the polynomial $6x^{2}+x - 15$ has a factor of $2x - 3$. what is the other factor?\n$3x - 5$\n$3x + 5$\n$4x…
the polynomial $6x^{2}+x - 15$ has a factor of $2x - 3$. what is the other factor?\n$3x - 5$\n$3x + 5$\n$4x - 5$\n$4x + 5$
Answer
Answer:
B. $3x + 5$
Explanation:
Step1: Let the other factor be $ax + b$.
We know that $(2x - 3)(ax + b)=6x^{2}+x - 15$.
Step2: Expand the left - hand side.
$(2x - 3)(ax + b)=2ax^{2}+2bx-3ax - 3b=2ax^{2}+(2b - 3a)x-3b$.
Step3: Compare the coefficients of $x^{2}$.
For the coefficient of $x^{2}$: $2a = 6$, so $a = 3$.
Step4: Compare the constant terms.
For the constant term: $-3b=-15$, so $b = 5$. So the other factor is $3x + 5$.