# Question Video: Finding the Value of βπβ Which Makes a Polynomial Divisible by a Given Binomial Mathematics • 10th Grade

Find the value of π that makes the expression π₯Β² β ππ₯ + 30 divisible by π₯ β 5.

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### Video Transcript

Find the value of π that makes the expression π₯ squared minus ππ₯ plus 30 divisible by π₯ minus five.

If we let π of π₯ equal π₯ squared minus ππ₯ plus 30, then if the expression is divisible by π₯ minus five, this means that π₯ minus five is a factor. If π₯ minus π is a factor of any equation, then we know the π of π equals zero. In our case π of five, must be equal to zero.

Substituting five into the expression gives us five squared minus π multiplied by five plus 30 equals zero. Five squared is equal to 25. And π multiplied by five can be written five π. Grouping the like terms gives us 55 minus five π equal zero.

Adding five π to both sides to balance the equation gives us five π equals 55. Dividing both sides of this equation by five gives us an answer of π of 11. Therefore, the value of π that makes the expression π₯ squared minus π π₯ plus 30 divisible by π₯ minus five is π equals 11.

This means that π₯ minus five is a factor of a quadratic expression π₯ squared minus 11 π₯ plus 30.