Question

1) In each pair of polynomials given below, find the number to be sub-
tracted from the first to get a polynomial for which the second is a factor.
Find also the second factor of the polynomial got on subtracting the
number.
(1) x2 – 3x + 5, x - 4​

Answer 1

Step-by-step explanation:

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$\large\pink{ {\boxed { Question :-}}}$

☆ In each pair of polynomials given below, find the number to be sub-

tracted from the first to get a polynomial for which the second is a factor.

Find also the second factor of the polynomial got on subtracting the

number.

⊙ x2 – 3x + 5, x - 4

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$\large\green{ {\boxed { Answer :-}}}$

$\large{ ⊙ \: (x - 4) \: \: \: ( {x}^{2} - 3x + 5)}$

⊙ Expand (x−4)(x² − 3x+ 5) (x-4) (x² -3x + 5) by multiplying each term in the first expression by each term in the second expression.

5) by multiplying each term in the first expression by each term in the second expression.x⋅ x²+ x (−3x) + x⋅5 − 4x2 −4 (−3x) − 4⋅5x⋅x² + x(-3x)+ x⋅5 -4x2 -4(-3x)

implify terms.

⊙ Simplify each term.

⊙ Multiply xx by x²x2 by adding the exponents.

⊙ Multiply x by x².

$\implies \large{Raise \:  x  \: to \: the \:  power  \: of  \: 11.}$

$\implies \large \red{\boxed{ {x}^{1} {x}^{2} +x (−3x)+x⋅5−4 {x}^{2} -4(−3x)−4⋅5}}$

$\implies \large{Use \: the \:  power \: rule \:   {a}^{m}{a}^{n} = \: {a}^{m + n} \: to \:  combine  \: exponents}$

⇒ x¹+² +x(−3x)+x⋅5−4x²−4(−3x)−4⋅5

⇒ Add 11 and 22.

⇒ x³+x(−3x)+x⋅5−4x²−4(−3x)−4⋅5x3+x(-3x)

+x⋅5-4x²-4(-3x)-4⋅5

⇒ Rewrite using the commutative property of

multiplication.

⇒ x³−3x⋅x+x⋅5−4x²−4(−3x

−4⋅5x3-3x⋅x+x⋅5-4x2-4(-3x)-4⋅5

⇒ Multiply xx by xx by adding the exponents.

⊙ Move x.

Move x.x³−3(x⋅x)+x⋅5−4x²−4(−3x)−4⋅5x3-3(x⋅x)

+x⋅5-4x2-4(-3x)-4⋅5

⊙ Multiply x by x.

Multiply x by x.x3−3x2+x⋅5−4x2−4(−3x)

−4⋅5x3-3x2+x⋅5-4x2-4(-3x)-4⋅5

⊙ Move 55 to the left of x.

Move 55 to the left of x.x3−3x2+5⋅x−4x2−4(−3x−4⋅5x3-3x2+5⋅x-4x2-4(-3x)-4⋅5.

⊙ Multiply −3-3 by −4-4.

Multiply −3-3 by −4-4.x3−3x2+5x−4x2+12x−4⋅5x3-3x2+5x-4x2+12x-4⋅5

⊙ Multiply −4-4 by 55.

Multiply −4-4 by 55.x3−3x2+5x−4x2+12x−20x3-3x2+5x-4x2+12x-20

Multiply −4-4 by 55.x3−3x2+5x−4x2+12x−20x3-3x2+5x-4x2+12x-20Simplify by adding terms.