Question

The area of a football field is x2 + 3x – 10. Find the length and width of the field in terms of x.

Answer 1

The area of a football field is
\[x^2+3x-10\]
Let's find factors of this, one factor is length other is width
\[x^2+3x-10\]
Note that the coefficient of x^2 is 1
and the term without x is -10
We have to find factors of \(1\times -10=-10\) such that their sum is +3
5 and -2 satisfy this
\[(5)+(-2)=3\]
and
\[5 \times -2=10\]
so 3x can be written as
\[3x=5x-2x\]
we have
\[x^2+5x-2x-10\]
take x common from the first two terms and -2 from the last two terms
\[x(x+5)-2(x+5)\]
now take (x+5) common from the terms
\[(x+5)(x-2)\]
So we have found the two factors
(x+5) is the length
(x-2) is the width
\[x(

Answer 2

Thanks :)

Answer 3

The area of a football field is
x2+3x−10

Let's find factors of this, one factor is length other is width
x2+3x−10

Note that the coefficient of x^2 is 1
and the term without x is -10
We have to find factors of 1×−10=−10 such that their sum is +3
5 and -2 satisfy this
(5)+(−2)=3

and
5×−2=10

so 3x can be written as
3x=5x−2x

we have
x2+5x−2x−10

take x common from the first two terms and -2 from the last two terms
x(x+5)−2(x+5)

now take (x+5) common from the terms
(x+5)(x−2)

So we have found the two factors
(x+5) is the length
(x-2) is the width
\[x(