The factorisation of the given polynomial is (x+2)(2x+3). Therefore, option D is the correct answer.
The given polynomial is 2x²+ 7x + 6.
We need to factorise the given polynomial.
How to factorise the quadratic polynomials?
In order to factorise a quadratic algebraic expression in the form ax² + bx + c into double brackets:
- Multiply the end numbers together ( a and c ) then write out the factor pairs of this new number in order.
- We need a pair of factors that + to give the middle number ( b ) and x to give this new number.
- Group the terms and take common factors out.
Now, 2x²+ 7x + 6=2x²+ 4x +3x+ 6
=2x(x+2)+3(x+2)
=(x+2)(2x+3)
Therefore, option D is the correct answer.
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