Factoring Trinomials into Binomials Practice AK

1. $(x+1)(x+2)$

$\eqalign{x^2+3x+2\\\text{Multiplication term: } 2 \text{ and Addition term: } 3\\ 2 \times 1 = 2 \text{ and }2 + 1=3\\x^2+2x+x+2\\x(x+2)+1(x+2)\\(x+1)(x+2)}$

2. $(x-3)(x+5)$

$\eqalign{x^2+2x-15\\\text{Multiplication term: } -15  \text{ and Addition term: } 2\\ 5 \times -3 = -15 \text{ and }5 +-3=2\\x^2+5x-3x-15\\x(x+5)-3(x+5)\\(x-3)(x+5)}$

3. $(x-2)(x-4)$

$\eqalign{x^2-6x+8\\\text{Multiplication term: }8  \text{ and Addition term: } -6\\ -2 \times -4 = 8 \text{ and } -2 +-4=-6\\x^2-2x-4x+8\\x(x-2)-4(x-2)\\(x-4)(x-2)}$

4.$(x+6)(x-6)$

$\eqalign{x^2-36\\\text{Multiplication term: } -36  \text{ and Addition term: } 0\\ 6 \times -6 = -36 \text{ and } 6 +-6=0\\x^2+6x-6x-36\\x(x+6)-6(x+6)\\(x+6)(x-6)}$

5.$(2x+1)(x+5)$

$\eqalign{2x^2+11x+5\\\text{Multiplication term: } 10  \text{ and Addition term: } 11\\ 10 \times 1 =10 \text{ and }10 +1=11\\2x^2+10x+x+5\\2x(x+5)+1(x+5)\\(2x+1)(x+5)}$

6.$(3x+2)(x-3)$

$\eqalign{3x^2-7x-6\\\text{Multiplication term: } -18  \text{ and Addition term: } -7\\ -9 \times 2 =-18 \text{ and }-9 +2=-7\\3x^2-9x+2x-6\\3x(x-3)+2(x-3)\\(3x+2)(x-3)}$

7.$(2x+2)(3x-3)$ or $(2x-2)(3x+3)$ or $6(x+1)(x-1)$ or $(6x-6)(x+1)$

$\eqalign{6x^2-6\\\text{Multiplication term: } -36  \text{ and Addition term: } 0\\ -6 \times 6 =-36 \text{ and }-6 +6=0\\6x^2-6x+6x-6\\3x(2x-2)+3(2x-2)\\(3x+3)(2x-2)}$

8.$(5x-5)(3x+2)$ or  $(15x+10)(x-1)$ or $5(x-1)(3x+2)$

$\eqalign{15x^2-5x-10\\\text{Multiplication term: } -150  \text{ and Addition term: } -5\\ -15 \times 10 =-150 \text{ and }-15 +10=-5\\15x^2-15x+10x-10\\15x(x-1)+10(x-1)\\(15x+10)(x-1)}$

9.$(6x-2)(3x-10)$ or $2(3x-1)(3x-10)$

$\eqalign{18x^2-66x+20\\\text{Multiplication term: } 360  \text{ and Addition term: } -66\\ -60 \times -6 =360 \text{ and }-60 + -6=-66\\18x^2-60x-6x+20\\(18^2-60x)+(-6x+20)\\6x(3x-10)-2(3x-10)\\(6x-2)(3x-10)}$

10.$(7x-3)(5x-2)$

$\eqalign{35x^2-29x+6\\\text{Multiplication term: } 210  \text{ and Addition term: } -29\\ -15 \times -14 =210 \text{ and }-15 + -14=-29\\35x^2-14x-15x+6\\(35x^2-14x)+(-15x+6)\\7x(5x-2)-3(5x-2)\\(7x-3)(5x-2)}$