Fully factor the expressions below.
a) x2-17x+72
b) 10x2+x-3
a) x2 - 17x + 72
To factorize this expression, we need to find two numbers whose sum is -17 and whose product is 72. The two numbers are -8 and -9 because (-8)(-9) = 72 and -8 + (-9) = -17.
Therefore, we can rewrite the expression as:
x2 - 8x - 9x + 72
Now, we can factor by grouping:
(x2 - 8x) - (9x - 72)
x(x - 8) - 9(x - 8)
(x - 8)(x - 9)
Therefore, the fully factored expression is:
(x - 8)(x - 9)
b) 10x2 + x - 3
To factorize this expression, we need to find two numbers whose sum is 1 and whose product is -30. The two numbers are 6 and -5 because (6)(-5) = -30 and 6 + (-5) = 1.
Therefore, we can rewrite the expression as:
10x2 + 6x - 5x - 3
Now, we can factor by grouping:
(10x2 + 6x) + (-5x - 3)
2x(5x + 3) - 1(5x + 3)
(2x - 1)(5x + 3)
Therefore, the fully factored expression is:
(2x - 1)(5x + 3)