Question

Write 'T' for true and 'F' for false​​
(i) In $-x$, the constant term is $-1$.
(ii) The coefficient of $x$ in $x^2-3x+5$ is $3$.
(iii) $(5x-7)-(3x-5)=2x-12$.
(iv) $(3x+5y)(3x-5y)=(9x^2-25y^2)$.
(v) If $a=2$ and $b=12$, then the value of $ab(a^2+b^2)$ is $414$.

Answer 1

(i)

Given polynomial function $-x=-x+0$.
So, the constant term is $0$.
Thus, the constant term is $-1$ is false.
Therefore, the given statement is false (F).
(ii)

Given polynomial $x^2-3x+5$
The coefficient of $x$ is $-3$.
So, the coefficient of $x$ is $3$ is false.
Therefore, the given statement is false(F).
(iii)

Given equation $(5x-7)-(3x-5)=2x-12$.
LHS$=(5x-7)-(3x-5)$
$=5x(3x-5)+7(3x-5)$
$=15x^2-25x+21x-35$
$=15x^2-4x-35$
$\ne$ RHS
Therefore, the given statement is false(F).
(iv)

Given $(3x+5y)(3x-5y)=(9x^2-25y^2)$
LHS$=(3x+5y)(3x-5y)$
$=3x(3x-5y)+5y(3x-5y)$
$=9x^2-15xy+15xy-25y^2$
$=9x^2-25y^2$
$=$RHS.
Therefore, the given statement is true(T).
(v)

If $a=2$ and $b=12$, then the value of $ab(a^2+b^2)$ is $414$.

$ab(a^2+b^2)$

$=2\left(12\right)(2^2+(12{)}^2)$

$=24(4+144)$

$=24\left(148\right)$

$=3552$

Therefore, the given statement is False (F).