Factorising (OCR GCSE Maths: Higher): Exam Questions

Factorise                 $x^2+3x-10$

Factorise               $y^2-10y+16$

i) Factorise                $x^2-12x+27$

[2]

ii) Solve the equation          $x^2-12x+27=0$

[1]

Factorise     

                $y^2-100$

Factorise

                 $y^2+7y+6$

Factorise  $x^2+3x-4$

Factorise         $x^2-49$

Factorise fully

      $8a^2+12a$

Factorise         $y^2-y-2$

Factorise

                   $e^2+e-12$

Factorise fully       $3x{y}^2-6xy$

Factorise              $6m-9$

Factorise fully       $2x^{2}y+4x{y}^2$

Simplify fully      $\frac{n^7\times n^3}{n^6}$

Expand and simplify      $x\left(x-2\right)+2x\left(x+3\right)$

Factorise   $5y-15$

Factorise fully      $18ab+27a{b}^2$

Factorise completely          $8x^2+4xy$

Factorise completely         $6y^2-9xy$

Factorise fully          $9x^2-6xy$

Factorise   $y^2-2y-35$

Factorise  $x^2–11x+24$

Circle the factor of  $x^2-5x$

Factorise $x^2–64$ Circle your answer.

Factorise fully       $20x^2-5$

Factorise           $y^2-16$

Factorise         $2p^2-p-10$

Factorise          $4x^2-9$

Factorise        $a^2-b^2$

Hence, or otherwise, simplify fully ${\left(x^2+4\right)}^2-{\left(x^2-2\right)}^2$

i) Factorise. $x^2–{43}^2$

[1]

ii) Calculate. ${57}^2–{43}^2$

[2]

Factorise fully  $15b^{5}c-35b^3{c}^9$

Factorise fully   $15y^4+20u{y}^3$

 Factorise fully  $25a^4{c}^{7}d+45a^9{c}^{3}h$

Factorise fully $2e^2–18$

Factorise  $4c^2–9d^2$

Factorise  $6y^2–y–5$

Factorise  $3x^2+11x–20$

Factorise fully     $144-4x^2$

Factorise   $5x^2+6x-8$

Simplify fully  $\frac{x^2+9x+14}{x^2-4}$

Here is an identity.

$x^2–y^2=(x+y)(x–y)$

Use the identity to work out the value of  ${193}^2-7^2$.

You must show your working.

Factorise  $100a^2–81b^2$

Factorise   $3x^2+14x+8$