Problem of the Week

Updated at Jun 21, 2021 4:30 PM

This week's problem comes from the algebra category.

How can we factor $$30{t}^{2}+17t-21$$?

Let's begin!

$30{t}^{2}+17t-21$

 1 Split the second term in $$30{t}^{2}+17t-21$$ into two terms.1 Multiply the coefficient of the first term by the constant term.$30\times -21=-630$2 Ask: Which two numbers add up to $$17$$ and multiply to $$-630$$?$$35$$ and $$-18$$3 Split $$17t$$ as the sum of $$35t$$ and $$-18t$$.$30{t}^{2}+35t-18t-21$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$30{t}^{2}+35t-18t-21$2 Factor out common terms in the first two terms, then in the last two terms.$5t(6t+7)-3(6t+7)$3 Factor out the common term $$6t+7$$.$(6t+7)(5t-3)$Done(6*t+7)*(5*t-3)