Question

answer part a and part b ill give 5

Answer 1

The given expression is:

$3x^{10}-48x^2$

Part a: Factor the two terms as below:

$\begin{gathered} 3x^{10}=3\times x\times x\times x\times x\times x\times x\times x\times x\times x\times x \\ 48x^2=3\times2\times2\times2\times2\times x\times x \end{gathered}$

As seen above the common factor is 3 and x and x so it follows:

$\text{GCF}=3x^2$

Take the GCF common from the expression to get:

$3x^{10}-48x^2=3x^2(x^8-16)$

Part b: The other bracket can be factored using the formula:

$x^2-a^2=(x-a)(x+a)$

So it follows:

$\begin{gathered} 3x^2(x^8-16)=3x^2((x^4)^2-4^2)=3x^2(x^4-4)(x^4+4) \\ =3x^2(x^4+4)((x^2)^2-2^2) \\ =3x^2(x^4+4)(x^2-2)(x^2+2) \\ =3x^2(x^4+4)(x^2+2)(x-\sqrt[]{2})(x+\sqrt[]{2}) \end{gathered}$

In this way the expression is factored. The final value is the last line given above.