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

5

(a)

Factorise \(12x^2-7x+1\)

5

(a)

Use suitable identities to find the following products: \(\left( { y }^{ 2 }+\frac { 3 }{ 2 } \right) \left( { y }^{ 2 }-\frac { 3 }{ 2 } \right) ​​\)

5

(a)

Write the various coefficients in the following polynomials:
x⁷ - 3x⁵ + 4

5

(a)

How many terms are there in the following polynomials?
t - 7t² + 5 - t³

5

(a)

Find the value of the polynomial \(p(z)={ 3z }^{ 2 }=4z+\sqrt { 17 } \)  when z=3.

5

(a)

If \(x=-2\) is the root of the equation \(\sqrt { 2 } (x+p)=0\) and is also the zero the zero of the polynomial  \({ px }^{ 2 }+kx+2\sqrt { 2 } \) then find the value of k.

5

(a)

If x+2y=10, xy=15, find \(x^3+8y^3\).

5

(a)

Evaluate Using suitable identity: (999)³

5

(a)

Factorise: \(a^2+b^2-2(ab-ac+bc)\)

5

(a)