Sagot :
Answer:
1. ( x + 3) ( x + 5)
2. (x - 6) ( x - 4)
3. ( x + 7) (x - 3)
Step-by-step explanation:
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[tex]\color{red}\underline { \huge{\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }}[/tex]
[tex]\underline{\mathbb{SOLUTION}:}[/tex]
[tex]\#1. \sf \: Factor \: {x}^{2} + 8x + 15[/tex]
[tex] \sf Solution : a = 1,b=8, c = 15[/tex]
[tex] \sf \: Since \: b \: and \: c \: are \: both \: positive, \: you \: must \: consider \: the \: pair \: of \: positive \: factors \: of \: 15.[/tex]
[tex]\begin{gathered}\tt \: \begin{gathered}\begin{gathered}\begin{array}{c|c}\bold{ \purple{ \tiny \:Factor \: of \: 12 }}&\bold{ \purple{ \tiny \:Sum \: of \: the \: Factors \: }} \\ 1 \: \rm{{ and }} \: 15&16 \\ \rm \: 5 \: and \: 3& 8\\ \end{array}\end{gathered}\end{gathered}\end{gathered}[/tex]
[tex] \therefore \sf Hence, {x}^{2} + 8x + 15 = (x + 3)(x + 5)[/tex]
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[tex]\#2. \sf \: Factor \: {x}^{2} - 10x + 24[/tex]
[tex]\sf Solution : a = 1,b= - 10, c = 24[/tex]
[tex]\sf \: Since \: b \: and \: c \: are \: both \: positive, \: you \: must \: consider \: the \: pair \: of \: negative \: factors \: of \: 24.[/tex]
[tex]\begin{gathered}\tt \: \begin{gathered}\begin{gathered}\begin{array}{c|c}\bold{ \purple{ \tiny \:Factor \: of \: 24 }}&\bold{ \purple{ \tiny \:Sum \: of \: the \: Factors \: }} \\ \: - 1, - 24& - 25 \\ - 2 , - 12& - 14\\ - 3, - 8& - 11\\ - 4, - 6& - 10\\ \end{array}\end{gathered}\end{gathered}\end{gathered}[/tex]
[tex] \sf \: Get \: the \: factors \: of \: 24 \: whose \: sum \: is \: - 10.[/tex]
[tex] \sf \: Write \: the \: binomial \: factors \: as \: (x - 4) (x - 6)[/tex]
[tex] \therefore \sf Hence, {x}^{2} - 10x + 24 = (x - 4)(x - 6)[/tex]
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[tex]\#3. \sf \: Factor \: {x}^{2} + 4x - 21[/tex]
[tex]\sf Solution : a = 1,b= 4, c = - 21[/tex]
[tex]\sf \: Since \: c \: is \: negative ,\: the \: factors \: must \: have \: opposite \: signs.[/tex]
[tex]\begin{gathered}\tt \: \begin{gathered}\begin{gathered}\begin{array}{c|c}\bold{ \purple{ \tiny \:Factor \: of \: - 21 }}&\bold{ \purple{ \tiny \:Sum \: of \: the \: Factors \: }} \\ \: - 1,21&20 \\1 , - 21& - 20\\ - 3,7&4\\ 3, - 7& - 4\\ \end{array}\end{gathered}\end{gathered}\end{gathered}[/tex]
[tex] \sf \: Get \: the \: factors \: of \: - 21 \: whose \: sum \: is \: 4.[/tex]
[tex] \sf \: Write \: the \: binomial \: factors \: as \: (x + 7) (x - 3)[/tex]
[tex] \therefore \sf Hence, {x}^{2} + 4x - 21 = (x + 7)(x - 3)[/tex]
[tex]\color{red}\underline { \huge{\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }}[/tex]
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