The sat skill exam 7 pptx

Example:

(3x + 1)(7x + 10)

3x and 7x are the first pair of terms,

3x and 10 are the outermost pair of terms,

1 and 7x are the innermost pair of terms, and

1 and 10 are the last pair of terms.

Therefore, (3x)(7x) + (3x)(10) + (1)(7x) +

(1)(10) = 21x2 + 30x + 7x + 10.

After we combine like terms, we are left with

the answer: 21x2 + 37x + 10.

Factoring

Factoring is the reverse of multiplication:

2(x + y) = 2x + 2y Multiplication

2x + 2y = 2(x + y) Factoring

THREE BASIC TYPES OF FACTORING

■ Factoring out a common monomial:

10x2 – 5x = 5x(2x – 1) and xy – zy = y(x – z)

■ Factoring a quadratic trinomial using the reverse

of FOIL:

y2 – y – 12 = (y – 4) (y – +3) and

z2 – 2z + 1 = (z – 1)(z – 1) = (z – 1)2

■ Factoring the difference between two squares

using the rule:

a2 – b2 = (a + b)(a – b) and

x2 – 25 = (x + 5)(x – 5)

REMOVING A COMMON FACTOR

If a polynomial contains terms that have common fac￾tors, the polynomial can be factored by using the

reverse of the distributive law.

Example:

In the binomial 49x3 + 21x, 7x is the greatest

common factor of both terms.

Therefore, you can divide 49x3 + 21x by 7x to

get the other factor.

49x3

7

+

x

21x =

4

7

9

x

x3

+

2

7

1

x

x

= 7x2 + 3

Thus, factoring 49x3 + 21x results in 7x(7x2 + 3).

ISOLATING VARIABLES USING FRACTIONS

It may be necessary to use factoring in order to isolate

a variable in an equation.

Example:

If ax – c = bx + d, what is x in terms of a, b, c,

and d?

1. The first step is to get the x terms on the same

side of the equation.

ax – bx = c + d

2. Now you can factor out the common x term on

the left side.

x(a – b) = c + d

3. To finish, divide both sides by a – b to isolate the

variable of x.

x(

a

a

–

–

b

b)

=

c

a

+

–

d

b

4. The a – b binomial cancels out on the left, result￾ing in the answer:

x =

c

a

+

–

d

b

Quadratic Trinomials

A quadratic trinomial contains an x2 term as well as an

x term. x2 – 5x + 6 is an example of a quadratic trino￾mial. It can be factored by reversing the FOIL method.

■ Start by looking at the last term in the trinomial,

the number 6. Ask yourself, “What two integers,

when multiplied together, have a product of posi￾tive 6?”

■ Make a mental list of these integers:

1 × 6 –1 × –6 2 × 3 –2 × –3

■ Next, look at the middle term of the trinomial, in

this case, the –5x. Choose the two factors from

the above list that also add up to –5. Those two

factors are:

–2 and –3

■ Thus, the trinomial x2 – 5x + 6 can be factored as

(x – 3)(x – 2).

–THE SAT MATH SECTION–

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