Question

How much x⁴+2x²-3x+7 be decreased to get x³+x²+x-1 Answer this in algebraic form​

Answer 1

Topic

• Polynomials

Concepts

① Like terms.

Like terms are terms with the same degree. We can add or subtract the like terms.

Solution

We want $A$ to decrease by $B$ to get $C$.

• $A=x^{4}+2x^{2}-3x+7$
• $B=\boxed{?}$
• $C=x^{3}+x^{2}+x-1$

Let's write the expression needed.

$\implies A-B=C$

$B$ is the required polynomial. Let's solve for $B$.

$\implies B=A-C$

$\implies B=(x^{4}+2x^{2}-3x+7)-(x^{3}+x^{2}+x-1)$

$\implies B=x^{4} - x^{3} + x^{2} - 4 x + 8$

So, it should decrease by $x^{4} - x^{3} + x^{2} - 4 x + 8$.

This is the required answer.