Question

select the correct numbers to create an equation that is true for all values of x
2(4x+3)(3x+5)=Ax^2+58x+B

a A=6, B=8
b A=12, B=15
c A=24, B=30
d A=29, B=58

Answer 1

First distribute (multiply), (4x+3) over (3x+5)

Answer 2

Once we distribute it all we can equate the two sides

Answer 3

Good, now distribute the 2 over it

Answer 4

24x^2+58x+30

Answer 5

Perfect, so we have \[24x^2+58x+30=Ax^2+58x+B\]

Answer 6

Now we can equate the two sides, notice \[24x^2=Ax^2\]\[58x=58x\]\[30=B\]

Answer 7

Haha, well I gave away B, but note the coefficient of A, which would be?

Answer 8

so a=24?

Answer 9

Yes

Answer 10

thank you