Answer:
[tex]p+9[/tex]
Step-by-step explanation:
[tex]\dfrac{p^2+14p+45}{p+5}\\\\=\dfrac{p^2+9p+5p+45}{p+5}\\\\=\dfrac{p(p+9)+5(p+9)}{p+5}\\\\=\dfrac{(p+9)(p+5)}{p+5}\\\\=p+9[/tex]
Answer:
(p^2 + 14p + 45) by (p + 5) is p + 9
Step-by-step explanation:
To divide the polynomial (p^2 + 14p + 45) by (p + 5), you can use long division or synthetic division. Here's how you can approach it using long division:
1. Divide the first term of the numerator by the first term of the denominator: p^2 ÷ p = p.
2. Multiply the entire denominator (p + 5) by the result from step 1 (p) to get p^2 + 5p.
3. Subtract this result from the original polynomial to get: (p^2 + 14p + 45) - (p^2 + 5p) = 9p + 45.
4. Bring down the next term: 9p.
5. Divide the first term of the new polynomial by the first term of the denominator: 9p ÷ p = 9.
6. Multiply the entire denominator by the result from step 5 (9) to get 9p + 45.
7. Subtract this result from the new polynomial to get 0, indicating that there is no remainder.
Therefore, the result of dividing (p^2 + 14p + 45) by (p + 5) is p + 9.
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