Exercice 2 : factoriser

Soit \(x \in \mathbb{R}\). Factoriser les expressions suivantes

Question

\(x^2 − 9\)

Solution

On a \(x^2 − 9 = (x − 3)(x + 3)\).

Question

\(x^4 − 16\)

Solution

On a \(x^4 − 16 = (x^2 − 4)(x^2 + 4) = (x − 2)(x + 2)(x^2 + 4)\).

Question

\((5 − 2x)(3 − x) − 3(3 − x) \)

Solution

On a \((5 − 2x)(3 − x) − 3(3 − x) = (3 − x)(5 − 2x − 3) = (3 − x)(2 − 2x) = 2(3 − x)(1 − x).\)

Question

\((5−2x)(2x−1)+(2−4x) \)

Solution

On a \((5−2x)(2x−1)+(2−4x) = (5−2x)(2x−1)−2(2x−1) = (2x−1)(5−2x−2) = (2x−1)(3−2x)\).

Question

\((x−1)(3x+2)+ (2x+3)(1−x) \)

Solution

On a \((x−1)(3x+2)+ (2x+3)(1−x) = (x−1)(3x+2)−(2x+3)(x−1) = (x−1)(3x+2−(2x+3)) = (x − 1)(3x + 2 − 2x − 3) = (x − 1)(x − 1) = (x − 1)^2\) .

Question

\(9x^2 −12x+ 4+ (4−3x)(3x−2)\)

Solution

On a \( 9x^2 −12x+ 4+ (4−3x)(3x−2) = (3x−2)^2 + (4−3x)(3x−2) = (3x−2)(3x−2+ 4−3x) = 2(3x−2)\).