Вправи: 918

918. Розкладіть квадратний тричлен на множники:

1) x² – 8х + 7.

D = (–8)² – 4 • 7 = 36;

x₁ = 8+62 = 7; x₂ = 8-62 = 1;

x² – 8x + 7 = (x – 7)(x – 1).

2) x² + 8х – 9.

D = 8² – 4 • (–9) = 100;

x₁ = -8+102 = 1; x₂ = -8-102 = –9;

x² + 8х – 9 = (x – 1)(х + 9).

3) 2x² – 7x + 3.

D = (–7)² – 4 • 2 • 3 = 25;

x₁ = 7+54 = 3; x₂ = 7-54 = 12;

2x² – 7x + 3 = 2(x – 3)(x – 12) = (x – 3)(2x – 1).

4) –x² + x + 12.

D = 1² – 4 • (–1) • 12 = 49;

x₁ = -1+7-2 = –3; x₂ = -1-7-2 = 4;

–x² + x + 12 = –(x + 3)(х – 4) = (x + 3)(4 – x).

5) –6x² – 5x + 1.

D = (–5)² – 4 • (–6) = 49;

x₁ = 5+7-12 = –1; x₂ = 5-7-12 = 16;

–6x² – 5x + 1 = –6(x + 1)(x – 16) = (x + 1)(1 – 6x).

6) 7x² + 19x – 6.

D = 19² – 4 • 7 • (–6) = 529; D = 23;

x₁ = -19+232 • 7 = 27; x₂ = -19-232 • 7 = –3;

7x² + 19x – 6 = 7(x – 27)(x + 3) = (7x – 2)(x + 3).