Is the expression below completely factored? If not, complete the factorization.
4y(8y3 – 12y2 + 6y)

A) No, because the greatest common factor is 8y?, and the completely factored form is 8y?(4y2 - 6y + 3).

B) Yes, because the greatest common factor is 4y, and the completely factored form is 44(8y3 - 12y2 + 6y).

C) No, because the greatest common factor 4y?, and the completely factored form is 4y?(8y2 - 12y + 6).

D) No, because the greatest common factor is sy, and the completely factored form is 8y(4y3 - 6y2 + 3y).

Answer:

A) No, because the greatest common factor is 8y?, and the completely factored form is 8y2(4y2 - 6y + 3).

Step-by-step explanation:

Considering the expression

4y(8y3 – 12y2 + 6y)

From the elements in the parenthesis, 2 and y can still be factored out such that what will be left of each element

8y3/2y = 4y2

12y2/2y = 6y

6y/2y = 3

Hence

4y(8y3 – 12y2 + 6y) = 4y*2y(4y2 - 6y +3)

= 8y2(4y2 - 6y + 3)

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Once upon a time, there was a lovely princess. But she had an enchantment upon her of a fearful sort, which could only be broken by love's first kiss. She was locked away in a castle, guarded by a terrible fire-breathing dragon. Many brave knights had attempted to free her from the dreadful prison, but none prevailed. She waited in the dragon's keep, in the highest room of the tallest tower, for her true love and true love's first kiss." [Laughing] Like that's ever gonna happen.
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Shrek: What a load of--
[Toilet Door slams]
Shrek hops out his outhouse and his routine like taking a mud shower and farting in his pool.
[♪ All-Star By Smash Mouth Playing]
Steve Harwell: ♪ Somebody once told me the world is gonna roll me, I ain't the sharpest tool in the shed. She was lookin' kind of du mb with her finger and her thumb in the shape of an "L" on her forehead. The years start comin', and they don't stop comin', fed to the rules and I hit the ground runnin', didn't make sense not to live for fun. Your brain gets smart but your head gets du mb. So much to do, so much to see, so what's wrong with takin' the backstreets. You'll never know if you don't go, you'll never shine if you don't glow. Hey, now, you're an all-star. Get your game on, go play. Hey, now, you're a rock star. Get the show on, get paid. And all that glitters is gold, only shootin' stars break the mold. It's a cool place, and they say it gets colder, you're bundled up now, but wait till you get older. But the meteor men beg to differ judging by the hole in the satellite picture. The ice we skate is gettin' pretty thin, the water's getting warm so you might as well swim. My world's on fire, how 'bout yours? That's the way I like it and I'll never get bored. Hey, now, you're an all-star. ♪
[Shouting]
Steve Harwell: ♪ Get your game on, go play. Hey, now, you're a rock star. Get the show on, get paid. And all that glitters is gold, only shootin' stars break the mold. ♪
[Belches]
Villagers: Go! Go!
[Record Scrating]
Steve Harwell: ♪ Go. Go. Go. Hey, now, you're an all-star. Get your game on, go play. Hey, now, you're a rock star, get the show on, get paid. And all that glitters is gold, only shootin' stars break the mold. ♪
Villagers: Think it's in there? All right! Let's get it!
Villager 1: Whoa. Hold on. Do you know what that thing could do to you?
Villager 2: Yeah, it'll grind your bones for its bread.
Shrek: [Laughs] Yes, well, actually, that would be a giant. Now, ogres-- they're much worse. They'll make a suit from your freshly peeled skin.
Villager 3: No!
Shrek: They'll shave your liver. Squeeze the jelly from your eyes! Actually, it's quite good on toast.
Villager 3: Back! Back, beast! Back! I warn ya!
[Gasping]
Villager 3: Right.
[Roaring]
[Shouting]
[Roaring]
[Roaring Continues]
[Shouting Continues]
Shrek: [Whispers] This is the part where you run away.
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Shrek: [Laughs] [Laughing] And stay out! "Wanted. Fairy tale creatures." [Sighs]
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[Gasps]
Guard 2: Move it along. Come on! Get up!
Captain of the Guards: Next!
Guard 3: Give me that! Your flying days are over.
Captain of the Guards: That's 20 pieces of silver for the witch. Next!
Guard 4: Get up!
Captain of the Guards: Twenty pieces.
Guard 5: Come on!
[Thudding]
Guard 6: Sit down there! Keep quiet!
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