Question

expand and simplify the following (x+5)(x-2)

Answer 1

Step-by-step explanation:

How do I expand and simplify the following (x+5) (x-2)

(x+5)(x−2) is a product of 2 linear polynomial, and thus a quadratic one. Let us find a,b,c such that:

(x+5)(x−2)=ax2+bx+c

By solving a system of 3 linear equations:

Plug x=0:

(x+5)(x−2)=(0+5)(0−2)=−10

So,

a⋅02+0b+c=−10⇒c=−10

Plug x=1:

(x+5)(x−2)=6⋅−1=−6⇒

⇒a⋅12+1b−10=−6⇒

⇒a+b−10=−6⇒a+b=4(1)

Now, let us plug x=2:

(x+5)(x−2)=(2+5)(2−2)=7⋅0−0

Thus,

a⋅22+2b−10=0⇒4a+2b=10

From 1:

4a+2(4−a)=10⇒4a+8−2a=10⇒

⇒2a+8=10⇒2a=2⇒

⇒a=1

Let us use (1) again:

a+b=4⇒1+b=4⇒b=3

∴(x+5)(x−2)=x2+3x−10