) If ( x+4) is one of the factors of (〖x 〗^2-16)(x^2+14x+49). Find the other irreducible factors of the given expression.
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Answer:
Given that: x
2
+14x+49
=x
2
+7x+7x+49, (split middle term so that resultant is same)
=(x
2
+7x)+(7x+49), (group pair of terms)
=x(x+7)+7(x+7), (factor each binomials)
=(x+7)(x+7), (factor out common factor (x+7))
=(x+7)
2
Aliter, use (a+b
2
)=a
2
+2ab+b
2
⇒x
2
+14x+49=x
2
+2×7x+7
2
=(x+7)
2
Step-by-step explanation:
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