Question
Using factor theorem, factorize the following polynomials:
$2y^3 - 5y^2 - 19y + 42$
$2y^3 - 5y^2 - 19y + 42$
✓
Answer
Let $f(y)=2 y^3-5 y^2-19 y+42$ be the given polynomial.
Now, putting $y=2$, we get
$f(2)=2(2)^3-5(2)^2-19(2)+42$
$=16-20-38+42$
$=-58+58=0$
Therefore, $(y-2)$ is a factor of polynomial $f(y)$.
Now,
$f(y)=2 y^2(y-2)-y(y-2)-21(y-2)$
$=(y-2)\left(2 y^2-y-21\right)$
$=(y-2)\left(2 y^2-7 y+6 y-21\right)$
$=(y-2)(y+3)(2 y-7)$
Hence $(y-2),(y+3)$ and $(2 y-7)$ are the factors of polynomial $f(y)$.
Now, putting $y=2$, we get
$f(2)=2(2)^3-5(2)^2-19(2)+42$
$=16-20-38+42$
$=-58+58=0$
Therefore, $(y-2)$ is a factor of polynomial $f(y)$.
Now,
$f(y)=2 y^2(y-2)-y(y-2)-21(y-2)$
$=(y-2)\left(2 y^2-y-21\right)$
$=(y-2)\left(2 y^2-7 y+6 y-21\right)$
$=(y-2)(y+3)(2 y-7)$
Hence $(y-2),(y+3)$ and $(2 y-7)$ are the factors of polynomial $f(y)$.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
In the adjoining figure, □PQRS and □MNRL are rectangles. If point M is the midpoint of side PR, then prove that,
i. SL = LR
ii. $LN =\frac{1}{2} S Q$.
→i. SL = LR
ii. $LN =\frac{1}{2} S Q$.
Given: □PQRS and □MNRL are rectangles. M is the midpoint of side PR.
The class size of distribution is 25 and the first class-interval is 200-224. There are seven class-intervals.
Write the class-marks of each interval.
Write the class-marks of each interval.
The blood groups of 30 students of class VIII are recorded as follows:
A, B, O, O, AB, O, A, O, B, A, O, B, A, O, O, A, AB, O, A, A, O, O, AB, B, A, O, B, A, B, O
Represent this data in the form of a frequency distribution table. Find out which is the most common and which is the most rarest blood group among these students.
A, B, O, O, AB, O, A, O, B, A, O, B, A, O, O, A, AB, O, A, A, O, O, AB, B, A, O, B, A, B, O
Represent this data in the form of a frequency distribution table. Find out which is the most common and which is the most rarest blood group among these students.
Water in a canal 30 dm wide and 12 dm deep, is flowing with a velocity of 100 km every hour.
What much area will it irrigate in 30 minutes if 8 cm of standing water is desired?
What much area will it irrigate in 30 minutes if 8 cm of standing water is desired?
The daily maximum temperatures (in degree Celsius) recorded in a certain city during the month of November are as follows:
25.8, 24.5, 25.6, 20.7, 21.8, 20.5, 20.6, 20.9, 22.3, 22.7, 23.1, 22.8, 22.9, 21.7, 21.3, 20.5, 20.9, 23.1, 22.4, 21.5, 22.7, 22.8, 22.0, 23.9, 24.7, 22.8, 23.8, 24.6, 23.9, 21.1.
Represent the data in the form of a frequency distribution table with class size 11°C.
25.8, 24.5, 25.6, 20.7, 21.8, 20.5, 20.6, 20.9, 22.3, 22.7, 23.1, 22.8, 22.9, 21.7, 21.3, 20.5, 20.9, 23.1, 22.4, 21.5, 22.7, 22.8, 22.0, 23.9, 24.7, 22.8, 23.8, 24.6, 23.9, 21.1.
Represent the data in the form of a frequency distribution table with class size 11°C.
Given below are the cumulative frequencies showing the weights of 685 students of a school. Prepare a frequency distribution table.
|
Weight (in kg)
|
No. of students
|
|
Below 30
|
0
|
|
Below 30
|
24
|
|
Below 35
|
78
|
|
Below 40
|
183
|
|
Below 45
|
294
|
|
Below 50
|
408
|
|
Below 55
|
543
|
|
Below 60
|
621
|
|
Below 65
|
674
|
|
Below 70
|
685
|
Diagonals $PR$ and $QS$ of a rhombus $\text PQRS$ are $20\ cm$ and $48\ cm$ respectively. Find the length of side $PQ$.
→Divide the polynomial $(2y^4 - 3y^3 + 5y - 4) ÷ (y - 1)$ By synthetic division method and Linear method.
→Why do we group data?
If one angle of a triangle is equal to the sum of the other two, show that the triangle is a right angle triangle.