The true statement is '-3 must be the root of the polynomial [tex]2x^{2} +9x+9[/tex]
The correct answer is an option (A)
"A number or mathematical expression that is being divided."
"It is the number that it is being divided by is called the divisor."
"The number or expression resulting from the division of one number (or expression) by another."
Dividend = Divisor × Quotient + Remainder.
"It is the value for which the value of the polynomial is zero."
For given question,
Dividend = [tex]2x^{2} +9x+9[/tex]
Divisor = x + 3
Quotient = 2x + 3
remainder = 0
Using the formula of dividend divisor quotient and remainder,
⇒ Dividend = Divisor × Quotient + Remainder
[tex]\Rightarrow 2x^{2} +9x+9=(x+3)\times (2x+3)+0\\\\ \Rightarrow 2x^{2} +9x+9=(x+3)\times (2x+3)[/tex]
Now, we find the roots of the polynomial.
[tex]\Rightarrow 2x^{2} +9x+9=0\\\\\Rightarrow (x+3)\times (2x+3)=0\\\\\Rightarrow x+3=0~~~or~~~2x+3=0\\\\\Rightarrow x = -3~~~~or~~~~x=-\frac{3}{2}[/tex]
This means the roots of the polynomial [tex]2x^{2} +9x+9[/tex] are [tex]-3,-\frac{3}{2}[/tex]
Therefore, the true statement is '-3 must be the root of the polynomial [tex]2x^{2} +9x+9[/tex]'
The correct answer is an option (A)
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