Write an equivalent expression in factored form.
1) \( x^2−4 \)
2) \( y^2−25 \)
3) \( 4x^2−9 \)
4) \( 9p^2−4 \)
5) \( 4z^2−1 \)
6) \( 25x^2−4y^2 \)
7) \( y^2−x^2 \)
8) \( 16x^2−49 \)
9) \( 100d^2−121 \)
10) \( -x^2+9 \)
1) \( x^2−4 \)
2) \( y^2−25 \)
3) \( 4x^2−9 \)
4) \( 9p^2−4 \)
5) \( 4z^2−1 \)
6) \( 25x^2−4y^2 \)
7) \( y^2−x^2 \)
8) \( 16x^2−49 \)
9) \( 100d^2−121 \)
10) \( -x^2+9 \)
Write an equivalent expression in factored form.
11) \( x^2+10x+25 \)
12) \( y^2−8y+16 \)
13) \( y^2+14y+49 \)
14) \( z^2−6z+9 \)
15) \( p^2−16p+64 \)
16) \( 4p^2−20p+25 \)
17) \( 9n^2+12n+4 \)
18) \( 4z^2−12z+9 \)
19) \( x^2+4xy+4y^2 \)
20) \( -x^2−10x−25 \)
11) \( x^2+10x+25 \)
12) \( y^2−8y+16 \)
13) \( y^2+14y+49 \)
14) \( z^2−6z+9 \)
15) \( p^2−16p+64 \)
16) \( 4p^2−20p+25 \)
17) \( 9n^2+12n+4 \)
18) \( 4z^2−12z+9 \)
19) \( x^2+4xy+4y^2 \)
20) \( -x^2−10x−25 \)
Write an equivalent expression in factored form.
21) \( m^2+6m+5 \)
22) \( x^2−13x+42 \)
23) \( \dfrac{1}{5}n^2−2n+5 \)
24) \( x^2+8x+7 \)
25) \( 0.1x^2−0.8x+1.6 \)
26) \( n^2+4n−12 \)
27) \( \dfrac{1}{3}x^{2}+3x−\dfrac{70}{3} \)
28) \( x^2+6x−72 \)
29) \( 0.25c^2−2.5c+4 \)
21) \( m^2+6m+5 \)
22) \( x^2−13x+42 \)
23) \( \dfrac{1}{5}n^2−2n+5 \)
24) \( x^2+8x+7 \)
25) \( 0.1x^2−0.8x+1.6 \)
26) \( n^2+4n−12 \)
27) \( \dfrac{1}{3}x^{2}+3x−\dfrac{70}{3} \)
28) \( x^2+6x−72 \)
29) \( 0.25c^2−2.5c+4 \)
What value of \( a \) makes the statement true?
30) \( x^2−18x+32 = (x−2)(x−a) \)
31) \( 2b^2+9b+4 = (2b+a)(b+4) \)
32) \( 5x^2−3x−2 = (ax+2)(x−1) \)
33) \( 2p^2−11p+15 = (2p−5)(p−a) \)
34) \( 7n^2+9n+2 = (7n+a)(n+1) \)
35) \( 5x^2−22x+8 = (5x−a)(x−4) \)
36) \( 3s^2+4s−4 = (3s−a)(s+a) \)
37) \( 3x^2+29x−44 = (3x−4)(x+a) \)
38) \( 28z^2−11z+1 = (az−1)(4z−1) \)
39) \( 5x^2−2x−7 = (x+1)(5x−a) \)
40) \( 3x^2+7x−6 = (3x−a)(x+3) \)
30) \( x^2−18x+32 = (x−2)(x−a) \)
31) \( 2b^2+9b+4 = (2b+a)(b+4) \)
32) \( 5x^2−3x−2 = (ax+2)(x−1) \)
33) \( 2p^2−11p+15 = (2p−5)(p−a) \)
34) \( 7n^2+9n+2 = (7n+a)(n+1) \)
35) \( 5x^2−22x+8 = (5x−a)(x−4) \)
36) \( 3s^2+4s−4 = (3s−a)(s+a) \)
37) \( 3x^2+29x−44 = (3x−4)(x+a) \)
38) \( 28z^2−11z+1 = (az−1)(4z−1) \)
39) \( 5x^2−2x−7 = (x+1)(5x−a) \)
40) \( 3x^2+7x−6 = (3x−a)(x+3) \)
Write an equivalent expression in factored form.
41) \( x^3−5x^2+6x \)
42) \( 2x^3+x^2−3x \)
43) \( 2x^3+6x^2−20x \)
44) \( 12x^3−x^2−4x \)
45) \( 2ab^2−8ab−42a \)
41) \( x^3−5x^2+6x \)
42) \( 2x^3+x^2−3x \)
43) \( 2x^3+6x^2−20x \)
44) \( 12x^3−x^2−4x \)
45) \( 2ab^2−8ab−42a \)
What value of a makes the statement true?
46) \( x^3+3x^2−10x = x(x−a)(x+5) \)
47) \( 2x^3+11x^2+12x = x(2x+a)(x+4) \)
48) If the length \( (l) \) of a rectangle is two more than its width what is and expression for the area?
49) If a rectangle has a width of \( (x+5) \) and a width of \( (x-2) \), what would be an expression for the area? What would be an expression for the perimeter?
50) Which are equivalent?
a) \( (x+1)(x−5) \)
b) \( (x−1)(x+5) \)
c) \( (x−2)^2+1 \)
d) \( (x−2)^2−9 \)
e) \( x^2−4x−5 \)
f) \( (x−3)(x−1)−8 \)
Solution Bank
46) \( x^3+3x^2−10x = x(x−a)(x+5) \)
47) \( 2x^3+11x^2+12x = x(2x+a)(x+4) \)
48) If the length \( (l) \) of a rectangle is two more than its width what is and expression for the area?
49) If a rectangle has a width of \( (x+5) \) and a width of \( (x-2) \), what would be an expression for the area? What would be an expression for the perimeter?
50) Which are equivalent?
a) \( (x+1)(x−5) \)
b) \( (x−1)(x+5) \)
c) \( (x−2)^2+1 \)
d) \( (x−2)^2−9 \)
e) \( x^2−4x−5 \)
f) \( (x−3)(x−1)−8 \)
Solution Bank