Answer:
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.
