Grade 11 Factoring Expressions Quiz

1) What is the missing factor? x² + 5x – 14 = (x +7)(?)

X–14

X+2

–2x

X–2

The correct missing factor is x-2. This can be determined by factoring the quadratic equation x^2 + 5x - 14 using the method of factoring by grouping or by using the quadratic formula. The factors of -14 that add up to 5 are -2 and 7, so the factored form of the equation is (x + 7)(x - 2). Therefore, the missing factor is x - 2.

Explanation

The correct missing factor is x-2. This can be determined by factoring the quadratic equation x^2 + 5x - 14 using the method of factoring by grouping or by using the quadratic formula. The factors of -14 that add up to 5 are -2 and 7, so the factored form of the equation is (x + 7)(x - 2). Therefore, the missing factor is x - 2.

2)

The area of the rectangle is x²+8x+12. If the length is x+2, what is the width?

X+3

X+4

X+6

X+10

The area of a rectangle is found by multiplying its length by its width. In this case, the area is given as x^2 + 8x + 12. We are also given that the length is x+2. To find the width, we can divide the area by the length. When we divide x^2 + 8x + 12 by x+2, we get x+6. Therefore, the width of the rectangle is x+6.

Explanation

The area of a rectangle is found by multiplying its length by its width. In this case, the area is given as x^2 + 8x + 12. We are also given that the length is x+2. To find the width, we can divide the area by the length. When we divide x^2 + 8x + 12 by x+2, we get x+6. Therefore, the width of the rectangle is x+6.

3) What is the missing factor? –7y + y² – 18 = (?)(y+2)

Y+9

Y–6

Y–7

Y–9

In the equation -7y + y^2 - 18 = ( ? )(y+2), the missing factor can be determined by comparing the given equation with the answer choices. By analyzing the equation, it can be observed that the missing factor should be y-9. This is because when y-9 is multiplied by (y+2), it will result in -7y + y^2 - 18, which is the same as the left side of the equation. Therefore, y-9 is the missing factor that completes the equation.

Explanation

In the equation -7y + y^2 - 18 = ( ? )(y+2), the missing factor can be determined by comparing the given equation with the answer choices. By analyzing the equation, it can be observed that the missing factor should be y-9. This is because when y-9 is multiplied by (y+2), it will result in -7y + y^2 - 18, which is the same as the left side of the equation. Therefore, y-9 is the missing factor that completes the equation.

4) Factor completely: k² -2k - 24

(k+4)(k-6)

(k+4)(k+6)

(k+6)(k-1)

(k-4)(k+6)

The given quadratic expression can be factored as (k+4)(k-6). This can be determined by finding two numbers whose product is -24 and whose sum is -2. The numbers -4 and 6 satisfy these conditions, so the expression can be written as (k-6)(k+4).

Explanation

The given quadratic expression can be factored as (k+4)(k-6). This can be determined by finding two numbers whose product is -24 and whose sum is -2. The numbers -4 and 6 satisfy these conditions, so the expression can be written as (k-6)(k+4).

5) Factor the quadratic equation fully. –2x² – 12x – 16

(x+2)(x+4)

–2(x+2)(x+4)

(–2x+8)(x–2)

2(x–2)(x–4)

The given quadratic equation is -2x^2 - 12x - 16. To factor it fully, we can find the common factors of the terms. The common factor here is -2. Factoring out -2, we get -2(x^2 + 6x + 8). Now, we need to factor the quadratic expression inside the parentheses. The factors of 8 that add up to 6 are 2 and 4. So, we can write the quadratic expression as (x + 2)(x + 4). Putting it all together, the fully factored form of the quadratic equation is -2(x + 2)(x + 4).

Explanation

The given quadratic equation is -2x^2 - 12x - 16. To factor it fully, we can find the common factors of the terms. The common factor here is -2. Factoring out -2, we get -2(x^2 + 6x + 8). Now, we need to factor the quadratic expression inside the parentheses. The factors of 8 that add up to 6 are 2 and 4. So, we can write the quadratic expression as (x + 2)(x + 4). Putting it all together, the fully factored form of the quadratic equation is -2(x + 2)(x + 4).

6) Which shows the factorization of the polynomial? w²–5w+6

(w–5)(w–1)

(w–3)(w+2)

(w–2)(w–3)

(w+1)(w–6)

The correct answer is (w–2)(w–3). This is the factorization of the given polynomial w^2–5w+6. By multiplying (w–2) and (w–3) together using the distributive property, we get w^2–2w–3w+6, which simplifies to w^2–5w+6. Therefore, (w–2)(w–3) is the correct factorization.

Explanation

The correct answer is (w–2)(w–3). This is the factorization of the given polynomial w^2–5w+6. By multiplying (w–2) and (w–3) together using the distributive property, we get w^2–2w–3w+6, which simplifies to w^2–5w+6. Therefore, (w–2)(w–3) is the correct factorization.

7)

Jasmine painted this design using black and white paint. She used (x²+x–6)/2 cm² of red paint. What are the dimensions of the black triangle?

B=x–6; h=x+1

B=x–1; h=x–5

B=x–2;h=x+3

B=x+2;h=x–3

The dimensions of the black triangle are b=x-2 and h=x+3.

Explanation

The dimensions of the black triangle are b=x-2 and h=x+3.

8) The formula for the surface area of a cube is SA=6e². If the surface area of this cube is 6x²–24x–24, what is the measure of one edge?

X–2

X–4

X+2

X–6

The given surface area of the cube is 6x^2 - 24x - 24. Comparing this with the formula SA = 6e^2, we can equate the expressions: 6x^2 - 24x - 24 = 6e^2. Simplifying this equation, we get x^2 - 4x - 4 = e^2. Since e represents the measure of one edge, the measure of one edge is equal to x - 2. Therefore, the correct answer is x - 2.

Explanation

The given surface area of the cube is 6x^2 - 24x - 24. Comparing this with the formula SA = 6e^2, we can equate the expressions: 6x^2 - 24x - 24 = 6e^2. Simplifying this equation, we get x^2 - 4x - 4 = e^2. Since e represents the measure of one edge, the measure of one edge is equal to x - 2. Therefore, the correct answer is x - 2.

9) Which value for k will allow this polynomial to be factored? x²+kx+18

6

7

8

11

To factor a polynomial, we need to find two binomials that multiply together to give us the original polynomial. In this case, we have x^2 + kx + 18. The coefficient of x^2 is 1, so the binomials will have the form (x + a)(x + b). To find the values of a and b, we need to find two numbers that add up to k and multiply to 18. The only pair of numbers that satisfies this condition is 9 and 2. Therefore, the polynomial can be factored as (x + 9)(x + 2). To make this possible, k must be equal to 11.

Explanation

To factor a polynomial, we need to find two binomials that multiply together to give us the original polynomial. In this case, we have x^2 + kx + 18. The coefficient of x^2 is 1, so the binomials will have the form (x + a)(x + b). To find the values of a and b, we need to find two numbers that add up to k and multiply to 18. The only pair of numbers that satisfies this condition is 9 and 2. Therefore, the polynomial can be factored as (x + 9)(x + 2). To make this possible, k must be equal to 11.

10) Which trinomial does not have (x–2) as a factor?

X^2–4

X^2–5x+6

X^2+x–6

X^2–2x–8

The trinomial x^2–2x–8 does not have (x–2) as a factor because when we factor out (x–2) from the trinomial, we get (x–4)(x+2), not (x–2)(x+4). Therefore, x^2–2x–8 is the correct answer.

Explanation

The trinomial x^2–2x–8 does not have (x–2) as a factor because when we factor out (x–2) from the trinomial, we get (x–4)(x+2), not (x–2)(x+4). Therefore, x^2–2x–8 is the correct answer.