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 thenumber.(1) x2 – 3x + 5, x – 4 About the author Adeline
Step-by-step explanation: _________________________________________________________ _________________________________________________________ [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 _________________________________________________________ _________________________________________________________ [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. Reply
Step-by-step explanation:
_________________________________________________________
_________________________________________________________
[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
_________________________________________________________
_________________________________________________________
[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.