CCSS.HSA1QE - A rectangular sheet of newspaper has an area of ( 5x^{2} + 15 x +10) ft^{2}. If the width is 5(x+1) ft what is the length of the sheet of the newspaper?

Sangeetha Pulapaka (last edited 4 years ago) (Expert, Educator @Qalaxia)

Step 1: Remember the formula for area of a rectangle

area = length \times width

length = \frac{area}{width}

Plug in the values of area and width

length = \frac {5x^{2} +15 x + 10}{5(x+1)}

Step 2: Factorise the quadratic function using one of the four methods of factorisation

Recall how to factorise the quadratic expression by grouping

Remember what a gcf is

Take out the gcf in the quadratic function 5x^{2} +15 x +10

we get

5(x^{2} + 3x +2)

Now factorising x^{2} +3x+2 we get

x^{2} + 2x + x + 2

Recall what is a greatest common factor (gcf)

Taking out the gcf in first two terms

x( x + 2) + 1 ( x+ 2)

(x+1)(x+2)

So the area will be 5(x+1)(x+2)

Step 3: Plug in the area and width

length = \frac{5(x+1)(x+2)}{5(x+1)}

length = (x+2) ft