NEED HELP PLEAASE IN Factoring Polynomials!? Determine whether the polynomial is a difference of squares and if it is, factor it. y2 − 16?
A polynomial that is the difference of two squares looks like A^2 - B^2, that is, two perfect squares separated by a minus sign. So, is y^2 a perfect square? Yes, the power is even. Is 16 a perfect square? Yes, it's 4^2. Is there a minus sign between them? Yes. So it is the difference of two squares. How does it factor? If the expression looks like A^2 - B^2, it always factors into (A - B)(A + B). So, plugging in, we get y^2 - 16 = (y - 4)(y + 4), choice D
Determine whether the polynomial is a difference of squares and if it is, factor it. y^2 - 25?
A. not a difference of squares B. is a difference of squares: (y - 5)^2 C. is a difference of squares: (y + 5)(y - 5) D. is a difference of squares: (y + 5)^2
Determine whether the binomial x² -100 is a difference of two squares?
As the name suggests, in order for a polynomial to be a difference of two squares, it must be a binomial (only have two terms), both terms must be perfect squares, and there must be a minus sign separating them. In this case, we have two terms (x^2 and 100), they are both perfect squares (100 can be written as 10^2), and there is a minus sign between them. Therefore, x^2 - 100 is a difference of two squares. I hope this helps!
Determine whether 81-49n^4 is a difference of two squares. If so, factor it. If not, explain why. ?
Since 81 - 49n^4 follows the difference of squares a² - b² = (a - b)(a + b), we can factor that given polynomial into: (9)² - (7n²)² ==> (9 - 7n²)(9 + 7n²) I hope this helps!
State whether each expression is a difference of two squares? 10 points?
1. x^2 and 4 are both squares, so yes. 2. This is a sum, not a difference, so no. 3. 35 is not a perfect square, so if you want a difference of perfect squares, then no.
How can you tell if a polynomial is a perfect square?
How can you tell if a polynomial is a perfect square? (ax + by)^2 = a^2x^2 + 2ab xy + b^2 y^2 The middle term 2 * the product of the square roots of the coefficients of x^2 and y^2 (2x + 3y)^2 = 4x2 + 12 xy + 9y^2 12 = 2 * 4^0.5 * 9^0.5 2 is the square root of 4 3 is the square root of 9 16 x^2 + 24 x + 9 Square root of 16 = 4 Square root of 9 = 3 2 * 4 * 3 = 24, the middle term = 2 * product of square root of 16 (4) times the square root of 9 (3) So 16 x^2 + 24 x + 9 is a perfect square. Also, how can you tell if a polynomial can't be factored any further? Polynomial Any quadratic can be factored using the quadratic equation x = [-b ± (b^2 – 4ac)] ÷ 2a check to see if the polynomial can be divided by a number 3x^2 + 9x + 12 = 3 * (x^2 + 2x + 4)
What is the difference between linear and quadratic equations?
Linear equations are generally in this format:2x - 4 = yAnd when graphing linear equations: (PS the equation and the graph below do not match - just a general format of linear equations’ graph)Whereas quadratic equations are in this type of format:x^2 + 5x + 6 = yAnd when graphing quadratic equations: (again, the equation and graph do not match)***So basically, when we say linear equations, we mean those equations that have a maximum of only one x-intercept, or in other words, when y = 0, they only have a maximum of one coordinate that passes through the x-axis -> as seen in the graph above.However, quadratic equations are a little bit different. Whereas linear equations have only a maximum of one x-intercept, quadratic equations’ graph (a parabola) has a maximum of two x-intercepts, meaning that when y = 0, the parabola passes through a maximum of two coordinates in the x-axis -> as seen in the graph above.PS- A parabola and a linear equation graph don’t have any minimum of points: for ex: a linear equation graph can have 0 x-intercepts, and a parabola can have 1 or even no x-intercept at all (Just some general information that I thought you might want to know for greater understanding).
If two factors of a third-degree polynimal P(x) are x+2 and x-4 and P(0) =8 and P(1) = -9, what is the remaining factor of P(x)?
We know the form of the remaining factor is going to be [math](ax-c)[/math] for constants [math]a[/math] and [math]c[/math] soWe can see the remaining mystery factor is in fact [math](2x-1)[/math].