One root of f(x) = 2x3 + 9x2 + 7x – 6 is –3. explain how to find the factors of the polynomial.

Asked by maham237 @ 15/12/2020 in Mathematics viewed by 526 People

Answered by maham237 @ 15/12/2020

We have the following polynomial:

$f(x)=2x^{3}+9x^{2}+7x-6$

The problem states that one root is -3. Thus, it is true that $(x+3)$ is a factor of the polynomial. Given that this is fulfilled, it is also true that:

$f(x)=(x+3)Q(x) \therefore Q(x)=\frac{f(x)}{x+3} \\ \\ where \ Q(x) \ has \ a \ degree \ of \ 2$

We can find Q(x) by applying Ruffini's rule, thus:

$\ \ \ \ \ \ \ \ \ \ \ \ 2 \ \ \ \ \ \ \ 9 \ \ \ \ \ \ \ \ 7 \ \ \ \ \ \ -6 \\ -3 \\ \rule{50mm}{0.1mm} \\ \ {} \ \ \ \ \ \ \ \ \ \ \ \ 2 \ \ \ \ \ \ \ 3 \ \ \ \ \ -2 \ \ \ \ \ \ \ \ 0$

Therefore:

$Q(x)=2x^{2}+3x-2$

The roots of this polynomial can be get as follows:

$x_{12}=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \rightarrow x_{12}=\frac{-3\pm\sqrt{3^2-4(2)(-2)}}{2(2)}\\x_{1}=\frac{1}{2};\ x_{2}=-2$

These are the roots along with $-3$ . Finally, the factored polynomial can be written as follows:

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

One root of f(x) = 2x3 + 9x2 + 7x – 6 is –3. explain how to find the factors of the polynomial.

Similar Questions

If a polynomial function f(x) has roots –9 and 7 – i, what must be a factor of f(x)?

Write the polynomial in factored form x^3-3x^2-10x

Find the zeroes of the polynomial 6x2 3 7x

Find the zeros of the polynomial x square 3

Which second degree polynomial function f(x) has a lead coefficient of 3 and roots 4 and 1?

Find the roots of 2x 2 7x 3 0

If a polynomial function f(x) has roots 3 and mc001-1.jpg, what must also be a root of f(x)?

If a polynomial function f(x) has roots –8, 1, and 6i, what must also be a root of f(x)?

If a polynomial function f(x) has roots 0, 4, and , what must also be a root of f(x)?

Given the function f(x) = −5x2 − x + 20, find f(3).

Find the inverse of the function. f(x) = the cube root of quantity x divided by seven. - 9

If a polynomial function f(x) has roots 0, 4, and mc002-1.jpg, what must also be a root of f(x)?

For f(x) = 0.01(2)x, find the average rate of change from x = 3 to x = 8.

Factor x 2 7x 6

If , which inequality can be used to find the domain of f(x)?

Most viewed questions in Mathematics

Unit 6 similar triangles homework 2 similar figures answer key

All things algebra unit 7 polygons and quadrilaterals answer key

Gina wilson all things algebra 2016 answer key unit 11

Unit 1 geometry basics homework 4 angle addition postulate answers

Unit 6 exponents and exponential functions homework 8 answer key

The manager of a vacation resort believes that the ages

What is 271 403 rounded to the nearest ten thousand

Unit 1 geometry basics homework 3 angle relationships answer key

Homework 2 parallelograms

Why would a prism beat a sphere in a competition?

John wants to send a letter to peter

An artist sells a painting for 20.50 but uses 5.75

Unit 4 congruent triangles homework 1 classifying triangles answer key

Unit 4 congruent triangles homework 2 angles of triangles

Compare the values of the 2s and 5s in 55220