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Solve quadratic equation with coefficient

Solve quadratic equation with a leading coefficient

This math skill demonstrates how to solve a quadratic equation with a leading coefficient by factoring. It involves multiplying the leading coefficient by the constant term to identify two numbers that both add and multiply to provided values, allowing the equation's middle term to be split and factored into binomials.

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Teaching Transcript

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Let's factor this quadratic equation that has a coefficient on the 'X' squared term.

We need to split our 'X' variables, and to find the way to split them, the trick is to multiply the 'X' squared coeffient by our constant of minus 10

Now we need two values that multiply to negative 120 and add to negative 7

Negative 15 and positive 8 meet that criteria, so we can split our 'X' variables into those two coefficients

We can rewrite our quadratic with the 'X' term split out

Now let's group into two binomials

We can remove a common factor of 3 'X' from the first

And we can remove a common factor of 2 from the second

We now have the entire term in brackets, 4 'X' minus 5, as a common factor, so we can remove that and we have our answer

Skill Practice

Solve quadratic equation with a leading coefficient

Test your understanding of solve quadratic equation with coefficient by practicing it! Work through the below exercises to use it in practice.