Test: Polynomials Basics - Grade 10 MCQ

A polynomial of degree 2 is called quadratic polynomial.
Quadratic polynomials are of the form ax²+bx+c and it can contain at most three terms namely ax², bx and c. Thus, we can say that a quadratic polynomial can have at most three terms.
Similarly, a polynomial of degree 1 is called linear polynomial and a polynomial of degree 3 is called cubic polynomial.

Degree of a non-zero constant polynomial is zero.
We can see that given polynomial 7 contain only one term and that is constant. 7 can also be written as 7x⁰.
Hence degree of 7 is zero.

Degree is the highest power of the variable in any polynomial.

Let p(x) = mx + n

Put x = a

p(a) = ma + n = 0

So, a is zero of p(x).

Let α be the third zero.

Given that two zeroes of the cubic polynomial are 0.

Sum of the zeroes = α + 0 + 0 = -b/a

α = -b/a

x² + 7x + 10 = x² + 2x + 5x + 10

= x(x + 2) + 5(x + 2)

= (x + 2)(x + 5)

Therefore, -2 and -5 are the zeroes of the given polynomial.

The product of the zeroes of the cubic polynomial ax³ + bx² + cx + d is -d/a.

Degree of the zero polynomial is not defined.
Zero polynomial is denoted by 0, and degree for that is not defined.

Coefficient is the number which is multiplied with respective variable.
In the given polynomial 6x⁴ + 3x² + 8x + 5, there is not an expression containing x³. So we can write 6x⁴ + 3x² + 8x+5 as 6x⁴ + 0x³ + 3x² + 8x + 5. We can see that 0 is multiplied with expression x³, so coefficient of x³ is 0.

For an expression to be a polynomial, exponent of variable has to be whole number.
can be written as x-1/2. We can see that exponent of x is -1/2 which is not whole number (W = {0, 1, 2, 3…}). Hence, is not a polynomial.