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Factor each polynomial completely. If a polynomial is prime, so indicate.$$36 a^{2}+49 b^{2}$$...

Question

Factor each polynomial completely. If a polynomial is prime, so indicate.$$36 a^{2}+49 b^{2}$$

Factor each polynomial completely. If a polynomial is prime, so indicate. $$36 a^{2}+49 b^{2}$$



Answers

Factor each polynomial. If a polynomial cannot be factored, write prime. Factor out the greatest common factor as necessary.
$$9 x^{2}+64$$

The first thing we should always look to do in factoring is graves Common factor. There was nothing in common to factor out here, so maybe it fits one of our models like difference of squares. This looks like it could be some of squares, but that does not exist. This is an example of a prime polynomial. This poem you cannot be broken down into a product.

This problem only on may seem a little tricky at first. Teoh um factor. You may be inclined to choose that its prime, but you can actually do a modified grouping here. The 1st 3 terms are factory ble in themselves to try no meal for a leading coefficient of one. So what? Two numbers multiplied positive 36 ads negative 12. And that would be X minus six times X minus six, which is a perfect square. By normal, we have two X minus six is we can express it is X minus six square. So now we have X minus X squared minus 49 y squared 49. Why square really is seven. Why square that's 49 life squared. And now we have a difference of perfect squares, which says we can write it as a sum and difference. So we have X minus six plus seven one an X minus six minus seven wine. Um, so you can write your answer as is here, or these could be reordered as well. It's the same thing to say. X plus seven. Why minus six If we were writing in standard form for each one in X minus seven Y minus six

So in the form, learn I X choir plus 36. We cannot factor out any term, so that is a crime.

Very here we have a difference of squares because they're both perfect squares. Every number to the perfect square of for X squared. The per squared of X squared is that And for 36 we have six for the sum for the difference of squares. What we have at point and minus, we have essentially the square of the first term this word of the first term and this word of a second term. Now we do have plugged them in their up here river post. What? The next minus six. That So we have to do when we found the difference of squares.


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