Question

3 which trinomial is written in standard form and has a constant term of five? (1) $x^5 - 4x^2 + 10$ (3) $5x^4 - 3x^2 + 1$ (2) $2x^2 + 6x^4 + 5$ (4) $4x^5 - 8x^2 + 5$

Explanation:

Step1: Recall standard form of polynomial

A polynomial in standard form is written with terms in descending order of exponents. The constant term is the term without a variable (exponent of \(x\) is \(0\)). We need to check each option:

Step2: Analyze Option (1)

For \(x^{5}-4x^{2} + 10\), the constant term is \(10\), not \(5\). So this is not the answer.

Step3: Analyze Option (2)

For \(2x^{2}+6x^{4}+5\), the terms are not in descending order of exponents (exponent of \(x\) in \(2x^{2}\) is \(2\) and in \(6x^{4}\) is \(4\), so it should be \(6x^{4}+2x^{2}+5\) to be in standard form). So this is not in standard form.

Step4: Analyze Option (3)

For \(5x^{4}-3x^{2}+1\), the constant term is \(1\), not \(5\). So this is not the answer.

Step5: Analyze Option (4)

For \(4x^{5}-8x^{2}+5\), the terms are in descending order of exponents (exponent of \(x\) in \(4x^{5}\) is \(5\), in \(- 8x^{2}\) is \(2\), and the constant term is \(5\)). So this polynomial is in standard form and has a constant term of \(5\).

Answer:

(4) \(4x^{5}-8x^{2}+5\)