Factorising by a common factor questions with answers

Questions

1. Question 1A number as the common factor

   Factorise $28x - 20$ completely.

   Show the worked solution

   1. Step 1: Find the HCF of the numbers in front of the letters$\text{HCF of } 28 \text{ and } 20 =$ $4$
   2. Step 2: Is there a letter in every term?No letter is in every term.
   3. Step 3: Take the common factor outside; divide every term by it to fill the bracket$28x - 20 = 4(7x - 5)$
   4. Step 4: Check by expanding$4(7x - 5) = 28x - 20$ ✓
2. Question 2A letter as the common factor

   Factorise $3xy - 8x$ completely.

   Show the worked solution

   1. Step 1: Find the HCF of the numbers in front of the letters$\text{HCF of } 3 \text{ and } 8 =$ $1$
   2. Step 2: Is there a letter in every term?Every term has an $x$, so $x$ is a common factor too.
   3. Step 3: Take the common factor outside; divide every term by it to fill the bracket$3xy - 8x = x(3y - 8)$
   4. Step 4: Check by expanding$x(3y - 8) = 3xy - 8x$ ✓
3. Question 3A number and a letter

   Factorise $25x^{2} - 5x$ completely.

   Show the worked solution

   1. Step 1: Find the HCF of the numbers in front of the letters$\text{HCF of } 25 \text{ and } 5 =$ $5$
   2. Step 2: Is there a letter in every term?Every term has an $x$, so $x$ is a common factor too.
   3. Step 3: Take the common factor outside; divide every term by it to fill the bracket$25x^{2} - 5x = 5x(5x - 1)$
   4. Step 4: Check by expanding$5x(5x - 1) = 25x^{2} - 5x$ ✓
4. Question 4Three terms

   Factorise $10x^{2} + 12x - 2$ completely.

   Show the worked solution

   1. Step 1: Find the HCF of the numbers in front of the letters$\text{HCF of } 10, 12 \text{ and } 2 =$ $2$
   2. Step 2: Is there a letter in every term?No letter is in every term.
   3. Step 3: Take the common factor outside; divide every term by it to fill the bracket$10x^{2} + 12x - 2 = 2(5x^{2} + 6x - 1)$
   4. Step 4: Check by expanding$2(5x^{2} + 6x - 1) = 10x^{2} + 12x - 2$ ✓
5. Question 5Expand first, then factorise

   Expand and simplify $4x + 5(x + 3y + 9)$. Then factorise your answer completely.

   Show the worked solution

   1. Step 1: Expand the bracket first$4x + 5(x + 3y + 9) = 4x + 5x + 15y + 45$
   2. Step 2: Collect like terms$= 9x + 15y + 45$
   3. Step 3: Find the HCF of the numbers$\text{HCF} =$ $3$
   4. Step 4: Take the HCF outside; divide every term by it to fill the bracket$= 3(3x + 5y + 15)$
   5. Step 5: Check by expanding$3(3x + 5y + 15) = 9x + 15y + 45$ ✓