Question

Find a value for y for which the expression (1-y)(3-y)(6-y) has each given value

i. -70

ii. 120

Answer 1

• i. y = 8, ii. y = -2

Explanation:

• (1 - y)(3 - y)(6 - y) = -70

We can see the divisors are 2 and 3 apart.

i.

Factorize -70 so that divisors are 2 and 3 apart:

• - 70 = (- 2)*(- 5)*(- 7)

The smallest one is 1 - y and -7:

• 1 - y = -7
• y = 1 + 7
• y = 8

ii

Factorize 120 so that divisors are 2 and 3 apart:

• 120 = 3*5*8

The smallest one is 1 - y and 3:

• 1 - y = 3
• y = 1 - 3
• y = -2

Answer 2

`\\ \tt\Rrightarrow (1-y)(3-y)(6-y)=-70`

`\\ \tt\Rrightarrow -y(1+1)(3+1)(6+1)=-70`

`\\ \tt\Rrightarrow y(2)(4)(7)=70`

`\\ \tt\Rrightarrow y(56)=70`

`\\ \tt\Rrightarrow y=(70)/(56)`

`\\ \tt\Rrightarrow y=(5)/(4)`

#2

`\\ \tt\Rrightarrow (1-y)(3-y)(6-y)=120`

`\\ \tt\Rrightarrow -y(1+1)(3+1)(6+1)=120`

`\\ \tt\Rrightarrow -y(2)(4)(7)=120`

`\\ \tt\Rrightarrow 56y=-120`

`\\ \tt\Rrightarrow y=(-120)/(56)`

`\\ \tt\Rrightarrow y=(-15)/(7)`