Answer :

Answer:

pairs of factors of +15, sum of +8

Step-by-step explanation:

in factoring trinomials (three terms, in this case being x^2, 6x, and 15), we want our two factors to multiply to equal the final number, so 15. factors of + 15 (positive because 15 has a plus sign before it in the trinomial) are

1 and 15

3 and 5

now which ones of these add to give + 8?

3 and 5

so now the binomials (two terms) are

(x + 3) and (x + 5)

notice how there are 2 terms in these separates by one plus sign, so they are binomials, you can foil to check your work as well

semsee45

Answer:

See attachments.

Step-by-step explanation:

Question 1

To factor the quadratic expression x² + 8x + 15, we first need to identify the pairs of factors of the product of the coefficient of x² and the constant.

In this case, the coefficient of x² is one and the constant is 15, so their product is 1 × 15 = 15. Therefore, we need to list pairs of factors of 15, which are:

  • 1 and 15
  • 3 and 5

Next, we need to identify the pair of factors that has a sum equal to the coefficient of the x-term in the quadratic expression. In this case, the coefficient of the x-term is 8, so we need to identify the pair that has a sum of 8. The pair of factors that has a sum of 8 is:

  • 3 and 5

To write the quadratic expression as the product of two binomials, rewrite the middle term as the sum of 3 and 5:

[tex]x^2+3x+5x+15[/tex]

Now, factor the first two terms and the last two terms separately:

[tex]x(x+3)+5(x+3)[/tex]

Finally, factor out the common term (x + 3):

[tex](x+3)(x+5)[/tex]

Therefore, the given quadratic expression written as a product of two binomials is:

[tex]\Large\boxed{\boxed{(x+3)(x+5)}}[/tex]

[tex]\dotfill[/tex]

Question 2

To factor the quadratic expression x² + 2x - 15, we first need to identify the pairs of factors of the product of the coefficient of x² and the constant.

In this case, the coefficient of x² is one and the constant is -15, so their product is 1 × 15 = -15. Therefore, we need to list pairs of factors of -15, which are:

  • -1 and 15
  • 1 and -15
  • -3 and 5
  • 3 and -5

Next, we need to identify the pair of factors that has a sum equal to the coefficient of the x-term in the quadratic expression. In this case, the coefficient of the x-term is 2, so we need to identify the pair that has a sum of 2. The pair of factors that has a sum of 2 is:

  • -3 and 5

To write the quadratic expression as the product of two binomials, rewrite the middle term as the sum of -3 and 5:

[tex]x^2-3x+5x-15[/tex]

Now, factor the first two terms and the last two terms separately:

[tex]x(x-3)+5(x-3)[/tex]

Finally, factor out the common term (x - 3):

[tex](x-3)(x+5)[/tex]

Therefore, the given quadratic expression written as a product of two binomials is:

[tex]\Large\boxed{\boxed{(x-3)(x+5)}}[/tex]

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