Question

1. Factor 7w^2−175

A. −7(w−25)
B. 7(w−5)(w−5)
C. 7(w−25)
D. 7(w−5)(w+5)
2. Factor 4y^2−32y+64
A. 4(y−4)(y+4)
B. 4(y−4)^2
C. 2(y−4)^2
D. 2(y−4)(y+4)
3. Factor 3x^2−12x+12
A. (3x−2)(x−2)
B. 3(x−2)(x+2)
C. 3(x−2)^2
D. 3(x+2)^2
4. Which of the following is the correct factorization of b^2+10b+25?
A. (b+5)^2
B. 2(b+5)(b−5)
C. (b+5)(b−5)
D. (b−5)^2
5. Factor 8x^2−72
A. 8(x+3)^2
B. 8(x−3)^2
C. (8x+3)(x−3)
D. 8(x+3)(x−3)

Answer 1

• 1. D. 7(w−5)(w+5)
• 2. B. 4(y-4)^2
• 3. C. 3(x-2)^2
• 4. A. (b+5)^2
• 5. D. 8(x+3)(x-3)

Solution :

#1

• To factor 7w^2 - 175 , we simply will isolate the common term ,'7' from the expression, leaving 7(w^2 - 25) = 7(w−5)(w+5) ,thus option D. is correct ✓

#2

• To factorise 4y^2−32y+64, we firstly will isolate the common term ,'4' , resulting in 4(y^2 - 8y + 16) and then factorise the expression within brackets using middle split method, resulting in 4(y -4)(y-4) or 4(y-4)^2 thus, option B. is correct ✓

#3

• To factorise 3x^2−12x+12,we firstly will isolate the common term ,'3', resulting in 3(x^2 - 4x + 4) and then factorise the braced term using middle split method, leaving us with simplest form : 3(x-2)(x-2) or 3(x-2)^2,thus, Option C. is correct ✓

#4

• We can factorise b^2+10b+25 using middle split method : b^2 + 5b + 5b + 25 = b(b+5)+5(b+5) = (b+5)(b+5) or (b+5)^2 ,thus Option A. is correct ✓

#5

• To factor 8x^2−72 , we will isolate the like term,'8', giving us 8(x^2 - 9) and since the term inside of brackets is in the form of a^2 - b^2 ( x^2 -3^2) ,thus, we get 8(x+3)(x-3) ,and hence , option D. is correct ✓