If possible, completely factor the expression. (If the polynomial is not factorable using integers, enter PRIME.)
x^2+9 x+20
imma teach you how i learn to factor
tak the x^2 and multiply it with the 20 giving you 20x^2
now figure out all the numbers that multiply to equal 20 which should be 4 and 4, and 1 and 20
now out of those 2 choices which one adds up to equal 9 (bc there is a 9x) the answer is 4 and 5 ( now if it was a negative 9x you would have to figure out how to get that negative 9 from adding the two numbers for example lets say it was 20x^2 but 18x^2 instead so you would have 6 and 3 multiplyiing to equal 18 but 6 + 3 doesnt equal a negative 9 but a -6 times a -3 equals positive 18 also and when you add them together they equal -9 too, i know i went off topic but i just wanted to point it out to you)
anyway our two numbers that multiply to equal 20 and add to equal 9 was 5 and 4
so your factor is (x+5 and x + 4) just put them equal to zero to get your x but the question only ask you to factor
To completely factor the expression x^2 + 9x + 20, we need to find two binomials whose product is equal to the given expression.
Step 1: Write down the expression.
x^2 + 9x + 20
Step 2: Identify two numbers whose product is equal to the product of the leading and constant terms of the expression (in this case, 1 * 20 = 20) and whose sum is equal to the coefficient of the middle term (in this case, 9).
The numbers that satisfy these conditions are 4 and 5 (since 4 * 5 = 20 and 4 + 5 = 9).
Step 3: Rewrite the expression using the two numbers identified in Step 2.
x^2 + 4x + 5x + 20
Step 4: Group the expression by pairs.
(x^2 + 4x) + (5x + 20)
Step 5: Factor out the greatest common factor from each pair.
x(x + 4) + 5(x + 4)
Step 6: Notice that we now have a common binomial factor, (x + 4), which can now be factored out.
(x + 4)(x + 5)
Therefore, the completely factored form of the expression x^2 + 9x + 20 is (x + 4)(x + 5).