Question

10. Is each statement true or false? Explain.

a. If the product of two integers is divisible by 5, one of the integers is also
divisible by 5.
b. If the product of two integers is divisible by 6, one of the integers is also
divisible by 6.
c. If the product of two real numbers is 5, one of the numbers is 5.
d. If the product of two expressions is x2 4, one of the expressions is x2 4.
e. If the product of two expressions is x2 + 4, one of the expressions is x2 + 4.

Answer 1

#a

Yes its true

Lets take two integers 2 and 5

• 2×5=10
• 5/5=1

Proved

#b

Same like before its true

• Take two integers as 2 and 6
• 2×6=12
• 6/6=1

#c

Not true at always(except 1 )

• Take two 5(1)=5
• -5(-1)=5

Hence its false

#d

Like option c its false

#e

Its false see no c

Answer 2

a. If the product of two integers is divisible by 5, one of the integers is also

divisible by 5.

• TRUE, Since 5 is prime number

b. If the product of two integers is divisible by 6, one of the integers is also

divisible by 6.

• FALSE, one of the factors could be divisible by 2 and another - by 3.

c. If the product of two real numbers is 5, one of the numbers is 5.

• FALSE, example: 2*2.5 = 5 or (-1.25)*(-4)

d. If the product of two expressions is x²- 4, one of the expressions is x²- 4.

• FALSE, x²- 4 is a complex number and the factors are (x - 2) and (x + 2)

e. If the product of two expressions is x² + 4, one of the expressions is x² + 4.

• TRUE, since we can't factor the product.