Question

Use the factor theorem to determine whether gx is factor of fx in each of the following cases fx 5 x cube + x square -5 x -1 gx is equals to X + 1

Answer 1

Given :

• A polynomial 5x³ + x² - 5x -1 .

To Find :

• Whether x +1 is a factor of given polynomial or not .

Solution :

$\longmapsto\tt{x+1=0}$

$\longmapsto\tt\bf{x=-1}$

Putting x = -1 :

$\longmapsto\tt{{5x}^{3}+{x}^{2}-5x-1}$

$\longmapsto\tt{5{(-1)}^{3}+{(-1)}^{2}-5(-1)-1}$

$\longmapsto\tt{5(-1)+1+5-1}$

$\longmapsto\tt{-5+1+5-1}$

$\longmapsto\tt{-4+4}$

$\longmapsto\tt\bf{0}$

So , x + 1 is the factor of 5x³ + x² - 5x - 1 ...

Answer 2

Step-by-step explanation:

Given:-

A polynomial namely ${5x}^{3}+{x}^{2}-5x-1$

To do:-

To check that (x+1)is a factor of polynomial or not

Solution:-

Let's understand the concept:-

• if (x+1) is a factor then x+1=0 $\mapsto$ x=(-1)
• If (x+1)is a factor of the polynomial then the value of f (-1)=0
• If (x+1) is not a factor of the polynomial then the value of ( $f(-1){\cancel {=}}0)$

Now

• Substitute the values of x in the polynomial

${:}\mapsto$$f (-1)=5 (-1){}^{3}+(-1){}^{2}-5 (-1)-1=0$

${:}\mapsto$$5×(-1)+1+5-1=0$

${:}\mapsto$$-5+1+5-1=0$

${:}\mapsto$$-4+5-1=0$

${:}\mapsto$$1-1=0$

${:}\mapsto$$0=0$

${:}\mapsto$${\underline{\boxed{\bf {f (-1)=0}}}}$

$\therefore$(x+1) is a factor of the polynomial (${5x}^{3}+{x}^{2}-5x-1)$