Answer:
a = p * q
b = p * s + q * r
c = r * s
Step-by-step explanation:
In the trinomial ax² + bx + c
a is the coefficient of x²
b is the coefficient of x
c is the numerical term
∵ The trinomial is ax² + bx + c
∵ Its factors are (px + r) and (qx + s)
∴ ax² + bx + c = (px + r)(qx + s)
∵ (px + r)(qx + s) = (px)(qx) + (px)(s) + r(qx) + (r)(s)
∴ (px + r)(qx + s) = pqx² + (psx + qrx) + rs
∴ ax² + bx + c = pqx² + (ps + qr)x + rs
→ By comparing the two sides
∵ ax² = pqx² ⇒ divide both sides by x²
∴ a = pq
∵ bx = (ps + qr)x ⇒ Divide both sides by x
∴ b = ps + qr
∴ c = rs
∴ a = p * q
∴ b = p * s + q * r
∴ c = r * s
Answer:
25 to the power of 3.
Step-by-step explanation:
we got 25 schools ordering newspapers for 25 classes of 25 kids. that's 25x25x25. it wants the number of pages total, and since there's 25 pages in each newspaper we add another 25. so it's 25x25x25x25, also known as 25 to the power of 3.
![\bf \begin{cases} x=3\implies &x-3=0\\ x=1+3i\implies &x-1-3i=0\\ x=1-3i\implies &x-1+3i=0 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ (x-3)(x-1-3i)(x-1+3i)=0 \\\\\\ (x-3)\underset{\textit{difference of squares}}{([x-1]-3i)([x-1]+3i)}=0\implies (x-3)([x-1]^2-[3i]^2)=0 \\\\\\ (x-3)([x^2-2x+1]-[3^2i^2])=0\implies (x-3)([x^2-2x+1]-[9(-1)])=0](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Bcases%7D%20x%3D3%5Cimplies%20%26x-3%3D0%5C%5C%20x%3D1%2B3i%5Cimplies%20%26x-1-3i%3D0%5C%5C%20x%3D1-3i%5Cimplies%20%26x-1%2B3i%3D0%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%28x-3%29%28x-1-3i%29%28x-1%2B3i%29%3D0%20%5C%5C%5C%5C%5C%5C%20%28x-3%29%5Cunderset%7B%5Ctextit%7Bdifference%20of%20squares%7D%7D%7B%28%5Bx-1%5D-3i%29%28%5Bx-1%5D%2B3i%29%7D%3D0%5Cimplies%20%28x-3%29%28%5Bx-1%5D%5E2-%5B3i%5D%5E2%29%3D0%20%5C%5C%5C%5C%5C%5C%20%28x-3%29%28%5Bx%5E2-2x%2B1%5D-%5B3%5E2i%5E2%5D%29%3D0%5Cimplies%20%28x-3%29%28%5Bx%5E2-2x%2B1%5D-%5B9%28-1%29%5D%29%3D0)
[ correction added, Thanks to @stef68 ]
![\bf (x-3)([x^2-2x+1]+9)=0\implies (x-3)(x^2-2x+10)=0 \\\\\\ x^3-2x^2+10x-3x^2+6x-30=0\implies x^3-5x^2+16x-30=f(x) \\\\\\ \stackrel{\textit{applying a translation with a -2f(x)}}{-2(x^3-5x^2+16x-30)=f(x)}\implies -2x^3+10x^2-32x+60=f(x)](https://tex.z-dn.net/?f=%5Cbf%20%28x-3%29%28%5Bx%5E2-2x%2B1%5D%2B9%29%3D0%5Cimplies%20%28x-3%29%28x%5E2-2x%2B10%29%3D0%20%5C%5C%5C%5C%5C%5C%20x%5E3-2x%5E2%2B10x-3x%5E2%2B6x-30%3D0%5Cimplies%20x%5E3-5x%5E2%2B16x-30%3Df%28x%29%20%5C%5C%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Bapplying%20a%20translation%20with%20a%20-2f%28x%29%7D%7D%7B-2%28x%5E3-5x%5E2%2B16x-30%29%3Df%28x%29%7D%5Cimplies%20-2x%5E3%2B10x%5E2-32x%2B60%3Df%28x%29)
There are several expanded forms for a decimal number. Pick the one that matches your requirements.
64,375 = 60,000 +4,000 +300 +70 +5
64,375 = 6×10,000 +4×1,000 +3×100 +7×10 +5×1
64,375 = 6×10⁴ +4×10³ +3×10² +7×10¹ +5×10⁰
