This is a quadratic equation question which will have two answers: 2x2+42 = x2+13x 2x2-x2-13x+42 = 0 x2-13x+42 = 0 Factorising the equation gives you: (x-6)(x-7) = 0 Therefore: x = 6 or x = 7
42 + x2 = 13x ∴ x2 - 13x + 42 = 0 ∴ (x - 6)(x - 7) = 0 ∴ x ∈ {6, 7}
(x - 6)(x - 7)
x2 + 13x + 4 = (x + 6½ + √38¼)(x + 6½ - √38¼). To find this, we need to find p and q, where p + q = 13, pq = 4. 4 = 42¼ - 38¼ = (6½ + √38¼)(6½ - √38¼); thus, p = (6½ + √38¼), q = (6½ - √38¼).
x3 + 13x2 + 42x = x(x2 + 13x + 42) = x(x2 + 6x + 7x + 42) = x[x(x + 6) + 7(x + 6)] = x(x + 7)(x + 6)
This is a quadratic equation question which will have two answers: 2x2+42 = x2+13x 2x2-x2-13x+42 = 0 x2-13x+42 = 0 Factorising the equation gives you: (x-6)(x-7) = 0 Therefore: x = 6 or x = 7
(x - 6)(x - 7)
42 + x2 = 13x ∴ x2 - 13x + 42 = 0 ∴ (x - 6)(x - 7) = 0 ∴ x ∈ {6, 7}
2x - 13x + 42 = x +ax + b a + b = 2(x - 6.5x + 21) = 34 = a + b
(x - 6)(x - 7)
It is (x+6)(x+7) when factored
-((2x + 7)(x - 6))
In order to factor this expression we are going to write it as 2 expressions (factors) which when multiplied together equal x2 - 13x + 42.We can see straight away that the simplest way to end up with x2 is to have an "x" in each factor.This then just leaves us to find two numbers which when added together result in -13 and when multiplied result in 42.It likely will not take you too long to see that -6 & -7 would do this.Thus we can factor this to:(x-6) (x-7)
x2 + 13x + 4 = (x + 6½ + √38¼)(x + 6½ - √38¼). To find this, we need to find p and q, where p + q = 13, pq = 4. 4 = 42¼ - 38¼ = (6½ + √38¼)(6½ - √38¼); thus, p = (6½ + √38¼), q = (6½ - √38¼).
Hopefully, one of the binomials below is either (x - 7) or (x - 6)
6(x + 7)
The easiest way to factor x2 + 13x + 42 is to look at the last number. The last number is 42. Now, think of what whole numbers you can multiply to equal 42. 1 x 42 2 x 21 3 x 14 6 x 7 If you look at the equation, we notice that the sign pattern is + + + When the sign pattern is + + +, we know that whatever two factors you choose must add up to the middle number, 13. So, automatically we can get rid of some of these factors. 1 x 42 --> 1 + 42 doesn't equal 13 2 x 21 --> 2 + 21 doesn't equal 13 3 x 14 --> 3 + 14 doesn't equal 13 Now, we're automatically left with 6 x 7. So, your answer would be (factored out), (x+6)(x+7) Where x = -7, -6