Question

The width of a box is 1 cm less than its length. The height of the box is 9 cm greater than the length. The dimensions can be represented by x, x − 1, and x + 9. Multiply the dimensions and find the greatest common factor of the terms.

A. x^4
B. x^3
C. x^2
D. x

Answer 1

Answer:

D. x

Step-by-step explanation:

The dimensions are:

$x(x-1)(x+9)$

We multiply out the dimensions to obtain;

$x(x^2+9x-x-9)$

$x(x^2+8x-9)$

$x^3+8x^2-9x$

The terms are:

$x^3$

$8x^2=2^3x^2$

$-9x=-3^2x$

The highest common factor is the product of the least powers of th comon factors.

TheHCF is x

Answer 2

Answer:

Option D) x  

Step-by-step explanation:

Let x be the length of the box. Then, we are given that:

Width of box = $x-1$

Height of box = $x + 9$

The volume of box is obtained by multiplying these terms.

$x\times (x-1)\times (x+9)\\=(x^2 - x)\times (x+9)\\=(x^2\times x) + (x^2\times 9) -(x\times x)- (x\times 9)\\=x^3 + 9x^2 - x^2 - 9x\\= x^3 + 8x^2 - 9x$

Now, in order to find greatest common factor:

$x^3 + 8x^2 - 9x\\=x(x^2 + 8x - 9)$

Hence, x is the greatest common factor of the terms of the expression as x could be taken as common from each term of the expression obtained.