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Question

# Factorize the polynomial expression 4x2−3x−7

A
(4x7)(x+1)
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B
(4x7)(x1)
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C
(4x+7)(x+1)
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D
(4x+7)(x1)
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Solution

## The correct option is A (4x−7)(x+1)Given a polynomial expression 4x2−3x−7. Factorizing this polynomial by splitting the middle term: Product of 4x2 and −7 =4x2×(−7) =−28x2 We need to find two numbers whose product is −28x2 and sum is −3x. The numbers are 4x and −7x. (∵−7x+4x=−3x) Now, splitting the middle term: 4x2−3x–––––−7 =4x2−7x+4x−7 Taking ′x′ common from the first two terms and 1 from the last two terms: =x(4x−7)+1(4x−7) Since, (4x−7) is the common factor in both the terms, we can take (4x−7) as the common factor: =(4x−7)(x+1) 4x2−3x−7=(4x−7)(x+1) The factorization of the polynomial expression 4x2−3x−7 is (4x−7)(x+1). Therefore, option (a.) is the correct answer.

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