Question

How do you write \[y=3\left( x-5 \right)\left( x+2 \right)\] in standard form?

Answer 1

Hint: From the question given, we have been asked to write \[y=3\left( x-5 \right)\left( x+2 \right)\] in standard form. We can write the given question in standard form by simply following the below written process. First of all, we have to multiply all terms and then we have to add all the terms. Then, for the equation to be in standard form, the polynomial must be arranged with the terms in descending degree order.

Complete answer:
From the question we have been given that \[y=3\left( x-5 \right)\left( x+2 \right)\]
First of all let us multiply \[\left( x-5 \right)\left( x+2 \right)\]
First, multiply the second group terms with the first term in the first group, by doing this process we get
\[x\left( x \right)+x\left( 2 \right)\]
\[\Rightarrow {{x}^{2}}+2x\]
Now, multiply the second group terms with the second term in the first group.
By doing this process, we get
\[-5\left( x \right)+-5\left( 2 \right)\]
\[\Rightarrow -5x-10\]
Now, as we have already discussed above, we have to add the terms which we got by multiplying the terms.
By adding all the terms, we get \[{{x}^{2}}+2x-5x-10\]
So, now we have to multiply it with the constant \[3\]
By multiplying with constant \[3\], we get
\[3\left( {{x}^{2}}+2x-5x-10 \right)\]
\[\Rightarrow 3{{x}^{2}}+6x-15x-30\]
\[\Rightarrow 3{{x}^{2}}-9x-30\]
 Now, we have to check whether the polynomial is arranged in descending degree order or not.
We can clearly observe that the polynomial obtained is in descending degree order.
Hence, standard form is \[3{{x}^{2}}-9x-30\]

Note: We should be well aware of the concept of standard form. Also, we should know how to write the given question in standard form. Also, we should be very careful while checking the descending degree order of the obtained polynomial. If the obtained polynomial is not in descending degree order, then students have to rearrange it. The zeroes of the given expression \[y=3\left( x-5 \right)\left( x+2 \right)\] will be given as $x=5$ and $x=-2$ .