Given:
The polynomial is
[tex]x(x-5)(2x+3)[/tex]
To find:
The standard form of the polynomial and correct statement for the polynomial.
Solution:
Let, [tex]P(x)=x(x-5)(2x+3)[/tex]
On multiplication, we get
[tex]P(x)=(x^2-5x)(2x+3)[/tex]
[tex]P(x)=x^2(2x)+x^2(3)-5x(2x)-5x(3)[/tex]
[tex]P(x)=2x^3+3x^2-10x^2-15x[/tex]
[tex]P(x)=2x^3-7x^2-15x[/tex]
Here,
Constant term is 0, leading coefficient is 2, degree is 3 and number of terms is 3.
Therefore, the correct option is 2.
The statement which is true about the resulting polynomial is the leading coefficient is 2. Option 2 is correct.
In the standard form of the polynomial equation, the highest degree term is placed first. The order of a standard polynomial equation is decreasing power of variable of term.
The standard form of the quadratic equation is,
[tex]ax^{n}+bx^{n-1}+cx^{n-2}......nx^{n-n}\\ax^{n}+bx^{n-1}+cx^{n-2}......nx^{0}\\ax^{n}+bx^{n-1}+cx^{n-2}......n[/tex]
Here, (a,b,c and n) are the real numbers and x is variable.
The given expression in the problem is,
[tex](x)(x - 5)(2x + 3)[/tex]
Simplify it further,
[tex](x)(x - 5)(2x + 3)\\(x^2-5x)(2x + 3)\\2x^3+3x^2-10x^2-15x\\2x^3-7x^2-15x[/tex]
In the above expression, the highest degree of the polynomial is 3 and the coefficient of it is 2 which is the leading coefficient.
Hence, the statement which is true about the resulting polynomial is the leading coefficient is 2. Option 2 is correct.
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