Question

1) разложите на множители
х⁴+7х²+16
х⁴+3х+2​

Answer 1

1. $x^{4} + 7x^{2} + 16 = x^{4} - x ^{3} + x^{3} + 4x^{2} - x^{2} + 4x^{2} + 4x - 4x + 16 = x^{2} \times (x^{2} - x + 4) + x \times (x^{2} - x + 4) + 4 \times (x ^{2} - x + 4) = <strong>(x^{2} - x + 4) \times (x ^{2} + x + 4)$

2. $x^{4} + 3x + 2 = x^{4} + x^{3} - x^{3} - x^{2} + x^{2} + x + 2x + x = x^{3} \times (x + 1) - x^{2} \times (x + 1) + x \times (x + 1) + 2 \times (x + 1) = <strong>(x + 1) \times (x^{3} - x^{2} + x + 2)</strong>$