Identify the factor: a) r2+7r+10 b) x2+4x+3 c) y2+6y+8

Question

Identify the factor:  a) r2+7r+10  b) x2+4x+3  c) y2+6y+8

Rita Miller · Accepted Answer

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} - 2 x + 4 x - 8

= x^{2} + 2 x - 8

Step 2
Given:

r^{2} + 7 r + 10

We have to find integers b and d such that

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

= r^{2} + d r + b r + b d

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

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

b d = 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} Factors b, d of 10 & Sum b + d = 7 \\ 5 \times 2 & 5 + 2 = 7 \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} + 2 r + 5 r + 10

= r^{2} + 7 r + 10

amarantha41 · Accepted Answer

Step 1  Given factor:  x2+4x+3  x2+4x+3=(x+b)(x+d)  =x2+dx+bx+bd  x2+4x+3=x2+(b+d)x+bd  Following table  Factors b, d of 3Sumb+d=43×13+1=4  To check:  (x+3)(x+1)=x(x+1)+3(x+1)  =x2+x+3x+3  =x2+4x+3

user_27qwe · Accepted Answer

Step 1Given:y2+6y+8Find integers b and d such thaty2+6y+8=(y+b)(y+d)=y2+dy+by+bdy2+6y+8=y2+(B+d)y+bdStep 2Table:Factors b, d of 8Sumb+d=64×24+2=61×81+8=9Step 3To check:(y+4)(y+2)=y(y+2)+4(y+2)=y2+2y+4y+8=y2+6y+8

Identify the factor: a) r^{2}+7r+10 b) x^{2}+4x+3 c) y^{2}+6y+8

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