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Write the polynomial $3{x^2} - 5x - 2$ as a product of two first degree polynomials.

Last updated date: 22nd May 2024
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Hint: Use the factorisation method to split the middle term.

Complete step-by-step answer:

We would be using the factorisation method (i.e. splitting the middle-term).

So, the expression we are given is,

$3{x^2} - 5x - 2$

So by splitting the mid - term (in a way that the sum is equal to -5 and the product is equal to -2*3=-6), we get

 $= 3{x^2} - 6x + x - 2$

 Now taking 3x common from the first 2 terms, we get

 $= 3x\left( {x - 2} \right) + 1\left( {x - 2} \right) \\$

 $= \left( {3x + 1} \right)\left( {x - 2} \right) \\$

 which is the required product of two first degree polynomials.

Note: These types of questions should be approached by quadratic factorization using splitting of middle term which is the coefficient of x. Use the formula:

 $x^2 + \left( {a + b} \right)x + ab = \left( {x + a} \right)\left( {x + b} \right) \\$ when coefficient of $x^2$ is 1.

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