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factoring day 1
score: 34/48 answered: 17/24
question 18
what is the greatest common factor of the terms of the polynomial
$25x^4 + 35x^3 + 15x^2$
$x^2$
$5x^2$
$5x^4$
$5x$

Explanation:

Step1: Find GCF of coefficients

List factors of 25, 35, 15:

• Factors of 25: $1, 5, 25$
• Factors of 35: $1, 5, 7, 35$
• Factors of 15: $1, 3, 5, 15$

Greatest common factor is $5$.

Step2: Find GCF of variable terms

Identify lowest power of $x$:

• $x^4$, $x^3$, $x^2$

Lowest exponent is $2$, so GCF is $x^2$.

Step3: Combine GCFs

Multiply coefficient and variable GCFs:
$5 \times x^2 = 5x^2$

Answer:

$\boldsymbol{5x^2}$ (Option: $5x^2$)