Polynomials (Edexcel IAL Maths): Exam Questions

Expand

(i) $3(x^{2}+4)$

(ii) $5y^{2}(y-6)$

(iii) $xy(2x+7y)$

Expand and simplify

(i)$(2x+3)(x-4)$

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

(iii) $(y-1)(y-2)^{2}$

(i) A triangle has base $(6x+8)$ and height $2x$ units. Find an expression for the area of the triangle.

(ii) A cube has side length of $\left(3 x - 5\right)$ units. Find an expression for the volume of the cube.

Factorise

(i) $5x-20$

(ii) $2y^{2}-4y$

(iii) $8xy^{2}+6xy$

Factorise

(i) $x^{2}+5x+4$

(ii) $x^{2}-7x+12$

(iii) $x^{2}+5x-14$

(iv) $x^{2}-81$

Factorise

(i) $4x^{2}-4x-15$

(ii) $3x^{3}+11x^{2}-4x$

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 $(3x+y)(2x-3y)(x-2y)=ax^{3}+bx^{2}y+cxy^{2}+dy^{3}$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 $(2x-3y)^{2}(y-2x)=ax^{3}+bx^{2}y+cxy^{2}+dy^{3}$, 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) $(x+3)^{2}+(x-2)(2x+4)$

(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 $(ax+by)(2x+y)(x-3y)=8x^{3}+cx^{2}y+dxy^{2}-9y^{3}$ , 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 $x^{5}y-xy^{5}.$