Question

Write two polynomials p(x)and q(x) such that the degree of both p(x)and q(x) is3 but degree of the polynomial p(x)+q(x) is 1.​

Answer 1

Answer:

Degree of p(x)=8

⇒ Degree of q(x)=m

⇒ Degree of p(x)q(x)=104

Since degrees are nothing but highest exponents to the variables multiplying two variables with powers of 8 and m, we will get

⇒8+m=104

⇒m=96.

Answer 2

Answer:

Two such polynomials shall be-

1) p(x) = 5$x^{3}$ + 16

q(x) = - 5 $x^{3}$ - 15

2) p(x) = 18$x^{3}$ + 10

q(x) = - 18 $x^{3}$ - 9

Step-by-step explanation:

The two polynomials of degree 3 will be-

1) p(x) = 5$x^{3}$ + 16

q(x) = - 5 $x^{3}$ - 15

p(x) + q(x)= (5$x^{3}$ + 16) + ( - 5 $x^{3}$ - 15)

               = 5$x^{3}$ + 16 - 5 $x^{3}$ - 15 = 16 - 15 = 1

Similarly, another two such polynomial can be-

2) p(x) = 18$x^{3}$ + 10

q(x) = - 18 $x^{3}$ - 9

p(x) + q(x)= (18$x^{3}$ + 10) + ( - 18 $x^{3}$ - 9)

               = 18$x^{3}$ + 10 - 18 $x^{3}$ - 9 = 10 - 9 = 1

Thus, Two such polynomials shall be-

1) p(x) = 5$x^{3}$ + 16

q(x) = - 5 $x^{3}$ - 15

2) p(x) = 18$x^{3}$ + 10

q(x) = - 18 $x^{3}$ - 9

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