On dividing 16x^2 - 24x + 9 by 4x - 3,find th | vedclass

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(B) To find the remainder when $16x^2 - 24x + 9$ is divided by $4x - 3$,we can use the Remainder Theorem or perform polynomial long division.Method $1

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$ 0 $

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(B) To find the remainder when $16x^2 - 24x + 9$ is divided by $4x - 3$,we can use the Remainder Theorem or perform polynomial long division.Method $1$: FactorizationNotice that $16x^2 - 24x + 9$ is a perfect square trinomial.$16x^2 - 24x + 9 = (4x)^2 - 2(4x)(3) + (3)^2 = (4x - 3)^2$.Since $(4x - 3)^2$ is exactly divisible by $(4x - 3)$,the remainder is $0$.Method $2$: Remainder TheoremSet the divisor equal to zero: $4x - 3 = 0 \implies x = 3/4$.Substitute $x = 3/4$ into the polynomial $P(x) = 16x^2 - 24x + 9$:$P(3/4) = 16(3/4)^2 - 24(3/4) + 9$$P(3/4) = 16(9/16) - 18 + 9$$P(3/4) = 9 - 18 + 9 = 0$.Thus,the remainder is $0$.

On dividing $16x^2 - 24x + 9$ by $4x - 3$,find the remainder.

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