Question

if (x-1) is a factor of the polynomial 5x³-4x²+x-k what is the number k ?​

Answer 1

Answer:

• k = 2

Explanation:

Given equation,

$\rm \implies \: {5x}^{3} - {4x}^{2} + x - k$

Whose one of the factor is (x - 1)

By factor theorem,

$\rm \implies x - 1 = 0$

$\rm \therefore x = 1$

Substituting ‘x’ in the equation:-

$\rm \implies \: {5(1)}^{3} - {4(1)}^{2} + (1) - k = 0$

$\rm \implies \: 5 - 4 + 1 - k = 0$

$\rm \implies \: 2 - k = 0$

$\rm \therefore \: k = 2$

∴ The value of ‘k’ is 2.

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FACTOR THEOREM:

According to fator theorem, if a linear polynomial let (x - a) is a factor of a polynomial p(x) then, p(a) = 0.

Answer 2

Given:-

• A polynomial=5x³-4x²+x-k
• A factor of the polynomial=(x-1)

To find:-

• Value of k.

Solution:-

We will first use the factor theorem to find the value of x. Then we will put the value of x in the equation.

Factor theorem:-

$\large\underline{\bf{ \implies x - 1 = 0}}$

$\large { \green{ \boxed{ \blue{\underline{\bf{ \red{ \implies x = 1}}}}}}}$

Now we will substance the value of x=1 in the equation.

$\large\underline{\bf{ \implies {5x}^{3} - {4x}^{2} + x - k = 0 }}$

$\large\underline{\bf{ \implies5 \times {1}^{3} - {4} \times {1}^{2} + 1 - k = 0 }}$

$\large\underline{\bf{ \implies5 \times 1 - 4 \times 1 + 1 - k = 0}}$

$\large\underline{\bf{ \implies5 - 4 + 1 - k = 0}}$

$\large\underline{\bf{ \implies 2 - k = 0}}$

$\large\underline{\bf{ \implies - k = 2}}$

$\large \blue{\underline{ \green{ \boxed{\bf{ \red{\implies k = - 2}}}}}}$

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