QuestionFactor the expression: $x^{2}+4 x+3$ .

Studdy Solution

STEP 1

Assumptions1. We are factoring a quadratic equation of the form $ax^ + bx + c$ . The equation we are factoring is $x^ +4x +3$

STEP 2

A quadratic equation can be factored into two binomial expressions of the form $(x + p)(x + q)$ , where $p$ and $q$ are numbers that satisfy the following conditions1. $p + q = b$
2. $p \times q = c$
In our case, $b =4$ and $c =$ .

STEP 3

We need to find two numbers that add up to (the coefficient of $x$ ) and multiply to3 (the constant term).

STEP 4

The numbers that satisfy these conditions are1 and3, because $1 +3 =4$ and $1 \times3 =3$ .

STEP 5

Substitute $p$ and $q$ with1 and3 into the binomial expressions $(x + p)(x + q)$ .
$(x +1)(x +3)$ So, the factored form of $x^2 +4x +3$ is $(x +1)(x +3)$ .

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QuestionFactor the expression: $x^{2}+4 x+3$ .

Studdy Solution

STEP 1

Assumptions1. We are factoring a quadratic equation of the form $ax^ + bx + c$ . The equation we are factoring is $x^ +4x +3$

STEP 2

A quadratic equation can be factored into two binomial expressions of the form $(x + p)(x + q)$ , where $p$ and $q$ are numbers that satisfy the following conditions1. $p + q = b$
2. $p \times q = c$
In our case, $b =4$ and $c =$ .

STEP 3

We need to find two numbers that add up to (the coefficient of $x$ ) and multiply to3 (the constant term).

STEP 4

The numbers that satisfy these conditions are1 and3, because $1 +3 =4$ and $1 \times3 =3$ .

STEP 5

Substitute $p$ and $q$ with1 and3 into the binomial expressions $(x + p)(x + q)$ .
$(x +1)(x +3)$ So, the factored form of $x^2 +4x +3$ is $(x +1)(x +3)$ .

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QuestionFactor the expression: x2+4x+3x^{2}+4 x+3x2+4x+3.

Studdy Solution

STEP 1

Assumptions1. We are factoring a quadratic equation of the form ax+bx+cax^ + bx + cax+bx+c . The equation we are factoring is x+4x+3x^ +4x +3x+4x+3

STEP 2

A quadratic equation can be factored into two binomial expressions of the form (x+p)(x+q)(x + p)(x + q)(x+p)(x+q), where ppp and qqq are numbers that satisfy the following conditions1. p+q=bp + q = bp+q=b2. p×q=cp \times q = cp×q=cIn our case, b=4b =4b=4 and c=c =c=.

STEP 3

We need to find two numbers that add up to (the coefficient of xxx) and multiply to3 (the constant term).

STEP 4

The numbers that satisfy these conditions are1 and3, because 1+3=41 +3 =41+3=4 and 1×3=31 \times3 =31×3=3.

STEP 5

Substitute ppp and qqq with1 and3 into the binomial expressions (x+p)(x+q)(x + p)(x + q)(x+p)(x+q).(x+1)(x+3)(x +1)(x +3) (x+1)(x+3)So, the factored form of x2+4x+3x^2 +4x +3x2+4x+3 is (x+1)(x+3)(x +1)(x +3)(x+1)(x+3).

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QuestionFactor the expression: $x^{2}+4 x+3$ .

Assumptions1. We are factoring a quadratic equation of the form $ax^ + bx + c$ . The equation we are factoring is $x^ +4x +3$

A quadratic equation can be factored into two binomial expressions of the form $(x + p)(x + q)$ , where $p$ and $q$ are numbers that satisfy the following conditions1. $p + q = b$
2. $p \times q = c$
In our case, $b =4$ and $c =$ .

We need to find two numbers that add up to (the coefficient of $x$ ) and multiply to3 (the constant term).

The numbers that satisfy these conditions are1 and3, because $1 +3 =4$ and $1 \times3 =3$ .

Substitute $p$ and $q$ with1 and3 into the binomial expressions $(x + p)(x + q)$ .
$(x +1)(x +3)$ So, the factored form of $x^2 +4x +3$ is $(x +1)(x +3)$ .