Question

reply fast friends

than i will mark as brainlist ok
SHOW THAT 2x-3 IS FACTOR OF
$2x {}^{3} - 9x {}^{2} + x + 12$

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Answer 1

Answer:

Yes 2x-3 is a factor of 2x³- 9x+ x + 12 by x²-3x-4

Step-by-step explanation:

        x²  -3x  -4

2x-3/2x³-9x²+x+12  2x³/2x=x2(÷1 term dividend w/1 term divisor)

      +2x³-3x²  ↓   ↓  

     (-)     (+) {change of sign, rules of subtraction in algebra}

        0   -6x²+x   -6x²/2x=-3x(÷2 term dividend w/1 term divisor)

             -6x²+9x

            (+)    (-) {change of sign, rules of subtraction in algebra}

              0    -8x+12  -8x/2x=4(÷3 term dividend w/1 term divisor)

                    -8x+12

                    (+) (-) {change of sign, rules of sub in algebra}

                        0

Since, 2x³-9x²+x+12 is completely divisible by 2x-3, it will be a factor of it too. Therefore, (2x-3)(x²-3x-4)=2x³-9x²+x+12