Answer:
The correct matches as follows :
1) The product of a linear monomial and a linear monomial is a - quadratic monomial
2) The product of a quadratic monomial and a quadratic trinomial is a - quartic trinomial
3) The product of a linear monomial and a linear binomial - Quadratic binomial
Step-by-step explanation:
The correct matches as follows :
1) The product of a linear monomial and a linear monomial is a - quadratic monomial
Monomial is a linear expression having only term with degree 1 (variable)
- For Example : Let x and y be two monomials which is linear
- If we product the two linear monomials we get
- [tex]x\times x=x^2[/tex] which is a quadratic monomial
2) The product of a quadratic monomial and a quadratic trinomial is a - quartic trinomial
For example : Let [tex]x^2[/tex] be the Quadratic monomial has one term with degree 2 and [tex]x^2+2x+3[/tex] be the quadratic trinomial ( has 3 terms with degree)
- If we product the quadratic monomial and quadratic trinomial we have
- [tex]x^2\times (x^2+2x+3)=x^2(x^2)+x^2(2x)+x^2(3)[/tex]
- [tex]=x^4+2x^3+3x^2[/tex]
- Therefore [tex]x^2(x^2+2x+3)=x^4+2x^3+3x^2[/tex] which is a quartic trinomial has degree 4 with three terms
3) The product of a linear monomial and a linear binomial - Quadratic binomial
For example : Let x be the linear monomial and [tex]x^2+5[/tex] be the linear binomial has two terms with degree 1
- If we product the linear monomial and quadratic binomial we get
- [tex]x\times (x+5)=x(x)+x(5)[/tex]
- [tex]=x^2+5x[/tex]
- Therefore [tex]x\times (x+5)=x^2+5x[/tex] which is a quadratic binomial with degree 2
