Question

Please Help! Factor the following trinomial x^2-24x+16" alt="9x^2-24x+16" align="absmiddle" class="latex-formula">
Please show work

Answer 1

=> 9x² - 24x + 16

Split the middle term(term with x) in such a manner so that the product of those parts is equal to the product of term with x² and constant. Here, those parts are 12 & 12 as 12*12 = 9*16.

=> 9x² - 24x + 16

=> 9x² - (12 + 12)x + 16

=> 9x² - 12x - 12x + 16

=> 3x(3x - 4) - 4(3x - 4)

=> (3x - 4)(3x - 4)

Method 2

=> 9x² - 24x + 16

=> (3x)² - 2(3x*4) + 4²

=> (3x - 4)²

=> (3x - 4)(3x - 4)

Method 3

In case if you can't find the factors of the middle term.

Say f(x) = 0, find the zeroes using quadratic formula. Zeroes of this eqⁿ are [-(-24) ± √24²-4(9)(16)] / 2(9) = 4/3 & 4/3

Therefore, f(x) = (x - 4/3)(x - 4/3) = (3x - 4)(3x - 4)/9

Ignore the numeric constant.

f(x) = (3x - 4)(3x - 4)

Answer 2

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The answer=>

For this,we need to know what's Middle splitting method

• In order to factorize x² + bx + c we have to find numbers p and q such that p + q = b and pq = c. After finding p and q, we split the middle term in the quadratic as px + qx and get desired factors by grouping the terms.

Step-by-step explanation:

$9x {}^{2} - 24x + 16 \\ = > 9x {}^{2} - 12x - 12x + 16 \\ = > 3x(3x - 4) - 4(3x - 4) \\ = > (3x - 4)(3x - 4) \\ so... \\ x = eitherway \: 4$

i.e

Alpha= Beta = 4