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When finding the greatest common factor of a polynomial can it ever be larger than the smallest coefficient?
Yes, the greatest common factor is less than or equal to the smallest coefficient. For example, the greatest common factor of 38 and 8 is 2.
What does a factor times a factor equal?
A product
What is factor times factor?
Factors are divisors. A factor times a factor will equal a product.
What is an equal factor?
a square root
Equal factor of 9x9x9x9x9x9x9x9x9?
387420489
Which part of the trinomial will equal the sum of p and q?
the coefficient of the x-term
What is the difference between a coefficient and a factor?
well i would say that a factor is a number add to another number and it equal something but a coefficient is not really what i know but i think its something similar to a factor
When finding the greatest common factor of a polynomial can it ever be larger than the smallest coefficient?
Yes, the greatest common factor is less than or equal to the smallest coefficient. For example, the greatest common factor of 38 and 8 is 2.
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.
81x2 - 72x plus 16 is a perfect square trinomial true or false?
If a trinomial is a perfect square, then the discriminant will equal 0. The discriminant is equal to B^2-4AC. The variables come from the standard form of a quadratic which is Ax^2+Bx+C In this problem, A=81, B=-72, and C=16 so the discriminant is: (-72)^2-4(81)(16)=5,184-5,184=0 so this is a perfect square trinomial. To factor, notice that 81=9^2 and 16=4^2, so 81x^2=(9x)^2. We can then factor the trinomial into (9x+4)(9x-4)
What is the difference in finding the m and n when factoring a polynomial with a leading coefficient that does not equal one?
The difference depends on what m and n equal. If they are both variable then it dpends on what the equations are for each variable.
Relationship between coefficient lift and coefficient drag?
For cylinders coefficient of lift is approximately half of coefficient of drag while they are equal for Aerofoils.
Can the coefficient of static friction be equal to the coefficient of kinetic friction?
No, the coefficient of static friction is typically greater than the coefficient of kinetic friction.
Which part of the trinomial will equal the product of p and q?
The answer depends on what p and q are!
Is the third term in a factorable trinomial equal to the product of the constants in its binomial factors?
Yes it is
Can the GCF be larger than the smallest coefficient?
No. The GCF can be less than or equal to the smallest coefficient.
How do you factor polynomials into binomials and trinomials?
Here are the steps to factoring a trinomial of the form x2 + bx + c , with c > 0 . We assume that the coefficients are integers, and that we want to factor into binomials with integer coefficients.Write out all the pairs of numbers which can be multiplied to produce c .Add each pair of numbers to find a pair that produce b when added. Call the numbers in this pair d and e .If b > 0 , then the factored form of the trinomial is (x + d )(x + e) . If b < 0 , then the factored form of the trinomial is (x - d )(x - e) .Check: The binomials, when multiplied, should equal the original trinomial.Note: Some trinomials cannot be factored. If none of the pairs total b , then the trinomial cannot be factored.
