Вправи: 1050

1050. Розкладіть на множники квадратний тричлен:

1) x² + Зх – 4.

D = З² – 4 • (–4) = 25; x₁ = -3+52 = 1; x₂ = -3-52 = –4.

x² + Зх – 4 = (х – 1)(х + 4).

2) 2x² – 7x – 4.

D = (–7)² – 4 • 2 • (–4) = 81; x₁ = 7+94 = 4; x₂ = 7-94 = –12.

2x² – 7x – 4 = 2(x – 4)(x + 12) = (x – 4)(2x + 1).

3) –x² + 3x + 18.

D = 9 + 4 • 18 = 81; x₁ = -3+9-2 = 6-2 = –3; x₂ = -3-9-2 = 6;

–x² + 3x + 18 = –(x + 3)(x – 6) = (x + 3)(6 – x).

4) –4x² + 9x – 2.

D = 9² – 4 • (–4) • (–2) = 49; x₁ = -9+7-8 = 14; x₂ = -9-7-8 = 2;