4. Add the proper constant to the binomial so that the resulting trinomial is a perfect square trinomial. Then factor the

trinomial.

x² + 17x+

What is the constant term?

(Type an integer or a simplified fraction.)

What is the factored form of the trinomial?

(Use integers or fractions for any numbers in the expression.)

The constant is 289/4

The factored form is (x + 17/2) ²

Step-by-step explanation:

Perfect square trinomials are in standard form ax² + bx + c; when the square root of "ax²", multiplied by the square root of "c", multiplied by 2, is equal to "bx". In equation form:

2√ (ax²) √c = bx

In x² + 17x + c:

ax² = x²

bx = 17x

c = the constant term we are finding

Substitute what we know into the equation, then find c.

2√ (ax²) √c = bx

2√ (x²) √c = 17x Simplify √ (x²) = x because √ and ² cancel out

2x√c = 17x

√c = 17x / 2x Divide both sides by 2x

√c = 17/2 Keep as a fraction to get the exact value of "c"

c = (17/2) ² Square both sides and simplify

c = 289/4

Therefore the constant term is 289/4.

To factor a perfect trinomial, use the form:

ax² + bx + c = (√ (ax²) ± √c) ²

Take the square root of the first term, plus/minus the square root of the last term, then square the entire equation.

Whether the middle sign is plus (+) or minus (-) depends on if bx is positive or negative.

The perfect trinomial is x² + 17x + 289/4 after having substituted "c".

Square root the first term, plus square root the last term and all squared:

(√ (x²) + √ (289/4)) ² Simplify. Find the square root of the numbers.

= (x + 17/2) ²

The factored form is (x + 17/2) ².