Factorising? x ² +3x-70....?

Question

I Am Soo Stuck!
Please Help =D
a] x ² +3x-70....
b] x ² + 4x + 3
c] x ² + 9x + 8
d] x ² - 6x + 9
e] x ² - 2x - 24
f] x ² + 7x +10

Answer 1

x² + 3x - 70 = 0

The middle term is + 3x

First Term x² = 1

find the sum for the middle term

Multiply the first term 1 times the last term 70 equals 70 and factor

factors of 70

1 x 70
2 x 35
5 x 14
7 x 10 . . .<= ..Use these factors

+ 10 and - 7 satisfy the sum of the middle term

insert + 10x and - 7x into the equation

x² + 3x - 70 = 0

x² + 10x - 7x - 70 = 0

Group Factor

(x² + 10x) - (7x - 70) = 0

x(x + 10) - 7(x + 10) = 0

(x - 7)(x + 10) = 0

- - - - - - - -

Roots

x - 7 = 0

x = 7 + 7 = 0 + 7

x = 7

- - - - - -

Roots

x + 10 = 0

x + 10 - 10 = 0 - 10

x = - 10

- - - - - - -

Do the remaining problems as shown above.

- - - - - - - -s-

Answer 2

a] x ² +3x-70
(x+10)(x-7)
b] x ² + 4x + 3
(x+3)(x+1)
c] x ² + 9x + 8
(x+8)(x+1)
d] x ² - 6x + 9
(x-3)(x-3)
e] x ² - 2x - 24
(x-6)(x+4)
f] x ² + 7x +10
(x+5)(x+2)

think of it this way the last number is the product of the two numbers in the answer and the number add to the middle number. Kinda like what numbers multiplys to 10 and make a sum of 5.
also it the last number is positive then the numbers are both the same sign. if it is negitive they are different. the middle sign shows the greatest numbers sign.

Answer 3

I'm not doing your entire homework assignment for you (let alone for free), so I'll just show you how to do the first two.

In x^2 + 3x - 70, we've got a negative last term, so that means
the answer is in the form of (x + ?)(x - ?), meaning one plus and one minus. We now need to find two numbers whose product is 70 but whose difference is 3. 10 and 7 work. We want 3 and -3 for the difference, so we need to make sure the 10 is in front of the plus and 7 is in front of the minus. So this factors into (x+10)(x-7)

For x^2 + 4x + 3, we've got a positive last term, so this means we have either (x + ?)(x + ?) or (x - ?)(x - ?). The fact we have a +4x in the middle and not -4x tells us that it's (x + ?)(x + ?). Once again, we have to find two numbers whose product is 3 and whose sum is 4. The obvious numbers are 1 and 3. So the answer is (x+1)(x+3).

Answer 4

1. x ² +3x-70

First: multiply the 1st & 3rd term to get -70. find two numbers that give you -70 when multiplied & 3 (2nd term) when added/subtracted. the numbers are (10 & - 7). rewrite the expression with the new middle terms.

x ² +10x - 7x - 70

SEc: with 4 terms - group "like" terms.

(x ² +10x) - (7x - 70)

Third: factor both sets of parenthesis.

x(x +10) - 7(x + 10)
(x+10)(x-7) or, (x-7)(x+10)

2. x ² + 4x + 3

First: multiply the 1st & 3rd term to get 3. find two numbers that give you 3 when multiplied & 4 (2nd term) when added/subtracted. the numbers are (1 & 3). rewrite the expression with the new middle terms.

x ² + 1x + 3x + 3

SEc: with 4 terms - group "like" terms.

(x ² + 1x) + (3x + 3)

Third: factor both sets of parenthesis.

x(x + 1) + 3(x + 1)
(x+1)(x+3) or, (x+3)(x+1)

P.S. try the rest with the same format from #1 & 2

Answer 5

a) (x+10)(x-7)
b) (x+1)(x+3)
c) (x+1)(x+8)
d) (x-3)(x-3)
e) (x-6)(x+4)
f) (x+5)(x+2)

Answer 6

each and every of the topics except A are extremely ordinary. you could basically aspect out an X. for instance: B: X^2+4x=X(X+4) A is slightly trickier. you should detect a pair of numbers that once further, equivalent 3, or maybe as higher, equivalent negative 70. those numbers are -7 and 10 (x-7)(x+10) is your answer to that one.

Answer 7

a)-----(x + 10).(x - 7)
b)-----(x + 1).(x + 3)
c)-----(x + 1).(x + 8)
d)-----(x - 3).(x - 3) = (x - 3)²
e)-----(x - 6).(x + 4)
f)------(x + 5).(x + 2)