Question

Which expression is the factorization of x2 + 10x + 21? (x + 3)(x + 7) (x + 4)(x + 6) (x + 6)(x + 15) (x + 7)(x + 14)

Answer 1

Hey mate,

Just split the middle term....

x^2 + 7x + 3x + 21 = 0

x(x + 7) +3 (x +7) = 0

(x+3)(x+7) = 0

hope this helps you out!

Answer 2

Answer:The factors of $x^{2} +10x+21$ are $(x+3)and(x+7)$  respectively.

Step-by-step explanation:

Given:We have given expression $x^{2} +10x+21$.

To find:We have to find the factors of of $x^{2} +10x+21$.

Explanation:

Step 1:As we have given  .To find the factor given expression we have to write middle term $10x$ into two terms such that the multiplication of two terms should be equal to product of first term and and third term and their addition or subtraction should be the middle term.

Step 2:So the multiplication of two term should be $21$$x^{2}$ and their addition or subtraction should be $10x$ .

Step 3: So we have,

⇒   $x^{2} +10x+21$ $= x^{2} +3x+7x+21$

                            $=(x^{2} +3x)+(7x+21)$

                            $= x(x+3)+7(x+3)$

                            $= (x+3)(x+7)$

∴ The factors of $x^{2} +10x+21$ are $(x+3)and(x+7)$  respectively.

Splitting the Middle Term for Factoring Quadratics:

The sum of the roots of the equation  can be given by,

α+β = -b/a

The product of the roots in the equation   can be given by,

α.β = c/a

We split the middle term b of the quadratic equation such that when we try to factorize quadratic equations. We determine the factor pairs of the product of a and c such that their sum is equal to b.

#SPJ2

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