Answer:
x-2 is a factor of following polynomials:
- b(x) = 3x² + 15x - 42
- d(x) = 3x³ - 2x² - 15x + 14
- e(x) = 8x⁴ - 41x³ - 18x² + 101x + 70
Step-by-step explanation:
In order to check that which polynomials might have x-2 as a factor, we will put
x-2 = 0 => x = 2 in each polynomial, if the value of polynomial on 2 is zero then x-2 is a factor otherwise not.
So,
a(x) = 6x² - 7x - 5
Putting x = 2
[tex]a(2) = 6(2)^2-7(2)-5\\= 6(4)-14-5\\=24-14-5\\=24-19\\=5 \neq 0[/tex]
b(x) = 3x² + 15x - 42
[tex]b(2) = 3(2)^2 + 15(2) - 42\\=3(4)+30-42\\=12+30-42\\=42-42 = 0[/tex]
c(x) = 2x³ + 13x² + 16x + 5
[tex]c(2) = 2(2)^3 + 13(2)^2 + 16(2) + 5\\=2(8)+13(4)+32+5\\=16+52+32+5\\=105 \neq 0[/tex]
d(x) = 3x³ - 2x² - 15x + 14
[tex]d(2) = 3(2)^3 - 2(2)^2 - 15(2) + 14\\= 3(8)-2(4)-30+14\\=24-8-30+14\\=38-38 = 0[/tex]
e(x) = 8x⁴ - 41x³ - 18x² + 101x + 70
[tex]e(2) = 8(2)^4 - 41(2)^3 - 18(2)^2 + 101(2) + 70\\= 8(16)-41(8)-18(4)+202+70\\=128-328-72+202+70\\=0[/tex]
[tex]f(2) = (2)^4 + 5(2)^3 - 27(2)^2 - 101(2) - 70\\=16+5(8)-27(4)-202-70\\=16+40-108-202-70\\=-324 \neq 0[/tex]
Hence,
x-2 is a factor of following polynomials:
- b(x) = 3x² + 15x - 42
- d(x) = 3x³ - 2x² - 15x + 14
- e(x) = 8x⁴ - 41x³ - 18x² + 101x + 70
