Polynomials (Edexcel International A Level (IAL) Maths: Pure 1): Exam Questions

Expand and simplify

(i) $5(x^2-3)+3x(x+8)$

(ii) $4y^2-2y^2(y-8)$

(iii) $2x^2(2x+4)-3x(2x-7)$

Expand and simplify $y(2x+2)(7-x)$.

A rectangle has side lengths of $(3x-2y+5)$ units and $(x+3y-1)$ units. Find an expression for the area of the rectangle in terms of $x$ and $y$.

Expand and simplify

(i) $(3x+2)(2x+6)$

(ii) $(3-p)(p-2)$

(iii) $(y+5{)}^2(y-8)$

Given that $(3x+y)(2x-3y)(x-2y)=a{x}^3+b{x}^{2}y+cx{y}^2+d{y}^3$where  $a$,$b$,$c$ and $d$ are constants, find the values of $a$,$b$,$c$ and $d$.

Factorise

(i) $5x^2-7x-6$

(ii) $2x^2+2x-12$

(iii) $15x^2+13x+2$

(iv) $9x^2-16$

Factorise completely $3x^3-51x^2+126x.$

Expand and simplify $(2-x)(3x+1)(x+1).$

A square has side lengths of $(5x-2y+3)$ units. Find an expression for the length of the diagonal of the square in terms of $x$and $y$ .

Expand and simplify

(i) $(x-2)(3x+2)(2x+6)$

(ii) $(2-p{)}^2(p+3)$

(iii) $(y+6{)}^3$

Given that $(2x-3y{)}^2(y-2x)=a{x}^3+b{x}^{2}y+cx{y}^2+d{y}^3$, where $a$,$b$,$c$ and $d$ are constants, find the values of $a$,$b$,$c$ and $d$.

Factorise

(i) $-x^2+26x–169$

(ii) $10x^2-11x+3$

(iii) $4x^2-25y^2$

(iv) $18x^3-6x^2-12x$

Factorise completely $15x^3+19x^2-10x.$

Expand and simplify

(i) $(x+3{)}^2+(x-2\left)\right(2x+4)$

(ii) $3x(8-x)(3x-3)$

(iii) $(p+6{)}^4$

Expand and simplify $(x+y)(x-y)(y-x)(-x-y).$

A cuboid has a length of $(2x-3y+3)$units , a width of $(2x+3y-3)$units, and a height of $(x-y)$units. Find an expression for the volume of the cuboid in terms of $x$ and $y$.

Given that $(ax+by)(2x+y)(x-3y)=8x^3+c{x}^{2}y+dx{y}^2-9y^3$ , where $a$,$b$,$c$ and $d$ are constants, find the values of $a$,$b$,$c$ and $d$.

Factorise

(i) $12x^2-17x-5$

(ii) $10x^3+55x^2+60x$

(iii) $15x^3-6x^2-9x$

Factorise completely $x^{5}y-x{y}^5.$