(x - (-3)) (x - (-5)) (x - 2), or
(x + 3) (x + 5) (x - 2)
You can multiply the binomials to get a polynomial of degree 3.
To subtract the multivariate polynomials (19x^3 + 44x^2y + 17) and (y^3 - 11xy^2 + 2x + 13x^3), we first rewrite the second polynomial with a negative sign: (- (y^3 - 11xy^2 + 2x + 13x^3)). Combining the polynomials gives us: [ (19x^3 - 13x^3) + 44x^2y + 17 - y^3 + 11xy^2 - 2x. ] This simplifies to: [ 6x^3 + 44x^2y + 11xy^2 - y^3 - 2x + 17. ] Thus, the resulting polynomial after subtraction is (6x^3 + 44x^2y + 11xy^2 - y^3 - 2x + 17).
To add polynomials, align the like terms, which are terms that have the same variable raised to the same power. Then, simply combine the coefficients of these like terms. For example, in the polynomials (3x^2 + 2x + 1) and (4x^2 + 3), you would add (3x^2 + 4x^2) to get (7x^2) and combine the constant terms (1 + 3) to get (4), resulting in (7x^2 + 2x + 4).
Equations will have an equals sign. Such as: x + 3 = 2 Polynomials will not. Such as: 2x + 3
The function ( g(x) = \frac{x^2 - 3x - 4}{x^2 + 1} ) is not a polynomial function because it is a rational function (the ratio of two polynomials). To find the zeros, we set the numerator equal to zero: ( x^2 - 3x - 4 = 0 ). The zeros can be found using the quadratic formula: ( x = \frac{3 \pm \sqrt{(3)^2 - 4(1)(-4)}}{2(1)} ), which simplifies to ( x = 4 ) and ( x = -1 ). The denominator ( x^2 + 1 = 0 ) gives imaginary zeros ( x = i ) and ( x = -i ).
3
He did not write 3 zeros in the middle of the number. Instead, he wrote 2 zeros.
Seeing as a googol of zeros would be 10^100 zeros, that number of zeros would be quite hard to write out. If you were to try and write out that many zeros by hand at 3 zeros per second, it would still take you 1.05699307 × 1092 years to write them all out.
To write 7 trillion 2 million 31 thousand as a single number, you need to add up the values of each part. 7 trillion is 7,000,000,000,000 (7 followed by 12 zeros), 2 million is 2,000,000 (2 followed by 6 zeros), and 31 thousand is 31,000 (31 followed by 3 zeros). Adding these together, you get 7,002,031,000,000.
Equations will have an equals sign. Such as: x + 3 = 2 Polynomials will not. Such as: 2x + 3
We won't be able to answer this accurately without knowing the polynomials.
The function ( g(x) = \frac{x^2 - 3x - 4}{x^2 + 1} ) is not a polynomial function because it is a rational function (the ratio of two polynomials). To find the zeros, we set the numerator equal to zero: ( x^2 - 3x - 4 = 0 ). The zeros can be found using the quadratic formula: ( x = \frac{3 \pm \sqrt{(3)^2 - 4(1)(-4)}}{2(1)} ), which simplifies to ( x = 4 ) and ( x = -1 ). The denominator ( x^2 + 1 = 0 ) gives imaginary zeros ( x = i ) and ( x = -i ).
3
Billion has 9 zeros Example: 3 billion = 3,000,000,000 Trillion has 12 zeros Example: 5 trillion = 5,000,000,000,000
9
There should be two zeros. * * * * * If you mean 1*2*3*...*99*100m then there will be 24 zeros at the end.
When you add polynomials, you combine only like terms together. For example, (x^3+x^2)+(2x^2+x)= x^3+(1+2)x^2+x=x^3+3x^2+x When you multiply polynomials, you multiply all pairs of terms together. (x^2+x)(x^3+x)=(x^2)(x^3)+(x^2)(x)+(x)(x^3)+(x)(x)=x^5+x^3+x^4+x^2 Basically, in addition you look at like terms to simplify. In multiplication, you multiply each term individually with every term on the opposite side, ignoring like terms.
Dividing polynomials is a lot easier for me. You'll have to divide it term by term like dividing normal numbers.