According to the synthetic division below, which of the following statements are true? check all that apply.

A, D and E are correct

given ( x - 4 ) is a factor then x =  4 is a root

the remainder on division by (x - 4 ) = 0 as indicated by the 0 on the right side of the quotient

(x - 4 ) is a factor of 3x² - 13x + 4 → A

the number 4is a root of f(x) = 3x² - 13x + 4 → D ( explained above )

thus 3x² - 13x + 4 ÷ (x - 4 ) = 3x - 1 → E

the quotient line 3 - 1 0

3 and - 1 are the coefficients of the linear quotient and 0 is the remainder

there has been genes found in the x chromosome of males that have been linked to [homo/hetero]sexuality. in addition to the reign of the x chromosome, a section of chromosome 8 has also been link to, "alot of ppl are so " these facts were proven true after a 2014 study of a gay male and his strait brother. according to newscientist.com,"chromosome 14 and is mainly active in the thyroid, but also the brain. called tshr, it makes a type of receptor protein that recognises and binds to a hormone that stimulates the thyroid. in this way, the gene plays an important role in controlling thyroid function. the fact that tshr seems to be involved in sexual orientation fits with evidence that thyroid function seems to be linked to sexuality."

in conclusion, "ppl are so gay" due to their genetics.

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.