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Polynomials

Simplify :

1) (4x^4 + 5x^2 - 7x ) ÷ x

Solution :

(4x^4÷x) +( 5x^2÷x) -( 7x÷x )

4x^3 + 5x - 7.

2) (7x^8 - 5x^5 + 9x^3 +x^2)÷ x

Sol) (7x^8 ÷ x) - (5x^5 ÷ x) + (9x^3 ÷ x) + (x^2 ÷x)

7x^7 - 5x^4 + 9x^2 + x

3) (8x^4 - 4x^3 + 6x) ÷ 2x

Solution:-

(8x^4 ÷ 2x) - (4x^3 ÷ 2x) + (6x ÷ 2x)

4x^3 - 2x^2 + 3

4)(8x^5 - 2x^3) ÷ 4x

Solution:-

(8x^5 ÷ 4x) - (2x^3 ÷ 4x)

2x^4 - (x^2 ÷ 2)

5)(-4x^2 + 6x^4 - 2x) ÷ -2x

Solution:-

(-4x^2 ÷ (-2x)) + (6x^4 ÷ (-2x)) - (2x ÷ (-2x))

2x - 3x^3 + 1

Simplify And Reduce Into Lowest Terms

1)\[\frac{(x+3)(x-2)}{(x-2)}\]

Solution:-

\[\frac{(x+3)(x-2)}{(x-2)}\]
 \[= (x+3)\]

2)(x+3)² ÷ (x+3)

Solution:-

(x+3)(x+3)) ÷ (x+3)

x+3

3)(x^2 + 9x +20) ÷ (x+4)

Solution:-

(x^2+4x+5x+20) ÷ (x+4)

(x(x+4) + 5(x+4)) ÷ (x+4)

((x+4)(x+5)) ÷ (x+4)

x+5

4)(x^2+3x+2) ÷ (x^2+5x+4)

Solution:-

(x^2+x+2x+2) ÷ (x^2+x+4x+4)

(x(x+1)+2(x+1)) ÷ (x(x+1)+4(x+1)

((x+1)(x+2)) ÷ ((x+1)(x+4))

(x+2) ÷ (x+4)

5)(2x^2+9x-18) ÷ ((x+6)(x+1))

Solution:-

(2x^2+12x-3x-18) ÷ ((x+6)(x+1))

(2x(x+6)-3(x+6)) ÷ ((x+6)(x+1))

((x+6)(2x+3)) ÷ ((x+6)(x+1))

(2x+3) ÷ (x+1)








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