Recall that the degree of a polynomial is the same as the highest degree of the terms in the polynomial. We write deg|P(x)| to
Let P(x)=anxn+an-1xn-1+…+a2x2+a1x and Q(x)=bmxm+bm-1xm-1+…+b2x2+b1x be two polynomials such that deg|Q(x)|≥deg|P(x)|. Then the
Example Let P(x)=-6x4+5x3-2x+5, Q(x)=x5+x3+x, and R(x)=2x5+x4-x2 Find each sum. A) P(x)+Q(x) B) P(x)+R(x) C) R(x)+Q(x) A)
Pleasant and interesting travel to you
33.27M
Category: mathematicsmathematics

Equality of two polynomials

1.

Polynomi
als

2.

Equality of
two
polynomials

3.

123456789101112
131415161718192
0
If two or more
terms contain
the same
variable (s) they
are called like
terms.

4.

For example,5x y and 3x y
like terms.
2 2
However, 7xy and 4 x y
are not like terms .
2
2

5.

Equal polynomials
Two polynomials are
equal if and only if
they have like terms
with the same
coefficients

6.

For example, P
x, y 5x
and Q x, y 8 x y 5 x
equal polynomials.
2
2
y 3xy 8x y
2
y 3xy
2 2
2
are

7.

8. Recall that the degree of a polynomial is the same as the highest degree of the terms in the polynomial. We write deg|P(x)| to

mean the degree of a
polynomial function P(x). For example, if
P(x)=x3-x2+1, then deg|P(x)| =3.

9. Let P(x)=anxn+an-1xn-1+…+a2x2+a1x and Q(x)=bmxm+bm-1xm-1+…+b2x2+b1x be two polynomials such that deg|Q(x)|≥deg|P(x)|. Then the

sum of these polynomials is defined as
P(x)+Q(x)=bmxm+…+(an+bn)xn+(an-1+bn-1)xn1+…+(a +b )x2+(a +b )x+a +b
2
2
1
1
0
0

10. Example Let P(x)=-6x4+5x3-2x+5, Q(x)=x5+x3+x, and R(x)=2x5+x4-x2 Find each sum. A) P(x)+Q(x) B) P(x)+R(x) C) R(x)+Q(x) A)

Example
Let P(x)=-6x4+5x3-2x+5, Q(x)=x5+x3+x, and R(x)=2x5+x4-x2
Find each sum.
A) P(x)+Q(x)
B) P(x)+R(x)
A) P(x)+Q(x)=x5-6x4+6x3-x+5
B)P(x)+R(x)= 2x5-5x4+5x3- x2 -2x+5
C) R(x)+Q(x)= 3x5-x4+x3- x2 +x
C) R(x)+Q(x)

11.

Travel to the world

12.

Ticket to travel to the
world

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

26. Pleasant and interesting travel to you

Pleasant and interesting travel to
Pleasant and interesting travel
you
to you
English     Русский Rules