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Write each expression as a product of linear factors 1. X^2+1/2x 2. X^2+2x-3 3. (2x-3)^2 4. X^3+2x^2-19x-20

User Nico R
by
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1 Answer

3 votes

Answer:

1. X^2+1/2x =
x(x+(1)/(2))

2. X^2+2x-3 =
(x-1)(x+3)

3. (2x-3)^2 = (2x-3)(2x-3)

4. X^3+2x^2-19x-20 =
(x+1)(x-4)(x+5)

Explanation:

Each expression can be written as a product of linear factors as follows

1. X^2+1/2x ⇒
x^(2) + (1)/(2)x


x^(2) + (1)/(2)x =
x(x+(1)/(2))

Hence, X^2+1/2x =
x(x+(1)/(2))

2. X^2+2x-3 ⇒
x^(2) +2x-3


x^(2) +2x-3 = x^(2) +3x-x-3


x^(2) +3x-x-3 = x(x+3) -1(x+3)


x(x+3) -1(x+3) = (x-1)(x+3)

Hence, X^2+2x-3 =
(x-1)(x+3)

3. (2x-3)^2 ⇒
(2x-3)^(2)


(2x-3)^(2) = (2x-3)(2x-3)

Hence, (2x-3)^2 = (2x-3)(2x-3)

4. X^3+2x^2-19x-20 ⇒
x^(3)+2x^(2) -19x -20


x^(3)+2x^(2) -19x -20 = (x+1)(x^(2) +x-20)

First,


x^(2) +x-20 = x^(2) +5x-4x-20\\x^(2) +5x-4x-20= x(x+5)-4(x+5)\\x(x+5)-4(x+5) = (x-4)(x+5)


(x+1)(x^(2) +x-20) = (x+1)(x-4)(x+5)

Hence, X^3+2x^2-19x-20 =
(x+1)(x-4)(x+5)

User Matteo Collina
by
7.6k points

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