Factor the trinomial and explain..?

Question

24y^2-14yz-3z^2

Answer 1

24y^2-14yz-3z^2
( 6y + ...)(4y - ...)
( 6y + z)(4y - 3z)

to check multiply 2 outside & 2 inside
i.e. 6y*-3z + z*4y
= -18yz + 4yz
= -14yz

Answer 2

(6y+z)(4y-3z)

By looking at -3z^2, you know that the factors will include 3z and z, one of which has to be negative. The first expression (24y^2) tells you that the first expressions in the parenthesis must be factors of 24 (i.e. 1and 24, 2 and 12, 3 and 8, 4 and 6). By just looking at 1 and 24 and 2 and 12, you can figure these can't be it. When you work out (6y*-3z)+(4y*z), you get -18yz+4yz=-14yz. Thats how you know those factors work in this expression.
Hope this helps.

Answer 3

This probably factors into binomials of the form:
(ay + bz)(cy + dz)

(Using FOIL to expand the general form would give
acy² + (bc+ad)yz + bdz²
which is the same as your initial problem. )

Multiply your y² coefficient by your z² coefficient
(24)(-3) = -72
Next, find factors of -72 that add up to -14:
1 & -72: no
2 & -36: no
3 & -24: no
4 & -18: yes
Rewrite the middle term, -14xy, as the sum of two terms of yz that have coefficients 4 and -18:
24y² + 4yz -18yz -3z²
Factor out of the first two terms and the last two terms:
4y(6y + z) -3z(6y + z)
Factor out the common binomial term:
(6y + z)(4y -3z)

Answer 4

(6y+z)(4y-3z) is the answer.

break down the 24 into 8x3 or 2x12 or 6x4 or 24x1 and look to see which pair will give you a difference of 14 if you multiply one of the numbers in the pair by 3? 3x6 =18 - 4 gives you the 14 you need.

Answer 5

24y^2-14yz-3z^2

=(6y+z)(4y-3z))