Question

Let p=x^2+6p=x 2 +6p, equals, x, start superscript, 2, end superscript, plus, 6. Which equation is equivalent to (x^2+6)^2-21=4x^2+24(x 2 +6) 2 ?21=4x 2 +24left parenthesis, x, start superscript, 2, end superscript, plus, 6, right parenthesis, start superscript, 2, end superscript, minus, 21, equals, 4, x, start superscript, 2, end superscript, plus, 24 in terms of p ?

Answer 1

Answer:

(p+3)(p-7) = 0

Step-by-step explanation:

Given p=x^2+6p and (x^2+6)^2-21=4x^2+24

We are to substitute the the p = x²+6 into the expression as shown;

The expression (x^2+6)^2-21=4x^2+24 will become

(x²+6)²-21 = 4(x²+6)

On substituting p, the expression becomes;

p²-21 = 4p

Subtract 4p from both sides

p²-21-4p = 4p-4p

p²-4p-21 = 0

p²-7p+3p-21 = 0

p(p-7)+3(p-7) = 0

(p+3)(p-7) = 0

Hence the expression in terms of p is (p+3)(p-7) = 0