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GED Math : Quadratic Equations

Study concepts, example questions & explanations for GED Math

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Example Questions

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Example Question #31 : Foil

On which of the following would one use the FOIL technique?

Possible Answers:

7x - 14

$w^{2}-5w-1$

(t +3)(t-4)

4y(y-2)

$\frac{3x+3}{x+1}$

Correct answer:

(t +3)(t-4)

Explanation:

The FOIL technique is used to multiply or expand two binomials. None of the other expressions represent two binomials. The closest representation would be 4y(y-2) . This expression calls for the multiplication of a binomial and a monomial, so a more straightforward application of the distributive property would work in that case.

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Example Question #61 : Quadratic Equations

Expand (2-h)(7+2h)

Possible Answers:

$-2h^{2}-11h-14$

$-2h^{2}+3h+14$

$-2h^{2}-3h+14$

$-2h^{2}+11h-14$

$14-2h^{2}$

Correct answer:

$-2h^{2}-3h+14$

Explanation:

One can use the FOIL method.

F: $2\cdot7=14$

O: $2\cdot 2h=4h$

I: $-h\cdot7=-7h$

L: $-h\cdot 2h=-2h^{^{2}}$

Adding them up, we get the polynomial $-2h^{^{2}}-3h+14$ , in the customary form of a polynomial.

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Example Question #34 : Foil

Evaluate $(s + 7)^{2}$

Possible Answers:

$s^{2} +14s+49$

$s^{2} + 7s +49$

$s^{2} +49$

$s^{2} + 14s + 14$

$s^{2} +49s+49$

Correct answer:

$s^{2} +14s+49$

Explanation:

$(s+7)^{2} \equiv (s+7)(s+7)$

So FOIL works in this case

F: $s\cdot s=s^{2}$

O: $s\cdot 7=7s$

I: $7\cdot s=7s$

L: $7\cdot 7=49$

$s^{2}+7s+7s+49=s^{2}+14s+49$

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Example Question #35 : Foil

Expand (y+4)(y-4)

Possible Answers:

$y^{2}-16$

$y^{2}+8y-16$

$y^{2}+16$

$y^{2}-8y-16$

$y^{2}-8y+16$

Correct answer:

$y^{2}-16$

Explanation:

This a case to FOIL

F: $y\cdot y=y^{2}$

O: $y\cdot -4=-4y$

I: $4\cdot y=4y$

L: $4\cdot -4=-16$

$y^{2}-4y+4y-16=y^{2} -16$

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Example Question #36 : Foil

Expand $(x^{2}+2)(x-8)$

Possible Answers:

$x^{2}-6x-8$

$x^{2}+2x-8$

$x^{3}-8x^{2}+2x-16$

$x^{3}-6x^{2}-8$

$x^{3}-8$

Correct answer:

$x^{3}-8x^{2}+2x-16$

Explanation:

Even though there is an $x^{2}$ in one of the expressions, the expression is STILL a binomial, and should be treated as such. FOIL is used with the multiplication of two binomials, so FOIL works here.

F: $x^{2}\cdot x= x^{3}$

O: $x^{2}\cdot -8=-8x^{2}$

I: $2\cdot x=2x$

L: $2\cdot -8=-16$

Add the terms: $x^{3} -8x^{2}+2x-16$

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Example Question #31 : Foil

Multiply (x+y)(r+s) .

Possible Answers:

xyr+xys

xr+xs+yr+ys

xr+ys

x+yr+s

xy+rs

Correct answer:

xr+xs+yr+ys

Explanation:

The FOIL method works because there are two binomials.

F: $x\cdot r=xr$

O: $x\cdot s=xs$

I: $y\cdot r=yr$

L: $y\cdot s=ys$

Adding gives the polynomial xr+xs+yr+ys

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Example Question #38 : Foil

Multiply (6w +1)(w+2)

Possible Answers:

$6w^{^{2}}+2$

$7w^{2}+13w+2$

$6w^{2}+8w+2$

$6w^{_{2}}+13w+2$

$6w^{2}+3$

Correct answer:

$6w^{_{2}}+13w+2$

Explanation:

We can use FOIL:

F: x $=6w^{2}$

O: x =12w

I: x =1w

L: x

$6w^{2}+12w+1w+2=6w^{2}+13w+2$

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Example Question #32 : Foil

What is the degree of the polynomial represented as the product of the following two binomials? $(x^{3}+4)(x^{2}-3)$

Possible Answers:

A polynomial of degree 5.

A polynomial of degree 6.

A polynomial of degree 2

A polynomial of degree 3.

A line.

Correct answer:

A polynomial of degree 5.

Explanation:

When the binomials are expanded, we get $x^{5}-3x^{3}+4x^{2}-12$ . This is a polynomial of degree 5.

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Example Question #40 : Foil

A rectangular prism-shaped box is given as having a width, , a height 5 more than the width, and a length 4 more than 2 times the width. Write a polynomial that represents the area of the box, using FOIL.

Possible Answers:

$2x^{3}-6x^{2}-20x$

$8x^{3}+40x^{2}$

$4x^{3}+22x^{2}+10x$

70x-350

$2x^{3}+14x^{2}+20x$

Correct answer:

$2x^{3}+14x^{2}+20x$

Explanation:

First, we need to establish the dimensions of the box. We have the width, . The length is 4 more than 2 times the width, so we have 2x+4 , and the height is 5 more than the width, so we have x+5 .

We need to find the area. The area of a rectangular prism is given as length times width times height. So, we can write x(2x+4)(x+5)

To set it up using FOIL, it can be arranged as $(x^{2}+5x)(2x+4)$ .

Through FOIL, we get $2x^{3}+4x^{2}+10x^{2}+20x$ , or $2x^{3}+14x^{2}+20x$ .

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Example Question #41 : Foil

Expand x(x+1)(x+3) , keeping FOIL in the work.

Possible Answers:

$3x^{2}+3x$

$x^{4}+x^{2}+4x+3$

$x^{3}+3x^{2}+3x$

$x^{3}+4x^{2}+3x$

$x^{2}+4x+3$

Correct answer:

$x^{3}+4x^{2}+3x$

Explanation:

There are several ways to solve this problem. We shall keep it so the solution is accessible to FOIL.

This requires an extra step as opposed to more common FOIL questions. Here one is not tasked to multiply two binomials, but two binomials AND a monomial. Multiplication is commutative, meaning we can multiply the terms in any order. It would help to multiply the monomial, x, by one of the binomials, to get it into the form that can be used with FOIL.

So, $x(x+1)=x^{2}+x$

Then, $(x^{2}+x)(x+3)$ $=x^{3}+3x^{2}+x^{2}+3x$ , by FOIL

Simplified, we have $x^{3}+4x^{2}+3x$

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GED Math : Quadratic Equations

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #31 : Foil

Example Question #61 : Quadratic Equations

Example Question #34 : Foil

Example Question #35 : Foil

Example Question #36 : Foil

Example Question #31 : Foil

Example Question #38 : Foil

Example Question #32 : Foil

Example Question #40 : Foil

Example Question #41 : Foil

All GED Math Resources

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