Question

Which expression is equivalent to this polynomial?

6x2 + 10x − 56

Answer 1

Given :

`\longrightarrow \sf \qquad {6x}^(2) + 10x - 56`

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We can write it as,

`\longrightarrow \sf \qquad2 \bigg({3x}^(2) + 5x - 28 \bigg)`

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We have to find the two numbers a and b such that,

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`\longrightarrow \sf \qquad a + b = 5`

`\longrightarrow \sf \qquad a b = 84`

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Obviously, the two numbers are 7 and 12.

`{\longrightarrow \sf \qquad2 \bigg({3x}^(2) - 7x + 12x- 28 \bigg)}`

`{\longrightarrow \sf \qquad2 \bigg[x \bigg(3x-7 \bigg) +4 \bigg(3x-7\bigg)} \bigg]`

`{\longrightarrow \sf \qquad{2 \bigg(3x - 7 \bigg) \bigg(x + 4\bigg)}}`

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Therefore,

`{\longrightarrow \bf \qquad{2 \bigg(3x - 7 \bigg) \bigg(x + 4\bigg)} \: is \: equivalent} \bf \: \: to \: \: {6x}^(2) + 10x - 56`