Question

Please answer it by 31-1-2022
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Answer 1

Answer:

(i) Simplify: (p^2 + 11p + 28)/(p + 4)

To simplify the expression, we need to factor the numerator and then cancel out common factors with the denominator:

Factor the numerator:

p^2 + 11p + 28 = (p + 7)(p + 4)

Now, rewrite the expression:

(p^2 + 11p + 28)/(p + 4) = [(p + 7)(p + 4)] / (p + 4)

Cancel out the common factor (p + 4):

(p^2 + 11p + 28)/(p + 4) = p + 7

(ii) Simplify: (10a^2 - 9a - 5)/(2a - 3)

Again, we need to factor the numerator and then cancel out common factors with the denominator:

Factor the numerator:

10a^2 - 9a - 5 = (5a + 1)(2a - 5)

Now, rewrite the expression:

(10a^2 - 9a - 5)/(2a - 3) = [(5a + 1)(2a - 5)] / (2a - 3)

Cancel out the common factor (2a - 3):

(10a^2 - 9a - 5)/(2a - 3) = 5a + 1

(iii) Simplify: (z^5 - 81)/(z + 3)

We have a difference of squares in the numerator (z^5 - 81), so we can use the formula (a^2 - b^2) = (a + b)(a - b) to factor it:

Factor the numerator:

z^5 - 81 = (z^2 + 9)(z^3 - 9z^2 + 81)

Now, rewrite the expression:

(z^5 - 81)/(z + 3) = [(z^2 + 9)(z^3 - 9z^2 + 81)] / (z + 3)

There are no common factors to cancel out, so the expression remains as it is.

Final results:

(i) Simplified expression: p + 7

(ii) Simplified expression: 5a + 1

(iii) Expression cannot be further simplified.