Sure, let's go through each question step-by-step.
### Q9. Which of the following is a constant polynomial?
A constant polynomial is a polynomial that does not contain any variables (no [tex]\( x \)[/tex] terms). It is simply a constant number.
Let's examine the given options:
- a) [tex]\( 4x + 1 \)[/tex]: This expression has a variable term [tex]\( 4x \)[/tex], so it is not a constant polynomial.
- b) [tex]\( 3 \)[/tex]: This expression does not have any variable terms; it is simply a constant number.
- c) [tex]\( 2x^2 \)[/tex]: This expression contains the variable term [tex]\( x^2 \)[/tex], so it is not a constant polynomial.
Therefore, among the given options, option b) [tex]\( 3 \)[/tex] is the constant polynomial.
Answer for Q9: 3
### Q10. Which of the following is an example of a quadratic polynomial?
A quadratic polynomial is a polynomial of degree 2, which means the highest power of the variable [tex]\( x \)[/tex] in the polynomial is 2. A general form of a quadratic polynomial is [tex]\( ax^2 + bx + c \)[/tex], where [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex] are constants, and [tex]\( a \neq 0 \)[/tex].
Let's examine the given options:
- a) [tex]\( 4x + 1 \)[/tex]: This is a linear polynomial since the highest power of [tex]\( x \)[/tex] is 1.
- b) [tex]\( 3 \)[/tex]: This is a constant polynomial as discussed in Q9.
- c) [tex]\( 2x^2 \)[/tex]: This expression has the term [tex]\( x^2 \)[/tex], which makes it a quadratic polynomial. It fits the general form [tex]\( ax^2 \)[/tex] where [tex]\( a = 2 \)[/tex].
Therefore, among the given options, option c) [tex]\( 2x^2 \)[/tex] is the quadratic polynomial.
Answer for Q10: [tex]\( 2x^2 \)[/tex]
