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What if you can't find two factors that equal the middle term in a trinomial factoring?
Wiki User
∙ 11y ago
That means you need to work a little bit more in order to factor it. For example,
x2 - 2x - 4
Complete the square and try to factor by using the difference of the two squares. So add and subtract 1. Since the sum of the subtracted number and the constant is negative, we can factor by using real numbers, otherwise we'll use imaginary numbers.
x2 - 2x + 1 - 1 - 4
= (x - 1)2 - 5 express 5 as (√5)2
= (x - 1)2 - (√5)2
= [(x - 1) - √5][(x - 1) + √5]
= (x - 1 - √5)(x - 1 + √5).
So we need to work a little bit more, but we can factor the trinomial. If you have a specific example, I will be happy to assist you with my answer.
Wiki User
∙ 11y ago
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When you have a number that has exactly two equal factors each factor is called?
If a number has equal factors, it is a perfect square and the equal factors would be square roots.
X2-14x plus 46 equals 0?
This is the generalized trinomial equation (aka quadratic):y = ax2 - bx - cBefore factoring, always check the discriminant of the quadratic equation, which is:b2 - 4acIf it is a rational square (16, 25, 196, 225), then it is factorable. If it is not, then it is not factorable.In this case, it is not, since the discriminant is equal to 2√3.Now, you will have to use the quadratic formula:(-b2 +/- √(b2 - 4ac))/2This will give you (14 +/- 2√3)/2
What are the factors of this quadratic trinomial 12x2 plus 13x 35?
12x2+13x-35 = (4x-5)(3x+7) 12x2 + 13x- 35 let's find two factors of -420 (12*-35) whose sum is 13, which are 28 and -15 (12x + 28)(12x - 15) now simplify by 4 and 3 (3x + 7)(4x - 5)
What are the factors of 640 and equal 50?
40 and 10
What are the factors of 945 that equal 26?
21 and 5
Is the third term in a factorable trinomial equal to the product of the constants in its binomial factors?
Yes it is
How do factor a trinomial expression with a leading coefficient not equal to 1?
To factor a trinomial in the form ax2 + bx + c, where a does not equal 1, the easiest process is called "factoring by grouping". To factor by grouping, you must change the trinomial into an equivalent tetranomial by rewriting the middle term (bx) as the sum of two terms. There is a specific way to do this, as demonstrated in the example.Take the quadratic trinomial 5x2 + 11x + 21. Find the product of a and c, or 5*2 = 10.2. Find factors of ac that when added together give you b, in this case 10 and 1.3. Rewrite the middle term as the sum of the two factors (5x2 + 10x + x + 2).4. Group terms with common factors and factor these groups.5x2 + x + 10x + 2x(5x + 1) + 2(5x + 1)5. Factor the binomial in the parentheses out of the whole polynomial, leaving you with the product of two binomials. 5x2 + 11x + 2 = (x + 2)(5x + 1)Notes:1. The same process is done if there are any minus signs in the trinomial, just be careful when factoring out a negative from a positive or vice versa.2. If you have a tetranomial on its own, you can skip the rewriting process and just factor the whole polynomial by grouping from the start.3. As in factoring any polynomial, always factor out the GCF first, then factor the remaining polynomial if necessary.4. Always look for patterns, like the difference of squares or square of a binomial, while factoring. It will save a lot of time.
How do you factor a trinomial with a leading coefficient is equal to 1?
Suppose the trinomial is x2 + Bx + C You need to find a factor pair of C whose sum is B. If the factors are p and q (that is, pq = C and p+q = B), then the trinomial can be factorised as (x + p)*(x + q).
How do you factor out 2x2-127x-48960?
Normal methods of factoring a trinomial do not work. So this would be referred to as prime. You can set it equal to zero and use the quadratic formula to find solutions. I'll refer to these as x = A and x = B Use these to write factors (x-A)(x-B) and you will have your factored form. My guess is that the answers are irrational or imaginary, NOT real nor integers.
When factoring a trinomial that is in the format ax2 plus bx c the number that is represented by B should be viewed as the?
The general form of a quadratic expression is given as ax2+bx+c where "a" cannot equal zero and "b" is the coefficient of the variable "x" and also the sum of the factors of "c" when "a" is unity. Example: x2+5x+6 = (x+2)(x+3) when factored
How do you factor q2-7q plus 12?
1. When factoring first always look for a GCF (greatest common factor). If each term has a greatest common factor, factor it out in from using parenthesis first. This problem does not have a GCF. 2. Next, since this is a trinomial, many times we can factor it down using backwards FOIL (First, Outter, Inner, Last). 3. To do this always put down two sets of parenthesis. (we do this because we are looking to factor into two binomials) ( )( ) 4. Next we complete the fist term in each set of parenthesis. The first term is simply going to be the variable we are using in the problem. In this problem the variable is q. (q )(q ) 5. Then find the factors of the last term (+12) in which the sum is equal to the coefficient of the middle term (-7). These factors are -3 and -4. 6. Complete the factoring by putting these factors into the second part of the parenthesis. (q - 3)(q - 4) * If you want to make sure you are correct, multiply you answer out and see if you get the same trinomial you started with.
How do you factor out 2x2 127x 4896?
You left out any signs. is this +127? +4896 Normal methods of factoring a trinomial do not work. So this would be referred to as prime. You can set it equal to zero and use the quadratic formula to find solutions. I'll refer to these as x = A and x = B Use these to write factors (x-A)(x-B) and you will have your factored form. My guess is that the answers are imaginary, NOT real nor integers.
Which part of the trinomial will equal the product of p and q?
The answer depends on what p and q are!
Which part of the trinomial will equal the sum of p and q?
the coefficient of the x-term
X2 plus 10x plus 21 equals 0?
The roots are -3 and -7. Easily by factoring and setting each factor equal to 0. The factors are x + 7 and x +3.
What two prime numbers equal 44?
To find the primes that equal a number, start with any factor pair of the number and keep factoring the composite factors until all factors are prime. 44 2 x 22 2 x 2 x 11 = 44 The two prime numbers that equal 44 are 2 (twice) and 11.
How do you factor in algebra?
factoring in algebraFollowing is one of the examples of solved algebra problems. Suppose you have the problem:x2 +6x+9you try to find two numbers that add to be 6 and multiply to be 9. in this case it's 3 and 3. so you exchange the 6x for 3x +3x . . .x2 +3x +3x +9 then you group the first two and the second two terms . . .(x2+3x)+ (3x+9)next you take out the biggest number they have in common.and leave whats left in the ( )x(x+3)+ 3(x+3)now the answer is the stuff inside the ( ) times the stuff outside(x+3)(x+3)more stuff . . .The example given above is known as factoring a trinomial into two binomials.Not all trinomials are factorable. The general form of a trinomial is:ax2 + bx + cIf the trinomial is indeed factorable, there must exist two factors for the product of the coefficients a and c, a x c, that will add together to equal the coefficient b.The signs of the coefficients are critical:If ac is positive, both factors are either negative or positiveIf ac is negative, only one of the two factors can be negativeIf b is negative, at least one of the two factors must be negative
