Question

I need help with this problem please and thank you

Answer 1

Solution:

Part - A:

To factor a polynomial, take out the factors of each term outside of the brackets. The terms of this expression are divisible by x⁴ (GCF), which can factorize completely. This will subtract 4 from the exponents.

• => x⁵ - x³
• => x⁴(x - 1)

Part - B:

To factor a polynomial, take out the factors of each term outside of the brackets. The terms of this expression are divisible by 3 (GCF), which can factorize completely. This will divide 3 from the terms.

• 3x² - 75
• 3(x² - 25)
• 3(x + 5)(x - 5)

Part - C:

To factor a polynomial, take out the factors of each term outside of the brackets. The terms of this expression are divisible by x²y (GCF), which can factorize completely.

• 3x⁵y + 4x⁴y - 5x²y
• => x²y(3x³ + 4x² - 5)

Part - D:

Unfortunately, this expression can't factor with rational numbers. The expression results in 81x³ - 125.

Answer 2

a) $x^5-x^3$

$x^3\left(x^2-1\right)$ ........take out x³

$x^3\left(x+1\right)\left(x-1\right)$ ......separated (x²-1)

b) $3x^2-75$

$3\left(x^2-25\right)$ ........took out 3.

$3\left(x+5\right)\left(x-5\right)$  .......separated (x²-25)

c) $3x^5y+4x^4y-5x^2y$

$x^2y\left(3x^3+4x^2-5\right)$ ............takeout x²y at the front.

d) $81x^3-125$

$81x^3-125$ ......cannot be factorised much more further.