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We could also apply quadratic formula:
b1 = [-(-21)+sqrt((-21)^2 + 4*108)]/2*1
b1 = (21+sqrt9)/2
b1 = (21+3)/2
b1 = 12
b2 = (21-3)/2
b2 = 9
We can write the quadratic expression as a product of linear factors:
b^2 - 21b + 108 = (b - b1)(b - b2)
b^2 - 21b + 108 = (b - 12)(b - 9)
Remark: b1 and b2 are the roots of the quadratic equation:
b^2 - 21b + 108 = 0
To factorise b^2-21b +108.
We do the factorisatio by gruouping method.
We split the middle term -21b in two in such a way that their product is equal to the product of end terms b^2 and 108, or equal to 108b^2.
Therefore middle term -21b = -12b -9b and
(-12b)(-9b) = 108b^2.
Therefore b^2-21b +108 = b^2-12b-9b+108
b^2-21b +108 = b(b-12)-9(b-12)
b^2-21b +108 = (b-12)(b-9).
Therefore the factor form of the given expression is b^2-21b+108 = (b-12)(b-9).
` b^2 - 21b + 108 `
a=1 b=-21 c=108
use axxc then find factors of 108 that add to -21
factors of 108 that = -21 are -9 and -12
plug them in
`b^2 - 9b-12b + 108 `
`(b^2 - 9b)(-12b + 108) `
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