Please help with factoring these x²-11x+18

2 answers:

8 0

X2-11x+18

Write - 11x as a difference:
x2- 2x - 9x + 18

Factor out x from the expression:
X x (x - 2) - 9x + 18

Factor out x - 2 from the expression and that would give you your answer:
(x - 2) x (x - 9)

lozanna [386]3 years ago

6 0

We want to factor x²-11x+18

In order to factor it, we must find two numbers that add to -11 and multiply to 18.

We will go through the list of factors of 18:

1, 2, 3, 6, 9, 18

We see that 9 and 2 multiply to 18. But we want two numbers that add to -11, so we will simply put a negative sign in front of 9 and 2.

-9 and -2 still multiply to 18 and they add to -11, so now we can factor the expression:

x²-11x+18 = (x-2)(x-9)

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alukav5142 [94]

In this problem, we need to plug in the given x values for $f(x)=0$ and find a and b.

When we plug in 1, we get: $2 \times {1}^{4} - 5 \times {1}^{3} - 14 \times {1}^{2} + a \times 1 + b = 0$

Simplify:
$2 - 5 - 14 + a + b = 0$
$- 17 + a + b = 0$
$a + b = 17$

We got our first statement about the values of the variables. If we find one more we can find those 2 variables.

We have another given root: 4.

Plug it in:
$2 \times {4}^{4} - 5 \times {4}^{3} - 14 \times {4}^{2} + a \times 4 + b = 0$
$512 - 320 - 224 + 4a + b = 0$
$- 32 + 4a + b = 0$
$4a + b = 32$

Now we have our second one. We can combine them:
$a + b = 17 \\ 4a + b = 32$

I use elimination method which is easier here.

Multiply the top equation by -1: $- a - b = - 17 \\ 4a + b = 32$

Add them up:
$3a = 15$

Simplify:
$a = 5$

Now we have a, we can plug in one of those equations to find b:
$5 + b = 17$
$b = 17 - 5$
$b = 12$

So, the answers are $a=5$ and $b=12$ .