Question

What is the leading coefficient of the polynomial −10x ⁴ −4x ² (x ² −8)+5x?

A) -4
B) -10
C) -40
D) 5

Answer 1

The leading coefficient of the polynomial −10x⁴ −4x²(x² −8)+5x is −14. We found this by distributing −4x² across the parenthesis, combining like terms, and identifying the coefficient of the highest power of x.

Step-by-step explanation:

The question asks for the leading coefficient of the polynomial −10x⁴ −4x²(x² −8)+5x. To find this, we need to simplify the polynomial. First, let's distribute the −4x² across the parenthesis:

• −4x² × x² = −4x⁴
• −4x² × (−8) = +32x²

Now we combine like terms:

• −10x⁴ + (−4x⁴) = −14x⁴
• We also have the term +5x, which does not combine with any other term.

So the simplified form of the polynomial is −14x⁴ + 32x² + 5x, and therefore the leading coefficient is the coefficient of the highest power of x which is −14.