Question

(1) 2+2 +x+
2. Use the Factor Theorem to determine whether g(x) is factor of
following cases
() -58 + x2 - 5x-1, g(x) = x+1​

Answer 1

${ \rm{ \large{Solution \colon}}}$

${ \rm{the \: factor \: is = x + 1 = 0 \implies x = ( - 1)}}$

${ \rm{remainder}}$

${ \rm{g(x) = ( - 58) + {x}^{2} - 5x - 1}}$

${ \rm{ \to g( - 1) = ( - 58) + {x}^{2} - 5x - 1}}$

${ \rm{ \to( - 58) + {( - 1)}^{2} - 5 \times( - 1) - 1}}$

${ \rm{ \to( - 58) + 1 + 5 - 1}}$

${ \rm{ \to - 58 + 5}}$

${ \rm{ \to( - 53)}}$

${ \rm{so \: the \remainder\: is \: ( - 53)}}$

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For finding the remainder, using Remainder Theoram :

Step1 : Put the divisor equal to zero and solve the equation obtained to get the values of its variable.

Step2 : Substitute the value of the variable, obtained in step 1, in the given polynomial and simplify it to get the required remainders.

Answer 2

$\mathtt{\huge{\underline{\red{Correct\:Question\:?}}}}$

✴ Use the Factor Theorem to determine whether g(x) is factor of following case :-

↗ (-58) + x² - 5x-1,

• g(x) = x+1

$\mathtt{\huge{\underline{\green{Answer:-}}}}$

➡ g(x) is not the factor because it have -55 as reminder.

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$\huge\sf\pink{Solution:-}$

Given :-

• (-58) + x² - 5x-1,

• g(x) = x+1

To Find :-

• Determine g(x) is factor of following case.

Calculation :-

According to the question,

• (-58) + x² - 5x-1,

• g(x) = x+1

We know,

f(x) = (-58) + x² - 5x - 1

Correcting the order ,

=> f(x) = x² -5x + (-58) - 1

=> x² -5x + (-59)

=> x² -5x -59

We have,

• g(x) = x+1

We are having the g(x) as the zero of f(x)

g(x) = 0

So , ( x + 1 ) = 0

=> x = -1

Putting x in f(x),

f(x) = x² -5x -59

f ( -1 ) = (1)² - 5 × 1 -59

f ( -1 ) = 1 - 5 -59

f ( -1 ) = 4 - 59

f ( -1 ) = -55

So, our remainder is -55.

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