the polynomial 3x² - 10x + 8 has a factor of 3x - 4. what is the other factor of 3x² - 10x + 8?\no x - 2\no…
the polynomial 3x² - 10x + 8 has a factor of 3x - 4. what is the other factor of 3x² - 10x + 8?\no x - 2\no x - 4\no x - 6\no x - 8
Answer
Explanation:
Step1: Set up the equation
Let the other factor be $ax + b$. Then $3x^{2}-10x + 8=(3x - 4)(ax + b)=3ax^{2}+(3b-4a)x-4b$.
Step2: Compare the coefficients of $x^{2}$
Comparing the coefficients of $x^{2}$: $3a = 3$, so $a = 1$.
Step3: Compare the constant - terms
Comparing the constant - terms: $-4b=8$, so $b=-2$.
Step4: Determine the factor
The factor $ax + b$ with $a = 1$ and $b=-2$ is $x - 2$.
Answer:
A. $x - 2$