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If (2x+3) and (x-1) are two factors of (2x2 + x)2 - 4(2x2 + x) + 3, then the remaining two factors are
- a)(2x+1)(x-1)
- b)(2x+3)(x+1)
- c)(x+1)(x-1)
- d)(2x-1)(x+1)
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
If (2x+3) and (x-1) are two factors of (2x2 + x)2 - 4(2x2 + x) + 3, th...
(2x2 + x)2 - 4(2x2 + x) + 3
= 4x4 + x2 + 4x3 - 8x2 - 4x + 3
= 4x4 + 4x3 - 7x2 - 4x + 3
= 4x3 (x - 1) + 8x2 (x - 1) + x (x - 1) - 3 (x - 1)
= (x - 1) (4x3 + 8x2 + x - 3)
= (x - 1) [2x2 (2x + 3) + x(2x + 3) - 1(2x + 3)]
= (x - 1) (2x + 3) (2x2 + x - 1)
= (x - 1) (2x + 3) [2x2 + 2x - x - 1]
= (x - 1) (2x + 3) [(2x (x + 1)) - 1(x + 1)]
= (x - 1) (2x + 3) (x + 1) (2x - 1)
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= 4x4 + x2 + 4x3 - 8x2 - 4x + 3
= 4x4 + 4x3 - 7x2 - 4x + 3
= 4x3 (x - 1) + 8x2 (x - 1) + x (x - 1) - 3 (x - 1)
= (x - 1) (4x3 + 8x2 + x - 3)
= (x - 1) [2x2 (2x + 3) + x(2x + 3) - 1(2x + 3)]
= (x - 1) (2x + 3) (2x2 + x - 1)
= (x - 1) (2x + 3) [2x2 + 2x - x - 1]
= (x - 1) (2x + 3) [(2x (x + 1)) - 1(x + 1)]
= (x - 1) (2x + 3) (x + 1) (2x - 1)
Most Upvoted Answer
If (2x+3) and (x-1) are two factors of (2x2 + x)2 - 4(2x2 + x) + 3, th...
Explanation:
Given:
(2x+3) and (x-1) are two factors of (2x^2 + x)^2 - 4(2x^2 + x) + 3
Step 1: Expand the given expression
(2x^2 + x)^2 - 4(2x^2 + x) + 3
= (4x^4 + 4x^3 + x^2) - 4(2x^2 + x) + 3
= 4x^4 + 4x^3 + x^2 - 8x^2 - 4x + 3
= 4x^4 + 4x^3 - 7x^2 - 4x + 3
Step 2: Factorize the expression
To factorize the expression, we need to find the remaining factors.
Step 3: Use the given factors to find the remaining factors
Since (2x+3) and (x-1) are factors of the expression, the remaining factors must be:
(2x+1) and (x-1)
Therefore, the correct answer is option 'd) (2x-1)(x+1)' because the remaining factors are (2x+1) and (x-1).
Given:
(2x+3) and (x-1) are two factors of (2x^2 + x)^2 - 4(2x^2 + x) + 3
Step 1: Expand the given expression
(2x^2 + x)^2 - 4(2x^2 + x) + 3
= (4x^4 + 4x^3 + x^2) - 4(2x^2 + x) + 3
= 4x^4 + 4x^3 + x^2 - 8x^2 - 4x + 3
= 4x^4 + 4x^3 - 7x^2 - 4x + 3
Step 2: Factorize the expression
To factorize the expression, we need to find the remaining factors.
Step 3: Use the given factors to find the remaining factors
Since (2x+3) and (x-1) are factors of the expression, the remaining factors must be:
(2x+1) and (x-1)
Therefore, the correct answer is option 'd) (2x-1)(x+1)' because the remaining factors are (2x+1) and (x-1).
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If (2x+3) and (x-1) are two factors of (2x2 + x)2 - 4(2x2 + x) + 3, then the remaining two factors area) (2x+1)(x-1) b) (2x+3)(x+1) c) (x+1)(x-1) d) (2x-1)(x+1) Correct answer is option 'D'. Can you explain this answer?
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