Let's factor: $$x^2+\textcolor{#800080}{5}x+\textcolor{#5cb85c}{4}$$ Factoring means we want something like: $$(x+\textcolor{#d9534f}{\_})(x+\textcolor{#2d6da3}{\_})$$
What numbers go in the blanks?
Let's put a and b in the blanks and use FOIL to multiply it out. $$(x+\textcolor{#d9534f}{a})(x+\textcolor{#2d6da3}{b})$$ $$=x^2+\textcolor{#2d6da3}{b}x+\textcolor{#d9534f}{a}x+\textcolor{#d9534f}{a}\textcolor{#2d6da3}{b}$$ $$=x^2+\textcolor{#800080}{(a+b)}x+\textcolor{#5cb85c}{ab}$$
We see that a and b need to be two numbers that...
Multiply together to get 4: $$\textcolor{#5cb85c}{ab=4}$$
And add together to get 5: $$\textcolor{#800080}{a+b=5}$$
Can you think of the two numbers?
Let's think of pairs of numbers that multiply together to get 4. $$1\textcolor{#5cb85c}{*}4=\textcolor{#5cb85c}{4}$$ $$2\textcolor{#5cb85c}{*}2=\textcolor{#5cb85c}{4}$$
For each pair. let's add the two numbers together to see which pair adds up to 5.
We see that: $$1\textcolor{#800080}{+}4=\textcolor{#800080}{5}$$
So 1 and 4 are the numbers we were looking for.
Let's go back and fill in the blanks with 1 and 4 to get... $$(x+\textcolor{#d9534f}{1})(x+\textcolor{#2d6da3}{4})$$ Let's check our answer using FOIL to multiply it out. We get: $$(x+\textcolor{#d9534f}{1})(x+\textcolor{#2d6da3}{4})$$ $$=x^2+\textcolor{#2d6da3}{4}x+\textcolor{#d9534f}{1}x+(\textcolor{#d9534f}{1})(\textcolor{#2d6da3}{4})$$ $$=x^2+5x+4$$ so we know our answer is correct.
To send feedback: You can use the contact form.
Subscribe to the MathPapa channel!