To factorise a quadratic expression like $x^2 + bx + c$, we need to find two numbers that:
1.
Multiply to give the last number ($c$).
2.
Add to give the middle number ($b$).
Once we find these two numbers, let's call them $p$ and $q$, the answer is written as $(x + p)(x + q)$.
Here are the solutions for each problem on the sheet:
1) $x^2 + 5x + 6$
* Multiply to 6, Add to 5: The numbers are
3 and
2.
* Answer: $(x + 3)(x + 2)$ *(This was already done in the example)*
2) $x^2 + 9x + 8$
* Multiply to 8, Add to 9: The numbers are
8 and
1.
* Answer: $(x + 8)(x + 1)$
3) $x^2 + 4x + 3$
* Multiply to 3, Add to 4: The numbers are
3 and
1.
* Answer: $(x + 3)(x + 1)$
4) $x^2 + 4x + 4$
* Multiply to 4, Add to 4: The numbers are
2 and
2.
* Answer: $(x + 2)(x + 2)$
5) $x^2 + 7x + 10$
* Multiply to 10, Add to 7: The numbers are
5 and
2.
* Answer: $(x + 5)(x + 2)$
6) $x^2 + 6x + 9$
* Multiply to 9, Add to 6: The numbers are
3 and
3.
* Answer: $(x + 3)(x + 3)$
7) $x^2 + 9x + 14$
* Multiply to 14, Add to 9: The numbers are
7 and
2.
* Answer: $(x + 7)(x + 2)$
8) $x^2 + 9x + 20$
* Multiply to 20, Add to 9: The numbers are
5 and
4.
* Answer: $(x + 5)(x + 4)$
9) $x^2 + 10x + 21$
* Multiply to 21, Add to 10: The numbers are
7 and
3.
* Answer: $(x + 7)(x + 3)$
10) $x^2 + 11x + 28$
* Multiply to 28, Add to 11: The numbers are
7 and
4.
* Answer: $(x + 7)(x + 4)$
11) $x^2 + 12x + 32$
* Multiply to 32, Add to 12: The numbers are
8 and
4.
* Answer: $(x + 8)(x + 4)$
12) $x^2 + 11x + 24$
* Multiply to 24, Add to 11: The numbers are
8 and
3.
* Answer: $(x + 8)(x + 3)$
13) $x^2 + 13x + 42$
* Multiply to 42, Add to 13: The numbers are
7 and
6.
* Answer: $(x + 7)(x + 6)$
14) $x^2 + 15x + 56$
* Multiply to 56, Add to 15: The numbers are
8 and
7.
* Answer: $(x + 8)(x + 7)$
15) $x^2 + 13x + 36$
* Multiply to 36, Add to 13: The numbers are
9 and
4.
* Answer: $(x + 9)(x + 4)$
16) $x^2 + 26x + 88$
* Multiply to 88, Add to 26: The numbers are
22 and
4.
* Answer: $(x + 22)(x + 4)$
17) $x^2 + 17x + 52$
* Multiply to 52, Add to 17: The numbers are
13 and
4.
* Answer: $(x + 13)(x + 4)$
18) $x^2 + 20x + 51$
* Multiply to 51, Add to 20: The numbers are
17 and
3.
* Answer: $(x + 17)(x + 3)$
Final Answer:
1) (x + 3)(x + 2)
2) (x + 8)(x + 1)
3) (x + 3)(x + 1)
4) (x + 2)(x + 2)
5) (x + 5)(x + 2)
6) (x + 3)(x + 3)
7) (x + 7)(x + 2)
8) (x + 5)(x + 4)
9) (x + 7)(x + 3)
10) (x + 7)(x + 4)
11) (x + 8)(x + 4)
12) (x + 8)(x + 3)
13) (x + 7)(x + 6)
14) (x + 8)(x + 7)
15) (x + 9)(x + 4)
16) (x + 22)(x + 4)
17) (x + 13)(x + 4)
18) (x + 17)(x + 3)
Parent Tip: Review the logic above to help your child master the concept of factorize worksheet.
