Question

resolve into factors a²-5a-24​

Answer 1

• As per the data given in the question, we have to find the value of the expression.

           Given data:- $a^{2} -5a-24.$

           To find:- Value of the expression.

           Solution:-

• We know that the identity,

            $\begin{array}{l}(x+a)(x-b) \\=(x+a)[x+(-b)] \\=x^{2}+(a-b) x+a \times(-b) \\=x^{2}+(a-b) x-a b.\end{array}$

          Similarly, we get,

              $a^{2} -5a-24\\\Rightarrow a^{2}+3 a-8 a-24\\\Rightarrow(a+3)-8(a+3)\\\Rightarrow(a-8)(a+3).$

     Hence we will get the factors  $a^{2} -5a-24=(a-8)(a+3).$

Answer 2

Given: The equation is$a^{2} -5a-24$.

We have to resolve the given equation into factors.

We are solving in the following way:

We have,

The equation is$a^{2} -5a-24$.

$=>a^{2}-5 a-24\\=>a^{2}-8 a+3 a-24\\\\=>a\left(\frac{a^{2}}{a}-\frac{2^{3} \cdot a}{a}\right)+3\left(\frac{3 a}{3}-\frac{2^{3} \cdot 3}{3}\right)\\\\=>a\left(a^{2-1}-\left(2^{3}\right)\right)+3\left(a-\left(2^{3}\right)\right)\\\\=>a(a-8)+3(a-8)$

$=>(a-8)\left(\frac{a(a-8)}{a-8}+\frac{3(a-8)}{a-8}\right)\\\\=>(a-8)(a+3)$

Hence, the factors of the above equation will be$(a-8)(a+3)$ that is$a=8,a=-3$.