solve by splitting middle term p square + 5p - 24 correct answers are awarded with 10 thanks
Answers
Answer:
p = 3 , -8
Step-by-step explanation:
Given polynomial : p² + 5p - 24
Let f(p) = p² + 5p - 24
=> It is of the form ax² + bx + c
By comparing, we get
a = 1, b = 5, c = -24
where
a - coefficient of x²
b - coefficient of x
c - constant term
By sum-product pattern,
>> Find the product of quadratic term [ax²] and constant term [c]
= p² × (-24)
= -24p²
>> find the factors of "-24p²" in pairs
p × (-24p)
(-p) × 24p
2p × (-12p)
(-2p) × 12p
(3p) × (-8p)
(-3p) × 8p
(4p) × (-6p)
(-4p) × 6p
>> From the above, find the pair that adds to get linear term [bx]
-3p + 8p = 5p
>> Split the middle term 5p as 8p and -3p
p ² + 5p - 24
p² + 8p - 3p - 24
>> Find the common factor,
p(p + 8) - 3(p + 8)
(p + 8) (p - 3)
∴ p² + 5p - 24 = (p + 8) (p - 3)
To find the zeroes, equal it to zero.
p² + 5p - 24 = 0
(p + 8) (p - 3) = 0
p + 8 = 0 (or) p - 3 = 0
p = -8 (or) p = +3
The zeroes of the polynomial are 3 and -8
p²+5p-24
p²+8p-3p-24
p(p+8)-3(p+8)
(p-3)(p+8)
Thnx✌️✌️