Question

Can i have some quick help? this is in trinomial method

Answer 1

#1

• 2x²+x-6

ac=6(-2)=-12

• 2x²+4x-3x-6
• 2x(x+2)-3(x+2)
• (2x-3)(x+2)

#2

• 10a²+3a-1
• 10a²+5a-2a-1
• 5a(a+2)-1(a+2)
• (5a-1)(a+2)

#3

• 2c²+5c-12

ac=-24

• 2c²+8c-3c-12
• 2c(c+4)-3(c+4)
• (2c-3)(c+4)

Answer 2

(a)
`(2x-3)(x+2)`

(b)
`(5a-1)(2a+1)`

(c)
`(2c-3)(c+4)`

Explanation:

To factor a quadratic in the form
`ax^2+bx+c`

• Find 2 two numbers that multiply to ac and sum to b.
• Rewrite b as the sum of these 2 numbers.
• Factorize the first two terms and the last two terms separately, then factor out the common term.

Part (a)

Given expression:
`2x^2+x-6`

`\implies ac=2 \cdot -6=-12`

Factors of -12 that sum to 1: 4 and -3

`\implies 2x^2+4x-3x-6`

Factor first two terms and last two terms separately:

`\implies 2x(x+2)-3(x+2)`

Factor out common term
`(x+2)`:

`\implies (2x-3)(x+2)`

Part (b)

Given expression:
`10a^2+3a-1`

`\implies ac=10 \cdot -1=-10`

Factors of -10 that sum to 3: 5 and -2

`\implies 10a^2+5a-2a-1`

Factor first two terms and last two terms separately:

`\implies 5a(2a+1)-1(2a+1)`

Factor out common term
`(2a+1)`:

`\implies (5a-1)(2a+1)`

Part (c)

Given expression:
`2c^2+5c-12`

`\implies ac=2 \cdot -12=-24`

Factors of -24 that sum to 5: 8 and -3

`\implies 2c^2+8c-3c-12`

Factor first two terms and last two terms separately:

`\implies 2c(c+4)-3(c+4)`

Factor out common term
`(c+4)`:

`\implies (2c-3)(c+4)`