What is the coefficient of (x) in ( (x+6)(x-1) )?
Answer and explanation
Correct answer: (5)
To find the coefficient of \\(x\\), expand the product and collect the terms containing exactly one \\(x\\). In \\((x+6)(x-1)\\), multiplying each term gives \\(x\cdot x+x\cdot(-1)+6\cdot x+6\cdot(-1)\\). The two terms containing \\(x\\) are \\(-x\\) and \\(6x\\). Their sum is \\(5x\\), so the coefficient of \\(x\\) is 5.
Equivalently, for \\((x+r)(x+s)\\), the coefficient of \\(x\\) is \\(r+s\\). Here, \\(r=6\\) and \\(s=-1\\), so \\(r+s=6-1=5\\). Therefore option A is correct. The number 6 is only one constant from the first bracket, and \\(-6\\) is the constant term after multiplication, not the coefficient of \\(x\\).
Frequently asked questions
What is the correct answer to this question?
(5)
Why is this the correct answer?
To find the coefficient of \\(x\\), expand the product and collect the terms containing exactly one \\(x\\). In \\((x+6)(x-1)\\), multiplying each term gives \\(x\cdot x+x\cdot(-1)+6\cdot x+6\cdot(-1)\\). The two terms containing \\(x\\) are \\(-x\\) and \\(6x\\). Their sum is \\(5x\\), so the coefficient of \\(x\\) is 5.
Equivalently, for \\((x+r)(x+s)\\), the coefficient of \\(x\\) is \\(r+s\\). Here, \\(r=6\\) and \\(s=-1\\), so \\(r+s=6-1=5\\). Therefore option A is correct. The number 6 is only one constant from the first bracket, and \\(-6\\) is the constant term after multiplication, not the coefficient of \\(x\\).
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Exploring Algebraic Identities. Topic: Algebraic identities.
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