Question

*x+6 is one of the factors of the algebraic expression-*

1️⃣ x²+7x+18

2️⃣ x²-9x+18

3️⃣ x²+9x+18

4️⃣ x-9x-18​

Answer 1

Answer:

2⃣x²-9x+18

Step-by-step explanation:

when factorizing 18 and -9 we get ,

( x-6)(x-3)=0

x=6 and x=3

Therefore it satisfies option 2

Answer 2

To Find :- x+6 is one of the factors of the algebraic expression :-

1) x²+7x+18

2) x²-9x+18

3) x²+9x+18

4) x²-9x-18

Concept used :-

• if (x + a) is a factor of p(x) , then p(-a) is equal to zero .

Solution :-

putting x + 6 equal to zero we get,

→ x + 6 = 0

→ x = (-6)

now, checking all given options at x = (-6) we get,

1) x² + 7x + 18

→ p(x) = x² + 7x + 18

→ p(-6) = (-6)² + 7 × (-6) + 18

→ p(-6) = 36 - 42 + 18

→ p(-6) = 54 - 42

→ p(-6) = 12

since p(-6) is not equal to zero . (x + 6) is not a factor of x² + 7x + 18 .

2) x² - 9x + 18

→ p(x) = x² - 9x + 18

→ p(-6) = (-6)² - 9 × (-6) + 18

→ p(-6) = 36 + 54 + 18

→ p(-6) = 108

since p(-6) is not equal to zero . (x + 6) is not a factor of x² - 9x + 18 .

3) x² + 9x + 18

→ p(x) = x² + 9x + 18

→ p(-6) = (-6)² + 9 × (-6) + 18

→ p(-6) = 36 - 54 + 18

→ p(-6) = 54 - 54

→ p(-6) = 0

since p(-6) is equal to zero . (x + 6) is a factor of x² + 9x + 18 .

4) x² - 9x - 18

→ p(x) = x² - 9x - 18

→ p(-6) = (-6)² - 9 × (-6) - 18

→ p(-6) = 36 + 54 - 18

→ p(-6) = 90 - 18

→ p(-6) = 72

since p(-6) is not equal to zero . (x + 6) is not a factor of x² - 9x - 18 .

Hence, we can conclude that, (x + 6) is one of the factors of the option (3) x² + 9x + 18 algebraic expression .

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