4.hitunglha.2³×4²-6³b.3⁴-8⁰×3⁴c.8⁴:2⁴+3³
Answer (4)
From the factor theorem that says, "The polynomial P(x) has x-r as a factor if and only if r is a root of the equation P(x) = 0." So if you plugged -1 into the x's in the equation and get 0 back then, x+1 is a factor. Let's do it. ( − 1 ) 3 − 57 ( − 1 ) − 56 = − 1 + 57 − 56 = 0 It works. When you plugged -1 into x, you got 0 back and that's what the factor theorem says. Now let's test it with synthetic division. If we divide x+1 into the original equation and get a remainder of 0, then we should be good. I'll write it up on Paint and upload it. As you can see, our remainder is 0 and our quotient is x 2 − x − 56 . This is the Factor the Polynomial part that you wanted. We can factor this into (x-8)(x+7). So our 3 roots of the equation are (x+1)(x-8)(x+7) Hope this helps and i'm so sorry for the long reply. I forgot to put 0x^2 when I was doing synthetic division. :/ and also sorry for the unclear paint image. you can zoom in if you want. it's nothing really important it just shows me doing the synthetic division part where i divide x+1 into the original equation.
x^3 - 57x - 56=0⇒ x(x^2-57)= 56
Verify if x= - 1 is a solution of this equation. (-1)* [(-1)^2 - 57]=56 (-1)[1 - 57] = 56 (-1)*(-56) = 56
56 =2 28 = (-2) (-28) = 4 14 = (- 4) (-14) = 8 7= (-8) (-7) x=8 ⇒ 8*(64-57)=56 ok⇒ x=8 is a solution x= -7 ⇒ (-7)*(49-57)=56 ok ⇒ x= - 7 is a solution
the smallest x= -7 x= - 1 the largest x= 8
We confirmed that x = − 1 is a solution by using synthetic division, which resulted in a remainder of zero. The polynomial can be factored as ( x + 1 ) ( x − 8 ) ( x + 7 ) , revealing the real solutions x = − 8 , − 1 , 8 . Therefore, the smallest value is x = − 8 , the other value is x = − 1 , and the largest value is x = 8 .
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Jawaban:4. Hitunglah:a. 2³ × 4² – 6³ = 8 × 16 – 216 = 128 – 216 = -88b. 3⁴ – 8⁰ × 3⁴ = 81 – 1 × 81 = 81 – 81 = 0c. 8⁴ : 2⁴ + 3³ = (4096 ÷ 16) + 27 = 256 + 27 = 283Jawaban:a. -88 b. 0 c. 283
