Question

course ap precalculus segment 28 - polynomials intro: end beha due tue, oct 14, 2025 degree / leading coefficient / end behavior default gallery 6. $y=(3x - 4)(x - 2)(5x - 3)(2 - x)$ text math set matrix answer

Explanation:

Step1: Expand the polynomial

First, rewrite $(2 - x)$ as $-(x - 2)$. Then $y=-(3x - 4)(x - 2)^2(5x - 3)$. Expand $(x - 2)^2=x^{2}-4x + 4$. Then multiply $(3x - 4)(x^{2}-4x + 4)=3x\times(x^{2}-4x + 4)-4\times(x^{2}-4x + 4)=3x^{3}-12x^{2}+12x-4x^{2}+16x - 16=3x^{3}-16x^{2}+28x - 16$. Next, multiply $(3x^{3}-16x^{2}+28x - 16)(5x - 3)=3x^{3}\times(5x - 3)-16x^{2}\times(5x - 3)+28x\times(5x - 3)-16\times(5x - 3)=15x^{4}-9x^{3}-80x^{3}+48x^{2}+140x^{2}-84x - 80x + 48=15x^{4}-89x^{3}+188x^{2}-164x + 48$. Since we had a negative sign at the start, $y=-15x^{4}+89x^{3}-188x^{2}+164x - 48$.

Step2: Determine the degree

The highest - power of $x$ in the polynomial $y=-15x^{4}+89x^{3}-188x^{2}+164x - 48$ is $4$, so the degree $n = 4$.

Step3: Determine the leading coefficient

The coefficient of the term with the highest - power of $x$ is $- 15$, so the leading coefficient $a=-15$.

Step4: Analyze the end - behavior

Since the degree $n = 4$ (even) and the leading coefficient $a=-15<0$, as $x\to\pm\infty$, $y\to-\infty$.

Answer:

Degree: $4$; Leading Coefficient: $-15$; End - behavior: as $x\to\pm\infty$, $y\to-\infty$