Question

4m²-3m-10 by factorisation methods
​

Answer 1

Answer:

Step by Step Solution

More Icon

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "m2" was replaced by "m^2".

Step by step solution :

STEP

1

:

Equation at the end of step 1

(22m2 - 3m) - 10 = 0

STEP

2

:

Trying to factor by splitting the middle term

2.1 Factoring 4m2-3m-10

The first term is, 4m2 its coefficient is 4 .

The middle term is, -3m its coefficient is -3 .

The last term, "the constant", is -10

Step-1 : Multiply the coefficient of the first term by the constant 4 • -10 = -40

Step-2 : Find two factors of -40 whose sum equals the coefficient of the middle term, which is -3 .

-40 + 1 = -39

-20 + 2 = -18

-10 + 4 = -6

-8 + 5 = -3 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -8 and 5

4m2 - 8m + 5m - 10

Step-4 : Add up the first 2 terms, pulling out like factors :

4m • (m-2)

Add up the last 2 terms, pulling out common factors :

5 • (m-2)

Step-5 : Add up the four terms of step 4 :

(4m+5) • (m-2)

Which is the desired factorization

Equation at the end of step

2

:

(m - 2) • (4m + 5) = 0

STEP

3

:

Theory - Roots of a product

3.1 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation:

3.2 Solve : m-2 = 0

Add 2 to both sides of the equation :

m = 2

Solving a Single Variable Equation:

3.3 Solve : 4m+5 = 0

Subtract 5 from both sides of the equation :

4m = -5

Divide both sides of the equation by 4:

m = -5/4 = -1.250

Answer 2

Given:-

• $\sf {4m}^{2} - 3m - 10$

We have to factorise it.

Answer:-

$\sf {4m}^{2} - 3m - 10$

For factorising it, we have to split it's middle term that is, (-3).

▪We have to split (-3) into two numbers "x" and "y" such a way that,

⠀⠀⠀⠀⦾ x + y = Coefficient of m = -3

⠀⠀⠀⠀⦾ xy = (Coefficient of m²) × (Constant term) = 4 × (-10) = -40

▪So, we can split (-3) into (-8) and 5, so that,

⠀⠀⠀⠀⦾ -8 + 5 = -3 ✓

⠀⠀⠀⠀⦾ (-8) × (5) = -40 ✓

So,

$\sf {4m}^{2} - 3m - 10$

$\sf \longrightarrow \: 4m {}^{2} - 8m + 5m - 10$

Taking 4m as common for the first two terms and taking 5 as common for the last two terms,

$\sf \longrightarrow \: 4m(m - 2) + 5(m - 2)$

$\sf \longrightarrow(m - 2)(4m + 5)$

Hence, the answer is,

$\longrightarrow \underline{\underline{\sf{\green{(m-2)(4m+5)}}}}$