Question
Resolve each of the following quadratic trinomial into factor:
$2 x^2-3 x-2$
$2 x^2-3 x-2$
✓
Answer
The given expression is $2 x^2-3 x -2$
(Co-efficient of $x^2=2$, co-efficient of $x=-3$ and the constant term $=-2$ )
We will split the co-efficient of $x$ into two number parts such that their sum is -3 and their product equals to the product of the co-efficient of $x ^2$ and constant term, i.e., $2 \times(-2)=-4$
Now,
$(-4)+1=-3 \text { And }(-4) \times 1=-4$
Replacing the middle term 3 x by $-4 x + x$, we have:
$2 x^2-3 x-2=2 x^2-4 x+x-2$
$=\left(2 x^2-4\right)+(x-2)$
$=2 x(x-2)+1(x-2)$
$=(x-2)(2 x+1)$
(Co-efficient of $x^2=2$, co-efficient of $x=-3$ and the constant term $=-2$ )
We will split the co-efficient of $x$ into two number parts such that their sum is -3 and their product equals to the product of the co-efficient of $x ^2$ and constant term, i.e., $2 \times(-2)=-4$
Now,
$(-4)+1=-3 \text { And }(-4) \times 1=-4$
Replacing the middle term 3 x by $-4 x + x$, we have:
$2 x^2-3 x-2=2 x^2-4 x+x-2$
$=\left(2 x^2-4\right)+(x-2)$
$=2 x(x-2)+1(x-2)$
$=(x-2)(2 x+1)$
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
A cistern can be filled by a tap in 4 hours and emptied by an outlet pipe in 6 hours. How long will it take to fill the cistern if both the tap and the pipe are opened together?
Find the area enclosed by the following figures as the sum of the areas of a rectangle and a trapezium:
The difference in simple interest and compound interest on a certain sum of money at $6\frac{2}{3}\%$ per annum for 3 years is Rs. 46 Determine the sum.
→Harpreet borrowed Rs. 20000 from her friend at 12% per annum simple interest. She lent it to Alam at the same rate but compounded annually. Find her gain after 2 years.
$\frac{5\text{x}}{3}+\frac{2}{5}=1$
→Look at the histogram given below and answer the question that follow:
- How many students have height more than or equal to 135cm but less than 150cm?
- Which class interval has the least number of students?
- What is the class size?
- How many students have height less than 140cm?
Factorize :
44x² – x – 3
The curved surface area of a cylinder is $1320 cm^2$ and its base has diameter 21 cm . Find the volume of the cylinder.
→Solve the following equation and verify your answer:
$\frac{2\text{x}-3}{3\text{x}+2}=-\frac{2}{3}$
→$\frac{2\text{x}-3}{3\text{x}+2}=-\frac{2}{3}$
Construct a frequency table with equal class intervals from the following data on the monthly wages (in rupees) of 28 labourers working in a factory, taking one of the class intervals as 210-230 (230 not included):
220, 268, 258, 242, 210, 268, 272, 242, 311, 290, 300, 320, 319, 304, 302, 318, 306, 292, 254, 278, 210, 240, 280, 316, 306, 215, 256, 236.
220, 268, 258, 242, 210, 268, 272, 242, 311, 290, 300, 320, 319, 304, 302, 318, 306, 292, 254, 278, 210, 240, 280, 316, 306, 215, 256, 236.