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3 years ago

12

How do I factorize a quadratic expression ?

1 answer:

Xelga [282]3 years ago

3 0

Answer:

Please check below the step-by-step explanation.

Step-by-step explanation:

Considering the quadratic expression

$ax^2+bx\:+\:c\:=0$

$a,\:b,\:and\:c\:can\:have\:any\:value,\:except\:that\:a\:can't\:be\:0.$

$To\:Factorise\:a\:Quadratic\:is\:to:$

" $find\:what\:to\:multiply\:to\:get\:the\:Quadratic$ "

For example, multiplying $(x + 3)$ and $(x - 2)$ together will bring $x^2+x-6$

i.e.

$\left(x+3\right)\left(x-2\right) = xx+x\left(-2\right)+3x+3\left(-2\right)$

$\mathrm{Apply\:minus-plus\:rules}$

$+\left(-a\right)=-a$

$\left(x+3\right)\left(x-2\right) = xx-2x+3x-3\cdot \:2$

$= x^2+x-6$

Therefore, $(x + 3)$ and $(x - 2)$ are factors of $x^2+x-6$

Keywords: factorize, quadratic expression

Learn more about quadratic expression from brainly.com/question/12182022

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a road follows the shape of a parabola f(x)=3x2– 24x + 39. A road that follows the function g(x) = 3x – 15 must cross the stream

Nonamiya [84]

the coordinates where the bridges must be built is $(3,-6)$ and $(6,3)$ .

<u>Step-by-step explanation:</u>

Here we have , a road follows the shape of a parabola f(x)=3x2– 24x + 39. A road that follows the function g(x) = 3x – 15 must cross the stream at point A and then again at point B. Bridges must be built at those points.We need to find Identify the coordinates where the bridges must be built. Let's find out:

Basically we need to find values of x for which f(x) = g(x) :

⇒ $f(x)-g(x)=0$

⇒ $3x^2- 24x + 39-(3x - 15 ) =0$

⇒ $3x^2- 24x + 39-3x + 15 =0$

⇒ $3x^2- 27x + 54 =0$

⇒ $x^2- 9x + 18 =0$

⇒ $x^2- 6x-3x + 18 =0$

⇒ $x(x- 6)-3(x - 6) =0$

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⇒ $x=3 , x=6$

Value of g(x) at x = 3 : y=3x -15 = 3(3)-15 = -6

Value of g(x) at x = 6 : y=3x -15 = 3(6)-15 = 3

Therefore , the coordinates where the bridges must be built is $(3,-6)$ and $(6,3)$ .

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Answer:

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Step-by-step explanation:

I would set this up as a proportion

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