Question

using division find 2x-3 is a factor of 6x³+x²-19x+6 or not I just want to know wether it is factor or not i also want full explaination also​

Answer 1

2x-3 is a factor of 6x³+x²-19x+6

Answer 2

$\large{\red{\underline{\underline{\bold{Given:-}}}}}$

• Using division find 2x-3 is a factor of 6x³+x²-19x+6 or use factor or remainder theorem to find if its a factor

$\large{\blue{\underline{\underline{\bold{To Find:-}}}}}$

• Whether 2x-3 is a factor of 6x³+x²-19x+6 by long divison or remainder theorem or factor theorem

$\large{\green{\underline{\underline{\bold{Solution:-}}}}}$

Let p(x)= 6x³+x²-19x+6 and f(x)= 2x-3

Remainder theorem or Factor theorem says that when p(x) is divided by f(x) then the value of x is x=3/2. So substitute the value of x in p(x)

$\longrightarrow$ p(x)= 6x³+x²-19x+6

$\longrightarrow$ p(3/2)= 6(3/2)³+(3/2)²-19(3/2)+6

$\longrightarrow$ p(3/2)= 6(27/8)+9/4-57/2+6

$\longrightarrow$ p(3/2)= 81/4+9/4-57/2+6

$\longrightarrow$ p(3/2)= 81+9-114+24/4

$\longrightarrow$ p(3/2)= 114-114/4

$\longrightarrow$ p(3/2)= 0/4= 0

$\long{\pink{\underline{\underline{\bold{Long Divison:-}$

• 2x-3)6x³+x²-19x+6(3x²+2x-2
• 6x³-9x²
• ----------------------------
• 10x²-19x
• 10x²-6x
• ----------------------------
• -4x+6
• -4x+6
• --------------------------
• 0
• ----------------------------

• As we got remainder as 0 2x-3 is a factor of 6x³+x²-19x+6