Which expression is equivalent to this polynomial? 6x2 + 10x − 56

Question

asked Nov 9, 2023 53.8k views

1 Answer

Lasse Meyer · Answer 1 · 2023-11-14T20:53:27+0000

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,

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