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

B.What is the maximum value of $ k $ if the polynomial $ {x^2} - 3x + k $ can be written as the product of two first degree polynomials?

Answer

Verified

179.1k+ views

**Hint**: In the first part factorize the given quadratic polynomial to write it as product of two first degree polynomials and in the second part factorize the polynomial and check whether for what value of $ k $ the equation can be factorized.

**:**

__Complete step-by-step answer__A.The polynomial is given as $ {x^2} - 3x + 2 $ .

As the given polynomial $ {x^2} - 3x + 2 $ is a quadratic polynomial. So, factorize the polynomial by breaking the $ - 3x $ term in two parts such that their coefficients multiplication is equal to $ 2 $ and addition is equal to $ - 3 $ .

So, factorize the given polynomial as shown below:

$

\Rightarrow {x^2} - 3x + 2 = {x^2} - x - 2x + 2 \\

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

= \left( {x - 2} \right)\left( {x - 1} \right) \;

$

So, the polynomial $ {x^2} - 3x + 2 $ can be written as $ \left( {x - 2} \right)\left( {x - 1} \right) $ in the form of product of two first degree polynomials.

**So, the correct answer is “ $ \left( {x - 2} \right)\left( {x - 1} \right) $ ”.**

B.Now in the second part factorize the given polynomial:

$

\Rightarrow {x^2} - 3x + k = {x^2} - 2x - x + k \\

= x\left( {x - 2} \right) - 1\left( {x - k} \right) \;

$

So, this polynomial can only be further written as product of two first degree polynomials if $ x - 2 = x - k $

$\Rightarrow k = 2 $

So, the maximum value of $ k $ for which the polynomial $ {x^2} - 3x + k $ can be written as a product of two first degree polynomials is equal to $ 2 $ .

**So, the correct answer is “k=2”.**

**Note**: In the first part the polynomial is given and need to write it as a product of two first degree polynomials but factorizing it. In the next part a polynomial contains a value as a constant which can only be found with the given condition that the polynomial can be written as a product of two first degree polynomials.

Recently Updated Pages

If ab and c are unit vectors then left ab2 right+bc2+ca2 class 12 maths JEE_Main

A rod AB of length 4 units moves horizontally when class 11 maths JEE_Main

Evaluate the value of intlimits0pi cos 3xdx A 0 B 1 class 12 maths JEE_Main

Which of the following is correct 1 nleft S cup T right class 10 maths JEE_Main

What is the area of the triangle with vertices Aleft class 11 maths JEE_Main

The coordinates of the points A and B are a0 and a0 class 11 maths JEE_Main

Trending doubts

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

A Short Paragraph on our Country India