mathieu is finding the x - intercepts of the function $f(x)=x^{2}+4x + 3$. his work is shown below.\n1…

mathieu is finding the x - intercepts of the function $f(x)=x^{2}+4x + 3$. his work is shown below.\n1. $0=x^{2}+4x + 3$\n2. $0=(x + 3)(x + 1)$\n3. $x + 3=x + 1$\n4. $x=x - 2$\n5. $0=-2$\n6. there are no x - intercepts.\nwhich error did mathieu make?\nhe factored incorrectly.\nhe did not use the constant as the x - intercept.\nhe set the factored expressions equal to each other.\nhe incorrectly solved the equation $x + 3=x + 1$.

mathieu is finding the x - intercepts of the function $f(x)=x^{2}+4x + 3$. his work is shown below.\n1. $0=x^{2}+4x + 3$\n2. $0=(x + 3)(x + 1)$\n3. $x + 3=x + 1$\n4. $x=x - 2$\n5. $0=-2$\n6. there are no x - intercepts.\nwhich error did mathieu make?\nhe factored incorrectly.\nhe did not use the constant as the x - intercept.\nhe set the factored expressions equal to each other.\nhe incorrectly solved the equation $x + 3=x + 1$.

Answer

Explanation:

Step1: Recall finding x - intercepts

To find x - intercepts of $y = f(x)$, we set $y = 0$ and solve for $x$. When we have a factored form $0=(x + a)(x + b)$, we use the zero - product property: if $AB = 0$, then $A=0$ or $B = 0$.

Step2: Analyze Mathieu's work

Mathieu factored $x^{2}+4x + 3$ correctly as $(x + 3)(x + 1)$. But instead of using the zero - product property ($x+3 = 0$ or $x + 1=0$), he set the two factors equal to each other ($x + 3=x + 1$).

Answer:

He set the factored expressions equal to each other.