Question

Match each function with its correct description. f(x) = (-x + 1)3(x + 2)2(x − 3) f(x) = (-2x + 1)2(x − 3)2(x + 1) f(x) = (x + 6)(2x − 3)(x − 1)2 f(x) = (x − 2)2(-2x − 1)2(-x + 1) The degree of the function is 4, and the leading coefficient is positive. arrowRight The degree of the function is 5, and the leading coefficient is negative. arrowRight The degree of the function is 6, and the leading coefficient is negative. arrowRight The degree of the function is 5, and the leading coefficient is positive. arrowRight

Answer 1

Answer:

Pairs The degree of the function is 4, and the leading coefficient is positive. arrowBoth  

f(x) = (x + 6)(2x − 3)(x − 1)2  

The degree of the function is 5, and the leading coefficient is positive. arrowBoth:

f(x) = (x − 2)2(-2x − 1)2(-x + 1)  

The degree of the function is 5, and the leading coefficient is negative. arrowBoth:

f(x) = (-2x + 1)2(x − 3)2(x + 1)  

The degree of the function is 6, and the leading coefficient is negative. arrowBoth:

f(x) = (-x + 1)3(x + 2)2(x − 3)  

Answer 2

Answer:

1.$f(x)=(-x+1)^3(x+2)^2(x-3)$

The degree of the function is 6, and the leading coefficient is negative.

2.$f(x)=(-2x+1)^2(x-3)^2(x+1)$

The degree of polynomial is 5 with leading coefficient positive.

3.$f(x)=(x+6)(2x-3)(x-1)^2$

The degree of the function is 4 with leading coefficient positive.

4.$f(x)=(x-2)^2(-2x-1)^2(-x+1)$

The degree of function is 5 with leading coefficient  negative.

Step-by-step explanation:

We are given that some functions and its description

We have to match with each function with its correct description

1.$f(x)=(-x+1)^3(x+2)^2(x-3)$

$f(x)=(-x^3+1+3x^2-3x)(x^2+4+4x)(x-3)$

Using identity:$(x-y)^3=x^3-y^3-3x^y+3xy^2$

$(x+y)^2=x^2+y^2+2xy$

$f(x)=(-x^3+3x^2-3x+1)(x^3+x^2-8x-12)$

$f(x)=-x^6+2x^5-14x^3-11x^2-12$

The degree of polynomial is the highest power of x and leading coefficient is coefficient of highest exponent. . Therefore, the degree of polynomial is 6 and leading coefficient is -1.

The degree of the function is 6, and the leading coefficient is negative.

2.$f(x)=(-2x+1)^2(x-3)^2(x+1)$

$f(x)=(4x^2+1-4x)(x^2-6x+9)(x+1)$

$f(x)=(4x^4-28x^3+61x^2-42x+9)(x+1)$

$f(x)=4x^5-24x^4+33x^3+19x^2-33x+9$

The degree of polynomial is 5 with leading coefficient positive.

3.$f(x)=(x+6)(2x-3)(x-1)^2$

$f(x)=(2x^2+9x-18)(x^2-2x+1)$

$f(x)=2x^4+5x^3-34x^2+45x-18$

The degree of the function is 4 with leading coefficient positive.

4.$f(x)=(x-2)^2(-2x-1)^2(-x+1)$

$f(x)=(x^2-4x+4)(4x^2+4x+1)(-x+1)$

$f(x)=-4x^5+16x^4-16x^3+x^2-4x+4$

The degree of function is 5 with leading coefficient negative.