Which of the following linear expression divides evenly into `6x ^(2) + 7x -20` ?

Options

A. `3x -10`
B. `3x -5`
C. `3x -4`
D. `3x -2`

Answer

C

Explanation

Understanding that in algebra "divides evenly" means "is factor" is the key to answering the question. You could use polynomial long division, but in most cases, factoring is quicker. The leading coefficient of the equation is no 1, so you'll need to use grouping to factor the equation. The general form of a quadratic is `ax ^(2) + bx +c.` To find the factors, multiply a by, c `x -20=-120,` and then look for two factors of that product whose sum is equal to b, the coefficient of the middle term. The two factors of `-120` that add up to 7 are 15 and `-8:`
`6x ^(2)+ 7x -20 =6x ^(2) + 15x -8x -20`
`=(6x ^(2) + 15x) - (8x + 20)`
` =3x (2x + 5)-4 (2x +5)`
`=(2x +5) (3x -4)`
Therefore, `3x -4` divides enenly into the expression, so (C ) is correct.