Question

Guys can you please help me with The Question #15 A). and B). of The Factoring for me, please? :)

Answer 1

See below ~

Explanation:

`\textsf {Question 15(A) :}`

`\textsf {Given :}`

`\implies \mathsf {7x^(2) - 13x + 6}`

`\textsf {Splitting the middle term :}`

`\implies \mathsf {7x^(2) - 7x - 6x + 6}`

`\textsf {Grouping common terms :}`

`\implies \mathsf {7x(x - 1) - 6(x - 1)}`

`\textsf {Dimensions are :}`

• 
  `\textsf {Length = (7x - 6)}`
• 
  `\textsf {Width = (x - 1)}`

`\textsf {Question 15(B) :}`

`\textsf {Formula for perimeter :}`

`\implies \mathsf {2 * (length + width)}`

`\implies \mathsf {2 * (7x - 6 + x - 1)}`

`\implies \mathsf {2 * (8x-7)}`

`\textsf {Substitute x = 8 :}`

`\implies \mathsf {2 * [8(8)-7]}`

`\implies \mathsf {2 * (64-7)}`

`\implies \mathsf {2 * 57}`

`\implies \mathsf {Perimeter = 114 cm}`

`\textsf {Now substitute x = 8 in the area formula :}`

`\implies \mathsf {7(8)^(2) - 13(8) + 6}`

`\implies \mathsf {7(64) - 104 + 6}`

`\implies \mathsf {448 - 98}`

`\implies \mathsf {Area = 350 cm^(2)}`

Answer 2

(a) width = (x - 1)

length = (7x - 6)

(b) Area = 350 cm²

Perimeter = 114 cm

Explanation:

Part (a)

Given equation:
`7x^2-13x+6`

⇒ a = 7, b = -13, c = 6

Find 2 two numbers that multiply to ac and sum to b: -6 and -7

Rewrite b as the sum of these 2 numbers:

`\implies 7x^2-7x-6x+6`

Factorize the first two terms and the last two terms separately:

`\implies 7x(x-1)-6(x-1)`

Factor out the common term (x - 1):

`\implies (7x-6)(x-1)`

Therefore:

• width = (x - 1)
• length = (7x - 6)

Part (b)

Substitute the given value of x = 8 into the equations to find the area and perimeter:

`\begin{aligned}x=8cm \implies \textsf{Area} & = 7(8)^2-13(8)+6\\& = 448-104+6\\& = 350 \sf \:\: cm^2\end{aligned}`

`\begin{aligned}\textsf{Perimeter} & = 2(\sf width+length)\\& =2[(x-1)+(7x-6)]\\ & = 2[(8-1)+(7(8)-6)]\\ & = 2[7+(56-6)] \\& = 2(7+50)\\& = 2(57)\\ & = 114 \sf \:\: cm\end{aligned}`