Factoring

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ACT Math › Factoring

Questions 1 - 10

Factor: $x^{2}+2x-24$

Explanation

$x^{2}+2x-24$

In the form of $ax^{2}+bx+c$ you must find two numbers which add to give you and multiply to give you and then put them in the form of ( + number) ( + number)

$6\ast-4=24$

Therefore is the answer.

To check, multiply the two expressions out and it should equal $x^{2}+2x-24$

Factor: $x^{2}+2x-24$

Explanation

$x^{2}+2x-24$

In the form of $ax^{2}+bx+c$ you must find two numbers which add to give you and multiply to give you and then put them in the form of ( + number) ( + number)

$6\ast-4=24$

Therefore is the answer.

To check, multiply the two expressions out and it should equal $x^{2}+2x-24$

Solve for all solutions of $\dpi{100} \small x$ :

$\dpi{100} \small 2x^{2}-10x=x^{2}-24$

$\dpi{100} \small 4,6$

$\dpi{100} \small -4,6$

$\dpi{100} \small -4,-6$

$\dpi{100} \small 3,8$

$\dpi{100} \small 3,-8$

Explanation

First move all of the variables to the left side of the equation. Combine similar terms, and set the equation equal to zero. Then factor the equation to get $\dpi{100} \small (x-4)(x-6)=0$

Thus the solutions of $\dpi{100} \small x$ are 4 and 6.

Solve for all solutions of $\dpi{100} \small x$ :

$\dpi{100} \small 2x^{2}-10x=x^{2}-24$

$\dpi{100} \small 4,6$

$\dpi{100} \small -4,6$

$\dpi{100} \small -4,-6$

$\dpi{100} \small 3,8$

$\dpi{100} \small 3,-8$

Explanation

First move all of the variables to the left side of the equation. Combine similar terms, and set the equation equal to zero. Then factor the equation to get $\dpi{100} \small (x-4)(x-6)=0$

Thus the solutions of $\dpi{100} \small x$ are 4 and 6.

Factor the following expression:

Explanation

To factor, you are looking for two factors of 40 that add to equal 13.

Factors of 40 include: (1, 40), (2, 20), (4, 10), (5, 8). Of these factors which two will add up to 13?

Also, since the first sign (-) and the second sign is (+) this tells us both binomials will be negative. This is because two negatives multiplied together will result in the positive third term, while two negatives added together will result in a larger negative number.

Thus,

Factor the following expression:

Explanation

To factor, you are looking for two factors of 40 that add to equal 13.

Factors of 40 include: (1, 40), (2, 20), (4, 10), (5, 8). Of these factors which two will add up to 13?

Thus,

Simplify:

$\frac{x^2+6x+9}{x+3}$

Explanation

$x^{2}+6x+9$ factors to

One cancels from the bottom, leaving

Simplify:

$\frac{x^2+6x+9}{x+3}$

Explanation

$x^{2}+6x+9$ factors to

One cancels from the bottom, leaving

Two consecutive positive multiples of five have a product of 300. What is their sum?

Explanation

Define the variables as x = 1st number and x + 5 = 2nd number, so the product is given as x(x + 5) = 300, which becomes x2 + 5x – 300 = 0.

Factoring results in (x + 20)(x – 15) = 0, so the positive answer is 15, making the second number 20.

The sum of the two numbers is 35.

Two consecutive positive multiples of five have a product of 300. What is their sum?

Explanation

Define the variables as x = 1st number and x + 5 = 2nd number, so the product is given as x(x + 5) = 300, which becomes x2 + 5x – 300 = 0.

Factoring results in (x + 20)(x – 15) = 0, so the positive answer is 15, making the second number 20.

The sum of the two numbers is 35.

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