Long Division Method: x 3 - 2x 2 + 2x - 1 = (x - 1)(x 2 + 6x + 5 ) x 2 + 6x + 5 = x 2 + 5x + x + 5 = x(x + 5) + (x + 5) = (x + 1)(x + 5 ) x 3 - 2x 2 + 2x - 1 = (x - 1)(x + 1)(x + 5) = 0 Hence Zeros of the cubic equation are 1, -1, -5.

Slide 37:

Question : If two zeroes of the polynomial are find other zeros = x² + 4 − 4x − 3 = x² − 4x + 1 is a factor of the given polynomial For finding the remaining zeroes of the given polynomial, we will find the quotient by dividing

Slide 38:

= = Or x = 7 or −5 Hence, 7 and −5 are also zeroes of this polynomial.

You do not have the permission to view this presentation. In order to view it, please
contact the author of the presentation.

Send to Blogs and Networks

Processing ....

Premium member

Use HTTPs

HTTPS (Hypertext Transfer Protocol Secure) is a protocol used by Web servers to transfer and display Web content securely. Most web browsers block content or generate a “mixed content” warning when users access web pages via HTTPS that contain embedded content loaded via HTTP. To prevent users from facing this, Use HTTPS option.