Fully factorise d² - 15d + 56

Understand the Problem

The question is asking to fully factor the quadratic expression d² - 15d + 56. This involves finding two binomials that multiply together to give the original quadratic expression.

Answer

$$(d - 7)(d - 8)$$

Steps to Solve

Identify the coefficients The quadratic is of the form $ad^2 + bd + c$. Here, we have:

$a = 1$
$b = -15$
$c = 56$

Find two numbers that multiply to $c$ and add to $b$ We need two numbers, say $m$ and $n$, such that:

$m \cdot n = c = 56$
$m + n = b = -15$

List factor pairs of 56 The factor pairs of 56 are:

(1, 56)
(2, 28)
(4, 14)
(7, 8)

Determine the correct pair We need a pair that adds to -15. Considering the positive factors, the correct pair is:

$-7$ and $-8$, since: $$ -7 + (-8) = -15 $$

Write the factors as binomials Using these values, we can express the quadratic in factored form: $$ d^2 - 15d + 56 = (d - 7)(d - 8) $$

The fully factored form of the quadratic expression is: $$(d - 7)(d - 8)$$

More Information

Factoring quadratics is a key skill in algebra. It helps in solving equations and understanding polynomial behavior. The numbers used for factoring must satisfy both addition and multiplication conditions based on the coefficients of the quadratic.

Tips

Forgetting to take the signs into account when looking for the pairs.
Misidentifying the pairs that do not satisfy the addition condition.

AI-generated content may contain errors. Please verify critical information

Thank you for voting!