1) In each pair of polynomials given below, find the number to be sub-
tracted from the first to get a polynomial for which t

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​

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  1. Step-by-step explanation:

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    [tex]\large\pink{ {\boxed { Question :-}}}[/tex]

    ☆ 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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    [tex]\large\green{ {\boxed { Answer :-}}}[/tex]

    [tex] \large{ ⊙ \: (x – 4) \: \: \: ( {x}^{2} – 3x + 5)}[/tex]

    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 4×2 −4 (−3x) 4⋅5x⋅x² + x(-3x)+ x⋅5 -4×2 4(-3x)

    implify terms.

    Simplify each term.

    Multiply xx by x²x2 by adding the exponents.

    Multiply x by x².

    [tex] \implies \large{Raise \: x \: to \: the \: power \: of \: 11.}[/tex]

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

    [tex] \implies \large{Use \: the \: power \: rule \: {a}^{m}{a}^{n} = \: {a}^{m + n} \: to \: combine \: exponents}[/tex]

    x¹+² +x(−3x)+x⋅5−4x²−4(−3x)−4⋅5

    Add 11 and 22.

    x³+x(−3x)+x⋅5−4x²−4(−3x)−4⋅5×3+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⋅5×3-3x⋅x+x⋅5-4×2-4(-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⋅5×3-3(x⋅x)

    +x⋅5-4×2-4(-3x)-4⋅5

    Multiply x by x.

    Multiply x by x.x3−3×2+x⋅5−4×2−4(−3x)

    −4⋅5×3-3×2+x⋅5-4×2-4(-3x)-4⋅5

    Move 55 to the left of x.

    Move 55 to the left of x.x3−3×2+5⋅x−4×2−4(−3x−4⋅5×3-3×2+5⋅x-4×2-4(-3x)-4⋅5.

    Multiply −3-3 by −4-4.

    Multiply −3-3 by −4-4.×3−3×2+5x−4×2+12x−4⋅5×3-3×2+5x-4×2+12x-4⋅5

    Multiply −4-4 by 55.

    Multiply −4-4 by 55.×3−3×2+5x−4×2+12x−20×3-3×2+5x-4×2+12x-20

    Multiply −4-4 by 55.×3−3×2+5x−4×2+12x−20×3-3×2+5x-4×2+12x-20Simplify by adding terms.

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