Question

show that m2
+ m + 1 is not a factor of m4 - 4m3 + m2 - 5m +6.
​

Answer 1

Step-by-step explanation:

The first term is, m2 its coefficient is 1 .

The middle term is, -5m its coefficient is -5 .

The last term, "the constant", is +6

Step-1 : Multiply the coefficient of the first term by the constant 1 • 6 = 6

Step-2 : Find two factors of 6 whose sum equals the coefficient of the middle term, which is -5 .

-6 + -1 = -7

-3 + -2 = -5 That's it

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

m2 - 3m - 2m - 6

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

m • (m-3)

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

2 • (m-3)

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

(m-2) • (m-3)

Which is the desired factorization

$\bold: (m - 2) • (m - 3) = 0$

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.

Answer 2

Answer:

(i) Let us first factorize the given expression 25a

2

−35a+12 as shown below:

25a

2

−35a+12

=25a

2

−15a−20a+12

=5a(5a−3)−4(5a−3)

=(5a−4)(5a−3)