Answer:
1A) Degree: 3
1B) 4 terms
1C) [tex]7x^3-5x^2-4x+10[/tex]
2A) [tex]3m-5n+1[/tex]
2B) [tex]-2b^3-3b+3[/tex]
Step-by-step explanation:
The given polynomial is [tex]-4x+7x^3-5x^2+10[/tex]
Let us rewrite the polynomial in decreasing powers of x.
This gives us the expression;
[tex]7x^3-5x^2-4x+10[/tex]-----> This is called the standard form.
So let us answer the question:
A) The degree is the exponent of the first term when the polynomial is written in standard form.
Degree: 3
B) The terms are separated by + or - signs.
Number of terms: 4
C) Standard form: [tex]7x^3-5x^2-4x+10[/tex]
2A) The given expression is [tex](7m-2n)+(-3n-4m+1)[/tex]
We expand using the distributive property to get:
[tex]7m-2n-3n-4m+1[/tex]
We regroup the terms to get:
[tex]7m-4m-2n-3n+1[/tex]
We simplify to obtain:
[tex]3m-5n+1[/tex]
2B) The given expression is [tex](b^3-2b+4)-(3b^3+b-1)[/tex]
[tex]b^3-2b+4-3b^3-b+1[/tex]
Regroup the terms to get:
[tex]b^3-3b^3-2b-b+4-1[/tex]
We simplify to get:
[tex]-2b^3-3b+3[/tex]
