### All Algebra 1 Resources

## Example Questions

### Example Question #4623 : Algebra 1

Factor the following:

**Possible Answers:**

no factors

**Correct answer:**

To factor a polynomial, first express the polynomial in the form . Then, if , you need to find factors of that add up to . Your answer will use those factors. The best answer for the equation above is:

### Example Question #4624 : Algebra 1

Factor the following:

**Possible Answers:**

no factors

**Correct answer:**

To factor a polynomial, first express the polynomial in the form . Then, if , you need to find factors of that add up to . Your answer will use those factors. The best answer for the equation above is:

### Example Question #4625 : Algebra 1

Factor the following:

**Possible Answers:**

**Correct answer:**

To factor a polynomial, first express the polynomial in the form . Then, if , you need to find factors of that add up to b. Your answer will use those factors. The best answer for the equation above is:

### Example Question #4625 : Algebra 1

Factor the following:

**Possible Answers:**

**Correct answer:**

To factor a polynomial, first express the polynomial in the form . Then, if , you need to find factors of that add up to b. Your answer will use those factors. The best answer for the equation above is:

### Example Question #4626 : Algebra 1

Factor the following:

**Possible Answers:**

**Correct answer:**

To factor a polynomial, first express the polynomial in the form . Then, if , you need to find factors of that add up to b. Your answer will use those factors. The best answer for the equation above is:

### Example Question #4627 : Algebra 1

Factor the following polynomial.

**Possible Answers:**

**Correct answer:**

When factoring a polynomial, you have to determine the numbers that when multiplied together will equal the last term of the polynomial but when added together will equal the second term of the polynomial.

The only factors of 9 are (1,3,9). The trick in this question is that the last term is positive, but the middle term is negative. The only way to achieve this is to make both of the factors negative, so when multiplied together they equal a positive.

### Example Question #391 : Polynomials

Factor:

**Possible Answers:**

**Correct answer:**

To factor a quadratic trinomial, list factors of the quadratic term and the constant (no variables) term, then combine them into binomials that when multiplied back out will give the original trinomial.

Here, the quadratic term has only one factorization: .

The constant term has factorizations of and .

We know the constant term is positive, so the binomials both have the same operation in them (adding or subtracting), since a positive times a positive OR a negative times a negative will both give a positive result.

But since the middle term is negative, both binomial factors must contain subtraction. And .

### Example Question #391 : Variables

Factor:

**Possible Answers:**

**Correct answer:**

To factor a quadratic trinomial, list factors of the quadratic term and the constant (no variables) term, then combine them into binomials that when multiplied back out will give the original trinomial.

Here, the quadratic term has only one factorization: .

The constant term has factorizations of and .

We know the constant term is negative, so the binomials have a different operation in each (adding or subtracting), since a positive times a negative will give a negative result.

Since the middle term is negative, we need the "larger" factor to "outweigh" the "smaller" by , and be negative.

### Example Question #81 : How To Factor A Polynomial

Factor:

**Possible Answers:**

**Correct answer:**

To factor a quadratic trinomial, list factors of the quadratic term and the constant (no variables) term, then combine them into binomials that when multiplied back out will give the original trinomial.

Here, the quadratic term has only one factorization: .

The constant term has factorizations of , , , and .

We know the constant term is positive, so the binomials both have the same operation in them (adding or subtracting), since a positive times a positive OR a negative times a negative will both give a positive result.

But since the middle term is positive, both binomial factors must contain addition. And .

### Example Question #83 : Factoring Polynomials

Factor completely:

**Possible Answers:**

The expression is not factorable.

**Correct answer:**

First, factor out the greatest common factor (GCF), which here is . If you don't see the whole GCF at once, factor out what you do see (here, either the or the ), and then check the result to see if any more factors can be pulled out.

Then, to factor a quadratic trinomial, list factors of the quadratic term and the constant (no variables) term, then combine them into binomials that when multiplied back out will give the original trinomial.

Here, the quadratic term has only one factorization: .

The constant term has factorizations of , , , and .

We know the constant term is positive, so the binomials both have the same operation in them (adding or subtracting), since a positive times a positive OR a negative times a negative will both give a positive result.

But since the middle term is negative, both binomial factors must contain subtraction. And .

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