Answer:
C
[tex]y=(5x+2)(x+3)[/tex]
[tex]\implies x=-\dfrac25,\ \ x=-3[/tex]
Step-by-step explanation:
Factor [tex]y=5x^2+17x+6[/tex]
Multiply the coefficient of [tex]x^2[/tex] and the constant:
⇒ 5 x 6 = 30
Find factors of 30 that add together to make the coefficient of [tex]x[/tex]:
⇒ 2 and 15
Rewrite 17x as 15x + 2x:
[tex]\implies y=5x^2+15x+2x+6[/tex]
Group:
[tex]\implies y=(5x^2+15x)+(2x+6)[/tex]
Factor brackets:
[tex]\implies y=5x(x+3)+2(x+3)[/tex]
Factor out common term [tex](x + 3)[/tex]:
[tex]\implies y=(5x+2)(x+3)[/tex]
To find the zeroes, set y to zero and solve for x:
[tex]\implies (5x+2)(x+3)=0[/tex]
[tex]\implies 5x+2=0 \ \ \textsf{and} \ \ x+3=0[/tex]
[tex]\implies x=-\dfrac25,\ \ x=-3[/tex]
