2. จงแยกตัวประกอบของพหุนามต่อไปนี้
1) \(\small\mathsf{x^2 \, – \, 5x}\)
วิธีทำ
\(\small\mathsf{x^2 \, – \, 5x}\) = x(x – 5)
ตอบ x(x – 5)
2) \(\small\mathsf{3m^2 \, – \, 3m}\)
วิธีทำ
\(\small\mathsf{3m^2 \, – \, 3m}\) = 3m(m – 1)
ตอบ 3m(m – 1)
3) \(\small\mathsf{-2y + y^2}\)
วิธีทำ
\(\small\mathsf{-2y + y^2}\) = -y(2 – y)
ตอบ -y(2 – y)
4) \(\small\mathsf{-5x^2 \, – \, 10x}\)
วิธีทำ
\(\small\mathsf{-5x^2 \, – \, 10x}\) = -5x(x + 2)
ตอบ -5x(x + 2)
5) \(\small\mathsf{x^2 + 4x + 3x + 12}\)
วิธีทำ
\(\small\mathsf{x^2 + 4x + 3x + 12}\)
= \(\small\mathsf{(x^2 + 4x) + (3x + 12)}\)
= x(x + 4) + 3(x + 4)
= (x + 4)(x + 3)
= (x + 4)(x + 3)
ตอบ (x + 4)(x + 3)
6) \(\small\mathsf{m^2 \, – \, 5m + 2m \, – \, 10}\)
วิธีทำ
\(\small\mathsf{m^2 \, – \, 5m + 2m \, – \, 10}\)
= \(\small\mathsf{(m^2 \, – \, 5m) + (2m \, – \, 10)}\)
= m(m – 5) + 2(m – 5)
= (m – 5)(m + 2)
= (m – 5)(m + 2)
ตอบ (m – 5)(m + 2)
7) \(\small\mathsf{x^2 + 9x + 14}\)
วิธีทำ
\(\small\mathsf{x^2 + 9x + 14}\)
= \(\small\mathsf{x^2 + (2 + 7)x + (2)(7)}\)
= (x + 2)(x + 7)
ตอบ (x + 2)(x + 7)
8) \(\small\mathsf{n^2 + 15n + 14}\)
วิธีทำ
\(\small\mathsf{n^2 + 15n + 14}\)
= \(\small\mathsf{n^2 + (14 + 1)n + (14)(1)}\)
= (n + 14)(n + 2)
ตอบ (n + 14)(n + 2)
9) \(\small\mathsf{y^2 + 10y + 24}\)
วิธีทำ
\(\small\mathsf{y^2 + 10y + 24}\)
= \(\small\mathsf{y^2}\) + (6 + 4)y + (6)(4)
= (y + 6)(y + 4)
ตอบ (y + 6)(y + 4)
10) \(\small\mathsf{x^2}\) + 7x – 18
วิธีทำ
\(\small\mathsf{x^2}\) + 7x – 18
= \(\small\mathsf{x^2}\) + [9 + (-2)]x + (9)(-2)
= (x + 9)(x – 2)
ตอบ (x + 9)(x – 2)
11) \(\small\mathsf{x^2}\) – 9x + 20
วิธีทำ
\(\small\mathsf{x^2}\) – 9x + 20
= \(\small\mathsf{x^2}\) + [(-4) + (-5)]x + (-4)(-5)
= (x – 4)(x – 5)
ตอบ (x – 4)(x – 5)
12) \(\small\mathsf{a^2}\) – 8a – 9
วิธีทำ
\(\small\mathsf{a^2}\) – 8a – 9
= \(\small\mathsf{a^2}\) + [(-9) + 1]a + (-9)(1)
= (a – 9)(a + 1)
ตอบ (a – 9)(a + 1)
13) \(\small\mathsf{b^2}\) + 9b – 10
วิธีทำ
\(\small\mathsf{b^2}\) + 9b – 10
= \(\small\mathsf{b^2}\) + [10 + (-1)]b + (10)(-1)
= (b + 10)(b – 1)
ตอบ (b + 10)(b – 1)
14) \(\small\mathsf{x^2}\) – 10x + 24
วิธีทำ
\(\small\mathsf{x^2}\) – 10x + 24
= \(\small\mathsf{x^2}\) + [(-6) + (-4)]x + (-6)(-4)
= (x – 6)(x – 4)
ตอบ (x – 6)(x – 4)
15) \(\small\mathsf{x^2}\) – 14x + 24
วิธีทำ
\(\small\mathsf{x^2}\) – 14x + 24
= \(\small\mathsf{x^2}\) + [(-12) + (-2)]x + (-12)(-2)
= (x – 12)(x – 2)
ตอบ (x – 12)(x – 2)
16) \(\small\mathsf{a^2}\) + 11a + 18
วิธีทำ
\(\small\mathsf{a^2}\) + 11a + 18
= \(\small\mathsf{a^2}\) + (9 + 2)a + (9)(2)
= (a + 9)(a + 2)
ตอบ (a + 9)(a + 2)
17) 56 + 15a + \(\small\mathsf{a^2}\)
วิธีทำ
56 + 15a + \(\small\mathsf{a^2}\)
= (7)(8) + (7 + 8)a + \(\small\mathsf{a^2}\)
= (7 + a)(8 + a)
ตอบ (7 + a)(8 + a)
18) \(\small\mathsf{m^2}\) – 13m + 42
วิธีทำ
\(\small\mathsf{m^2}\) – 13m + 42
= \(\small\mathsf{m^2}\) + [(-6) + (-7)]m + (-6)(-7)
= (m – 6)(m – 7)
ตอบ (m – 6)(m – 7)
19) \(\small\mathsf{x^2}\) – 20x – 21
วิธีทำ
\(\small\mathsf{x^2}\) – 20x – 21
= \(\small\mathsf{x^2}\) + [(-21) + 1]x + (-21)(1)
= (x – 21)(x + 1)
ตอบ (x – 21)(x + 1)
20) \(\small\mathsf{x^2}\) – 15x + 36
วิธีทำ
\(\small\mathsf{x^2}\) – 15x + 36
= \(\small\mathsf{x^2}\) + [(-12) + (-3)]x + (-12)(-3)
= (x – 12)(x – 3)
ตอบ (x – 12)(x – 3)
21) \(\small\mathsf{y^2}\) + 13y + 12
วิธีทำ
\(\small\mathsf{y^2}\) + 13y + 12
= \(\small\mathsf{y^2}\) + (12 + 1)y + (12)(1)
= (y + 12)(y + 1)
ตอบ (y + 12)(y + 1)
22) \(\small\mathsf{t^2}\) – 11t + 30
วิธีทำ
\(\small\mathsf{t^2}\) – 11t + 30
= \(\small\mathsf{t^2}\) + [(-6) + (-5)]t + (-6)(-5)
= (t – 6)(t – 5)
ตอบ (t – 6)(t – 5)
23) \(\small\mathsf{a^2}\) – a – 72
วิธีทำ
\(\small\mathsf{a^2}\) – a – 72
= \(\small\mathsf{a^2}\) + [(-9) + 8]a + (-9)(8)
= (a – 9)(a + 8)
ตอบ (a – 9)(a + 8)
24) \(\small\mathsf{x^2}\) – 17x + 70
วิธีทำ
\(\small\mathsf{x^2}\) – 17x + 70
= \(\small\mathsf{x^2}\) + [(-10) + (-7)]x + (-10)(-7)
= (x – 10)(x – 7)
ตอบ (x – 10)(x – 7)
25) \(\small\mathsf{y^2}\) – 18y + 81
วิธีทำ
\(\small\mathsf{y^2}\) – 18y + 81
= \(\small\mathsf{y^2}\) + [(-9) + (-9)]y + (-9)(-9)
= (y – 9)(y – 9)
ตอบ (y – 9)(y – 9)
26) \(\small\mathsf{n^2}\) + 15n – 54
วิธีทำ
\(\small\mathsf{n^2}\) + 15n – 54
= \(\small\mathsf{n^2}\) + [(18) + (-3)]n + (18)(-3)
= (n + 18)(n – 3)
ตอบ (n + 18)(n – 3)
27) \(\small\mathsf{x^2}\) – 30x – 99
วิธีทำ
\(\small\mathsf{x^2}\) – 30x – 99
= \(\small\mathsf{x^2}\) + [(-33) + 3]x + (-33)(3)
= (x – 33)(x + 3)
ตอบ (x – 33)(x + 3)
28) \(\small\mathsf{m^2}\) – 22m + 121
วิธีทำ
\(\small\mathsf{m^2}\) – 22m + 121
= \(\small\mathsf{m^2}\) + [(-11) + (-11)]m + (-11)(-11)
= (m -11)(m -11)
ตอบ (m -11)(m -11)
29) \(\small\mathsf{x^2}\) – 12x – 85
วิธีทำ
\(\small\mathsf{x^2}\) – 12x – 85
= \(\small\mathsf{x^2}\) + [(-17) + 5]x + (-17)(5)
= (x – 17)(x + 5)
ตอบ (x – 17)(x + 5)
30) 144 + 24a + \(\small\mathsf{a^2}\)
วิธีทำ
144 + 24a + \(\small\mathsf{a^2}\)
= (12)(12) + (12 + 12)a + \(\small\mathsf{a^2}\)
= (12 + a)(12 + a)
ตอบ (12 + a)(12 + a)