Question

– Division of Polynomials –

– Complete each item below by finding the missing factor. Write your answer on the space provided.

1. x² - 16 = ( x + 4 ) ( ___________ ).

2. x³ + 4x² - 9 = ( x + 3 ) ( __________ ).

3. 3x³ + 4x² + 11x - 10 = ( 3x - 2 ) ( __________ ).

4. 4x³ + 11x² - 11x + 2 = ( 4x - 1 )( __________ ).

5. 5x³ + 10x² + x + 2 = ( x + 2 )( __________ ).

– Nonsense will be deleted to our Moderator!​

Answer 1

Answer:

x² - 16 = ( x + 4 ) ( ___________ ).

2. x³ + 4x² - 9 = ( x + 3 ) ( __________ ).

3. 3x³ + 4x² + 11x - 10 = ( 3x - 2 ) ( __________ ).

4. 4x³ + 11x² - 11x + 2 = ( 4x

Answer 2

Division of Polynomials.

1. $x^{2} - 16 = ( x + 4 ) ( x - 4 ).$

2. $x^{3} + 4x^{2} - 9 = ( x + 3 ) ( x^{2}+x-3).$

3. $3x^{3} + 4x^{2} + 11x - 10 = ( 3x - 2 ) ( x^{2}+2x+5 ).$

4. $4x^{3}+ 11x^{2} - 11x + 2 = ( 4x - 1 )( x^{2} + 3x -2 ).$

5. $5x^{3} + 10x^{2} + x + 2 = ( x + 2 )(5x^{2}+1).$$(3x-2)(x^{2} +2x+5)$

Explanation:

• Factorizing the given value we get,

         1. $x^{2}-16$ - we can write as $x^{2} - 4^{2}$. Using formula, The given value can be written as $(x+4)(x-4)$.

        2. $x^{3} + 4x^{2} -9$ - By taking common factors $(x+3)(\frac{x^{3}+4x^{2}-9}{x+3})$. Simplifying the numerator and denominator we get $x^{2} +x-3$. Result is $(x+3)(x^{2} +x-3)$.

         3. $3x^{3} + 4x^{2} + 11x - 10$    - Taking the Common Factors out we get,

$(3x-2)(\frac{3x^{3} + 4x^{2} + 11x - 10}{3x-2} )$ which is simplified as $(3x-2)(x^{2} +2x+5)$.

         4. $4x^{3} + 11x^{2} - 11x + 2$   - Taking the Common Factors out we get,

$(4x-1)(\frac{4x^{3}+11x^{2} -11x+2 }{4x-1} )$ which gives $(4x-1)(x^{2} +3x-2)$.

         5. $5x^{3} + 10x^{2} + x + 2$  segregating the values we get ,$(5x^{3}+10x^{2} ) ( x+2)$

Factoring out $5x^{2}$ from the equation $5x^{2} (x+2)+(x+2) = (x+2)(5x^{2} +1)$.