Answer:
1d = -3
2b = 2
2c = 1
3a = 3
3d = 4
Step-by-step explanation:
Polynomial 1: [tex]x^2-8x+15[/tex]
Multiply the leading coefficient, 1, and the last term, 15. You get: 15.
Then, list out the factors of 15 and the addends of -8 until you get two of numbers that are the same:
Factors of 15: -5 * -3
Addends of -8: -5 + -3
Replace the -8x with -5x - 3x:
[tex]x^2-5x-3x+15[/tex]
Put parentheses around the first 2 terms & last 2 terms and factor like so:
[tex](x^2-5x)-(3x+15)[/tex]
[tex]x(x-5)-3(x-5)[/tex]
[tex](x-5)(x-3)[/tex]
Looking at the answer (ax + b)(cx + d), d would correspond with -3.
Polynomial 2: [tex]2x^3-8x^2-24x[/tex]
First factor out the x:
[tex]x(2x^{2}-8x-24)[/tex]
Divide the polynomial inside by 2 and place the 2 outside with the x:
[tex]2x(x^2-4x-12)[/tex]
Then find the factors of 1*-12 and the addends of -4 and see which two numbers match:
Factors of -12: -6 * 2
Addends of -4: -6 + 2
Replace the -8x with -6x + 2x:
[tex]2x(x^2-6x+2x-12)[/tex]
Put parentheses around the first 2 terms & last 2 terms and factor like so:
[tex]2x((x^2-6x)+(2x-12))[/tex]
[tex]2x(x(x-6)+2(x-6))[/tex]
[tex]2x((x+2)(x-6))[/tex]
[tex]2x(x+2)(x-6)[/tex]
Looking at the answer (2x)(ax + b)(cx + d), b & c would correspond with 2 & 1.
Polynomial 3: [tex]6x^2+14x+4[/tex]
Divide the polynomial by 2:
[tex](2)(3x^2+7x+2)[/tex]
Find the factors of 3*2 and the addends of 7 and see which two numbers match:
Factors of 6: 6 * 1
Addends of 7: 6 + 1
Replace the 7x with 6x + x:
[tex](2)(3x^2+6x+x+2)[/tex]
Put parentheses around the first 2 terms & last 2 terms and factor like so:
[tex](2)((3x^2+6x)+(x+2))[/tex]
[tex](2)(3x(x+2)+(x+2))[/tex]
[tex](2)((3x+1)(x+2))[/tex]
[tex](2)(3x+1)(x+2)[/tex]
Then multiply the 2 with the (x+2) and here's your final answer:
[tex](3x+1)(2x+4))[/tex]
Looking at the answer (ax + b)(cx + d), a & d correspond with 3 & 4.
Hope that helps (●'◡'●)
(This took a while to write, sorry about that)
