Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.
\({ 4x }^{ 2 }-3x+7\)

3

(a)

Write the coefficients of x² in the following:
2 + x² + x

3

(a)

Give one example each of a binomial of degree 35, and of a monomial of degree 100.

3

(a)

Write the degree of the following polynomials:
5x³ + 4x² + 7x

3

(a)

Classify the following as linear, quadratic and cubic polynomials:
r²

3

(a)

Find p(0), p(1) and p(2) for each of the following polynomials:
p(x) = x³

3

(a)

Find p(0), p(1) and p(2) for each of the following polynomials:
p(x) = (x - 1) (x + 1)

3

(a)

Verify whether the following are zeroes of the polynomial, indicated against them.
\(p(x)={ 3x }^{ 2 }-1,x=-\frac { 1 }{ \sqrt { 3 } } ,\frac { 2 }{ \sqrt { 3 } } \)

3

(a)

Find the remainder when \(x^3+3x^2+3x+1\) is divided by \(x\)

3

(a)

Find the remainder when \(x^3+3x^2+3x+1\) is divided by \(x+\pi\)

3

(a)

Determine which of the following polynomials has (x+1) a factor:  \(x^4+3x^3+3x^2+x+1\)

3

(a)

Determine which of the following polynomials has (x+1) a factor: \({ x }^{ 3 }-{ x }^{ 2 }-(2+\sqrt { 2 } )x+\sqrt { 2 } .\)

3

(a)

Factorise \({ 3 }x^{ 2 }-x-4\)

3

(a)

Factorise \(x^3-2x^2-x+2\)

3

(a)

Factorise  \(x^3+13x^2+32x+20\)

3

(a)