Remainder theorem and Factor theorem.pptx

Grade 10 lesson in Remainder theorem and Factor theorem. Grade 10 lesson in Remainder theorem and Factor theorem. Grade 10 lesson in Remainder theorem and Factor theorem. Grade 10 lesson in Remainder theorem and Factor theorem. Grade 10 lesson in Remainder theorem and Factor theorem. Grade 10 lesson in Remainder theorem and Factor theorem. Grade 10 lesson in Remainder theorem and Factor theorem. Grade 10 lesson in Remainder theorem and Factor theorem. Grade 10 lesson in Remainder theorem and Factor theorem. Grade 10 lesson in Remainder theorem and Factor theorem. Grade 10 lesson in Remainder theorem and Factor theorem. Grade 10 lesson in Remainder theorem and Factor theorem. Grade 10 lesson in Remainder theorem and Factor theorem. Grade 10 lesson in Remainder theorem and Factor theorem. Grade 10 lesson in Remainder theorem and Factor theorem. Grade 10 lesson in Remainder theorem and Factor theorem. Grade 10 lesson in Remainder theorem and Factor theorem. Grade 10 lesson in Remainder theorem and Factor theorem. Grade 10 lesson in Remainder theorem and Factor theorem. Grade 10 lesson in Remainder theorem and Factor theorem. Grade 10 lesson in Remainder theorem and Factor theorem. Grade 10 lesson in Remainder theorem and Factor theorem. Grade 10 lesson in Remainder theorem and Factor theorem. Grade 10 lesson in Remainder theorem and Factor theorem. Grade 10 lesson in Remainder theorem and Factor theorem. Grade 10 lesson in Remainder theorem and Factor theorem. Grade 10 lesson in Remainder theorem and Factor theorem. Grade 10 lesson in Remainder theorem and Factor theorem. Grade 10 lesson in Remainder theorem and Factor theorem. Grade 10 lesson in Remainder theorem and Factor theorem. Grade 10 lesson in Remainder theorem and Factor theorem. Grade 10 lesson in Remainder theorem and Factor theorem. Grade 10 lesson in Remainder theorem and Factor theorem. Grade 10 lesson in Remainder theorem and Factor theorem. Grade 10 lesson in Remainder theorem and Factor theorem. Grade 10 lesson in Remainder theorem and Factor theorem. Grade 10 lesson in Remainder theorem and Factor theorem. Grade 10 lesson in Remainder theorem and Factor theorem. Grade 10 lesson in Remainder theorem and Factor theorem. Grade 10 lesson in Remainder theorem and Factor theorem. Grade 10 lesson in Remainder theorem and Factor theorem. Grade 10 lesson in Remainder theorem and Factor theorem. Grade 10 lesson in Remainder theorem and Factor theorem. Grade 10 lesson in Remainder theorem and Factor theorem. Grade 10 lesson in Remainder theorem and Factor theorem. Grade 10 lesson in Remainder theorem and Factor theorem. Grade 10 lesson in Remainder theorem and Factor theorem. Grade 10 lesson in Remainder theorem and Factor theorem. Grade 10 lesson in Remainder theorem and Factor theorem. Grade 10 lesson in Remainder theorem and Factor theorem. Grade 10 lesson in Remainder theorem and Factor theorem. Grade 10 lesson in Remainder theorem and Factor theorem. Grade 10 lesson in Remainder theorem

1. Remainder theorem and factor theorem Shahanie dulnuan Grade 10

2. Factor theorem is a special kind of polynomial  remainder theorem  that links the  factors  of a polynomial and its zeros. The factor theorem removes all the known zeros from a given polynomial equation and leaves all the unknown zeros. The resultant polynomial has a lower degree in which the zeros can be easily found. WHAT IS FACTOR THEOREM?

3. The factor theorem states that if f(x) is a polynomial of degree n greater than or equal to 1, and 'a' is any real number, then (x - a) is a factor of f(x) if f(a) = 0. In other words, we can say that (x - a) is a factor of f(x) if f(a) = 0. Let us now understand the meaning of some concepts related to the factor theorem. FACTOR THEOREM STATEMENT

4. 1.) p (y)= y 2  + 2y − 15 = (y+5)(y−3) ⇒ y =−5 and y = 3 Thus, this second-degree polynomial y 2  + 2y − 15 has two zeros or roots which are - 5 and 3. CHECKED: y=-5 P(y)=y 2  + 2y − 15 P(y)=(-5) 2  + 2(-5) − 15 P(y)= CHECKED: y=3 P(y)=y 2  + 2y − 15 P(y)=(3) 2  + 2(3) − 15 P(y)= Using the Factor Theorem To Factor a Second-Degree Polynomial

5. 2.) Check whether (y + 5) is a factor of 2y 2  + 7y – 15 or not. Given that, y + 5 = 0. Then, y = - 5.  P(y) = 2y 2  + 7y – 15 P(-5) = 2 (-5) 2  + 7(-5) – 15 P(-5) = 0 Using the Factor Theorem To Factor a Second-Degree Polynomial

6. 3.) Let's show that (y+2) is a factor of y3 − 6y2 − y + 30 and then find the remaining factors Using the Factor Theorem To Factor a Third-Degree Polynomial

7. 3y 4  + y 3  – y 2  + 3y + 2 ACTIVITY : SOLVING

8. 3y 4  + y 3  – y 2  + 3y + 2 ACTIVITY : SOLVING Factors ( y + 1) is a factor of 3y 3 -2y 2 +y+2

9. The remainder after 2x 2 −5x−1 is divided by x−3 P(x) = 2x 2 −5x−1 P(x) = 2(3) 2 −5(3)−1 P(x) = 2

10. Factor Theorem 2y 2 +7y+6 2x 3 -3x 2 -11x+6 x 2 +12x+36 m 2 -10x+25 x 2 -4

11. Factor Theorem 2y 2 +7y+6 2x 3 -3x 2 -11x+6 x 2 +12x+36 m 2 -10x+25 x 2 -4 (y − 1) (y+2) (2y+3) (x+2) (2x-1) (x-3) (x + 6) (x+6) (m-5) (m+5) (x+2) (x+2)