Question

If all terms in expression A are like the terms in expression B, then which of the following can be an integer value of y?

$\text{Expression A}$	$\text{Expression B}$
$x^{(y+1{)}^2}+4x^3+21x$	$x^4+x^3+x+1$

• A. –1
• B. 3
• C. –4
• D. 2

Answer 1

The correct option is A –1

Like terms have the same variables with the same powers.

The exponents of the variables in expression B are 4, 3, 1, and 0.

So, the value of $(y+1{)}^2$ has to be one of these values.

It is given that $y$ is an integer.
So, $(y+1{)}^2$ cannot be equal to 3.

Let's compare with the other exponents.
If $(y+1{)}^2=4$
$\Rightarrow (y+1)=\pm 2\Rightarrow y=1\text{(or)}–3$

If $(y+1{)}^2=1$
$\Rightarrow (y+1)=\pm 1\Rightarrow y=0\text{(or)}–2$

If $(y+1{)}^2=0$
$\Rightarrow (y+1)=0\Rightarrow y=–1$

Hence, the values of $y$ can be –3, –2, –1, 0, and 1.