# How do you write a polynomial of least degree with integral coeffients that has 5, -3 as zeros?

##### 1 Answer

Mar 8, 2018

#### Answer:

#### Explanation:

#"given a polynomial with zeros "x=a" and "x=b#

#"then "(x-a)" and "(x-b)" are it's factors"#

#"the polynomial can then be expressed as"#

#y=k(x-a)(x-b)larrcolor(blue)"k is a multiplier"#

#"here "x=5" and "x=-3#

#rArr(x-5)" and "(x+3)" are the factors"#

#rArry=k(x-5)(x+3)#

#"let k = 1 and expand factors"#

#rArry=x^2-2x-15larrcolor(blue)"is a possible polynomial"#