Question

plz tell ans to this ques Its urgent ​

Answer 1

GIVEN :-

• divisor :- ( 3x + 1 )

• dividend :- ( x² + 17x + 5 )

TO FIND :-

• (3x + 1) is a factor of (x² + 17x + 5)

SOLUTION:-

WE CAN'T USE FACTOR THEOREM

HENCE ,

TO CHECK WETHER ITS A FACTOR OR NOT WE WILL PUT THE VALUE OF ‘ X’ OF DIVISOR IN VALUES OF DIVIDEND

IF THE RESULTS COMES 0 SO ITS A FACTOR

$\implies \rm{ \: 3x + 1 \: = 0}$

$\implies \rm{ \: 3x \: = - \: 1}$

$\implies \rm{ \: x \: = - \dfrac{1}{3} }$

NOW PUT THE VALUE OF X IN DIVIDEND

$\implies \rm{ {x}^{2} + 17x + 5 }$

$\implies \rm{ { ( - \dfrac{1}{3})}^{2} + 17( - \dfrac{1}{3}) + 5 }$

$\implies \rm{ { \dfrac{1}{9}} - \dfrac{17}{3} + 5 }$

$\implies \rm{ { \dfrac{1 - 51}{9}} + 5 }$

$\implies \rm{ - { \dfrac{50}{9}} + 5 }$

$\implies \rm{ { \dfrac { - \: 50 + 45 \: \: \: \: }{9}} }$

$\implies \rm{ { \dfrac { - \: 5 \: \: \: \: }{9}} }$

$\implies \rm{ { \dfrac { - \: 5 \: \: \: \: }{9}} \neq 0 }$

$\implies \boxed { \boxed{\rm{ \: 3x + 1 \: is \: not \: a \: factor \: of \: {x}^{2} - 17x + 5}}}$

OTHER INFORMATION :-

DIVISOR :

Key Points to Remember

• Divisor divides the number into parts.

• The divisor can divide the dividend either completely or partially. When divided completely, the remainder is zero and when divided partially, the remainder is a non-zero integer.

• Divisor could be a positive or negative number.

• A number that divides an integer exactly, leaving no remainder, is also termed as the divisor.

• The divisor 1 and -1 can divide every integer, present in the number line.

DIVIDEND :

• The division frequently is shown in algebra by putting the dividend over the divisor with a horizontal line between them. This horizontal line is also called a fraction bar. For example, x divided by y can be represented as x/y and this can be read as “divide x by y” or “x over y”. Here, x is the dividend and y is the divisor.

QUOTEINT :

• In the division method, a number is divided by another number to get a different number as an output. Here, the number/integer which is getting divided is known as a dividend and the integer which divides a given number is the divisor. The divisor which does not divide a number entirely gives a number, which is said to be the remainder.

REMINDER :

• A remainder in mathematics is what's left over in a division problem. In the division process, the number we want to divide up is known as the dividend, while the number we are dividing by is referred to as the divisor; the result is the quotient. We can find the remainder of a division problem by using long division