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sin 2θ = 2 sin θ cos θ y = ax² + bx + c tan θ = sin θ⁄cos θ m = Δy⁄Δx 45–45–90 P(A|B)<br>Focused on<br>Test Preparation<br>Every section of the SAT and ACT, drilled adaptively.<br>SATMath section<br>SAT Math<br>Linear equations & inequalities<br>Nonlinear functions<br>Geometry<br>And more
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a² + b² = c² ∫₀¹ x² dx = ⅓ sin²θ + cos²θ = 1 E = mc² limx→0 sinx⁄x = 1 Σn = n(n+1)/2 y = mx + b f(x) = x² − 4 7 × 8 = 56 e^(iπ) + 1 = 0 √2 ≈ 1.414 A = πr² log₂ 8 = 3 (a+b)² = a²+2ab+b² tan θ = sin θ⁄cos θ n! = n·(n−1)!<br>Making Something<br>Different ✨
DESK VIEW
Q5 — divide<br>(x³+2x²−5x−6)<br>÷ (x+3)<br>x² − x − 2
check it:<br>(x−2)(x+1)<br>= x² − x − 2 ✓<br>x+3 is a factor
Q5 — divide<br>(x³+2x²−5x−6)<br>÷ (x+3)<br>x² − x − 2
Q5 — divide<br>(x³+2x²−5x−6)<br>÷ (x+3)<br>x² − x − 2
check it:<br>(x−2)(x+1)<br>= x² − x − 2 ✓<br>x+3 is a factor
check it:<br>(x−2)(x+1)<br>= x² − x − 2 ✓<br>x+3 is a factor
Q5 — divide<br>(x³+2x²−5x−6)<br>÷ (x+3)<br>x² − x − 2
Q5 — divide<br>(x³+2x²−5x−6)<br>÷ (x+3)<br>x² − x − 2
Factors check out ✓
Reading: x² − x − 2
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x = −b ± √(b²−4ac)⁄2a d/dx eˣ = eˣ π ≈ 3.14159 √144 = 12 V = 4⁄3 πr³ 3² + 4² = 5² y′ = 2x gcd(12, 18) = 6 |−5| = 5 2⁵ = 32 C = 2πr<br>Check if Your Device is Compatible ⚙️<br>Enter the model of your MacBook or iPhone and we’ll tell you if it qualifies
m∠A + m∠B + m∠C = 180° x² − 9 = (x−3)(x+3) ½bh 5! = 120 slope = Δy⁄Δx 9 ÷ 3 = 3<br>Algebra II 1:12<br>What is (x³ + 2x² − 5x − 6) ÷ (x + 3)?<br>Ax² + x − 2<br>Bx² − x − 2<br>Cx² − x + 2
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So a remainder of 0 means x + 3 divides it evenly?
Milo<br>Exactly — a remainder of 0 means x + 3 is a factor. Now look at your quotient: which two numbers multiply to −2 and add to −1?
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DESK VIEW
Q5 — Divide the polynomials<br>(x³ + 2x² − 5x − 6) ÷ (x + 3)<br>x² − x − 2<br>x + 3 x³ + 2x² − 5x − 6<br>x³ + 3x²<br>− x² − 5x
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Worked example
x² − x − 2 → multiply to −2, add to −1 → (x − 2)(x + 1) ✓
Exercise · Nonlinear functions<br>Now you — factor: x² + 3x − 10<br>A.(x + 5)(x − 2)<br>B.(x − 5)(x + 2)
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cos 2θ = 1 − 2sin²θ ∫ 2x dx = x² + C aⁿ · aᵐ = aⁿ⁺ᵐ x² − 4 = (x−2)(x+2) f(g(x))
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Algebra II ✦ Adaptive 18:42
Q5 — Divide the polynomials<br>(x³ + 2x² − 5x − 6) ÷ (x + 3)
x² − x − 2<br>x + 3 x³ + 2x² − 5x − 6<br>x³ + 3x²<br>− x² − 5x<br>− x² − 3x<br>− 2x − 6<br>− 2x − 6<br>0 ← r<br>⇒ x² − x − 2
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DESK VIEW
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Algebra II 1:12<br>What is (x³ + 2x² − 5x − 6) ÷ (x + 3)?<br>Ax² + x − 2
Bx² − x − 2
Cx² − x + 2
Next problem
Q5 — Divide the polynomials
(x³ + 2x² − 5x − 6) ÷ (x + 3)
x² − x − 2<br>x + 3 x³ + 2x² − 5x − 6<br>x³ + 3x²<br>− x² − 5x<br>− x² − 3x<br>− 2x − 6<br>− 2x − 6<br>0 ← remainder
⇒ x² − x − 2<br>= (x − 2)(x + 1) ✓
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