Question

1. Show that X+1 and 2x-3 are factor of 2x³-9x²+X+12

2. for what values of a is 2x³ +ax²+11x+a+3 exactly divisible by (2x-1)

3. If x²-1 is a factor of ax⁴+bx³+cx²+dx+e, show that a+c+e=b+d=0

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Answer 1

1.

We need to check if (2x-3) is a factor of the polynomial 2x³-9x²+x+12

Fir.st equate 2x-3 to 0 and find value of x.

2x - 3 = 0

⇒ 2x = 3

⇒ x = 3/2

If x=3/2 is a root of the polynomial, then (2x-3) is a factor.

at x=3/2, value of polynomial is

2(3/2)³ - 9(3/2)² + 3/2 + 12

= 2×(27/8) - 9×(9/4) + 3/2 + 12

= 27/4 - 81/4 + 3/2 + 12

= (27 - 81 + 6 + 48)/4

= (81-81)/4

= 0

So 3/2 is a root of the polynomial. Hence (2x-3) is a factor of the polynomial.

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Answer 2

Step-by-step explanation:

Strong acid is an acid that ionizes completely in aqueous solution. It always loses a proton (H+) when dissolved in water. Weak acid is an acid that ionizes partially in a solution. It gives off only a few of its (H+) atoms when dissolved in water.

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