Factor. x^(2)-17 x+72 Answer:

Identify Factors: To factor the quadratic expression x^2 - 17x + 72, we need to find two numbers that multiply to 72 (the constant term) and add up to -17 (the coefficient of the x term).Find Correct Pair: We list pairs of factors of 72 and check which pair adds up to -17: 1 and 72 (1 + 72 = 73) 2 and 36 (2 + 36 = 38) 3 and 24 (3 + 24 = 27) 4 and 18 (4 + 18 = 22) 6 and 12 (6 + 12 = 18) 8 and 9 (8 + 9 = 17) We notice that none of the pairs add up to -17, but if we consider negative pairs, we find that -8 and -9 multiply to 72 and add up to -17.Use Negative Pairs: Now we can write the quadratic expression as a product of two binomials using the numbers -8 and -9: x^2 - 17x + 72 = (x - 8)(x - 9).Write as Binomials: To check our work, we can use the FOIL method (First, Outer, Inner, Last) to expand the binomials and verify that we get the original expression: (x - 8)(x - 9) = x^2 - 9x - 8x + 72 = x^2 - 17x + 72.

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Factor. $\newline$ $x^{2}-17 x+72$ $\newline$ Answer:

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Q. Factor.

\newline

x^{2}-17 x+72

\newline

Answer:

Identify Factors: To factor the quadratic expression $x^2 - 17x + 72$ , we need to find two numbers that multiply to $72$ (the constant term) and add up to $-17$ (the coefficient of the $x$ term).
Find Correct Pair: We list pairs of factors of $72$ and check which pair adds up to $-17$ :
$1$ and $72$ ( $1 + 72 = 73$ )
$2$ and $36$ ( $2 + 36 = 38$ )
$3$ and $24$ ( $3 + 24 = 27$ )
$1$ $0$ and $1$ $1$ ( $1$ $2$ )
$1$ $3$ and $1$ $4$ ( $1$ $5$ )
$1$ $6$ and $1$ $7$ ( $1$ $8$ )
We notice that none of the pairs add up to $-17$ , but if we consider negative pairs, we find that $72$ $0$ and $72$ $1$ multiply to $72$ and add up to $-17$ .
Use Negative Pairs: Now we can write the quadratic expression as a product of two binomials using the numbers $-8$ and $-9$ : $x^2 - 17x + 72 = (x - 8)(x - 9)$ .
Write as Binomials: To check our work, we can use the FOIL method (First, Outer, Inner, Last) to expand the binomials and verify that we get the original expression: $\newline$ $(x - 8)(x - 9) = x^2 - 9x - 8x + 72 = x^2 - 17x + 72$ .