Question

Find the common factor of the expression: $6x^3{y}^4{z}^5+9x^5{y}^2{z}^6+24x^2{y}^7{z}^4$.

• A. 6x³y²z²
• B. 3x²y²z⁴
• C. 2x³y²z⁴
• D. 3x⁵y⁷z⁵

Answer 1

The correct option is B

3x²y²z⁴

$6x^3{y}^4{z}^5=2\times 3\times x^3\times y^4\times z^5$.​

$9x^5{y}^2{z}^6=3\times 3\times x^5\times y^2\times z^6$​

$24x^2{y}^7{z}^4=2\times 2\times 2\times 3\times x^2\times y^7\times z^4$​

The highest common factor of 6, 9 and 24 = 3

The highest power of x that is a factor in all the terms = $x^2$​

The highest power of y that is a factor in all the terms = $y^2$​

The highest power of z that is a factor in all the terms = $z^4$​

Thus, the highest common factor of the terms = $3x^2{y}^2{z}^4$​