David Young

2021-12-28

Identify the factor:

a)${r}^{2}+7r+10$

b)${x}^{2}+4x+3$

c)${y}^{2}+6y+8$

a)

b)

c)

Rita Miller

Beginner2021-12-29Added 28 answers

Step 1

a) We can get a quadratic by multiplying two first-degree polynomials.

Method:

$(x+4)(x-2)=x(x-2)+4(x-2)$

$={x}^{2}-2x+4x-8$

$={x}^{2}+2x-8$

Step 2

Given:

${r}^{2}+7r+10$

We have to find integers b and d such that

${r}^{2}+7r+10=(r+b)(r+d)$

$={r}^{2}+dr+br+bd$

${r}^{2}+7r+10={r}^{2}+(b+d)r+bd$

Since the constant coefficients on each side of the equation ought to be equal, we must have$bd=10$ (i.e) b and d are factors of 10.

Similarly, the coefficients of r must be the same, so that$b+d=7$

The following table shows the possibilities.

$$\begin{array}{|cc|}\hline \text{Factors b, d of 10}& \text{Sum}b+d=7\\ 5\times 2& 5+2=7\\ \hline\end{array}$$

There is no need to list negative factors, such as$(-5)(-2)$ , since their sum is negative. So the factors are 5 and 2.

To check:

$(r+5)(r+2)=r(r+2)+5(r+2)$

${r}^{2}+2r+5r+10$

$={r}^{2}+7r+10$

a) We can get a quadratic by multiplying two first-degree polynomials.

Method:

Step 2

Given:

We have to find integers b and d such that

Since the constant coefficients on each side of the equation ought to be equal, we must have

Similarly, the coefficients of r must be the same, so that

The following table shows the possibilities.

There is no need to list negative factors, such as

To check:

amarantha41

Beginner2021-12-30Added 38 answers

Step 1

Given factor:

${x}^{2}+4x+3$

${x}^{2}+4x+3=(x+b)(x+d)$

$={x}^{2}+dx+bx+bd$

${x}^{2}+4x+3={x}^{2}+(b+d)x+bd$

Following table

$$\begin{array}{|cc|}\hline \text{Factors b, d of 3}& \text{Sum}b+d=4\\ 3\times 1& 3+1=4\\ \hline\end{array}$$

To check:

$(x+3)(x+1)=x(x+1)+3(x+1)$

$={x}^{2}+x+3x+3$

$={x}^{2}+4x+3$

Given factor:

Following table

To check:

user_27qwe

Skilled2022-01-05Added 375 answers

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