Question

Hello, please help me solve to find the correct polynomials!

Answer 1

INFORMATION:

We have the next polynomials

And we must factor them to complete the next table

STEP BY STEP EXPLANATION:

1.

`x^2-8x+15`

To factor it, we must look for two number that multiplied be equal to 15 and added up be equal to -8.

These two numbers would be -5 and -3.

- -5 x -3 = 15

- -5 - 3 = -8

So, when we factor this polynomial, we obtain

`\begin{gathered} x^2-8x+15=(x-5)(x-3) \\ \text{ So, }a=1,b=-5,c=1,d=-3 \end{gathered}`

2.

`2x^3-8x^2-24x`

To factor it, we must first take the common factor 2x from the expression

`2x(x^2-4x-12)`

Now, we must factor the terms in the parenthesis. We must look for two number that multiplied be equal to -12 and added up be equal to -4. These two numbers would be -6 and 2.

- -6 x 2 = -12

- -6 + 2 = -4

So, when we factor this polynomial, we obtain

`\begin{gathered} 2x(x+2)(x-6) \\ \text{ So, }a=1,b=2,c=1,d=-6 \end{gathered}`

3.

`6x^2+14x+4`

To factor it, we must first take the common factor 2 from the expression

`2(3x^2+7x+2)`

Then, we divide the 7x term in the parenthesis in two terms

`2(3x^2+6x+x+2)`

Now, we can take the common factor x + 2 in the parenthesis

`2(3x(x+2)+(x+2))`

Finally, we can take the common factor x + 2 in the complete expression

`\begin{gathered} 2(x+2)(3x+1) \\ \text{ Simplifying,} \\ =\left(3x+1\right)(2x+4) \\ \text{ So, }a=3,b=1,c=2,d=4 \end{gathered}`

ANSWER: