Question

rainbow multiplying
express $(5x - 3)(-2x + 7)$ as a trinomial in standard form.

• 2 points $f(x) = g(x)$

this prompts you to use the grapher to determine where two graphs intersect
31 graph $f(x) = -3x$ and $g(x) = x^2 + 2$ on the set of axes below.
state the values of $x$ that satisfy the equation $f(x) = g(x)$.
given $f(x) = x^2$ and $g(x) = 8x - 15$ graphed on the same set of axes, which value(s) of $x$ will make $f(x) = g(x)$?
) 3, only (3) 3 and 5
) 9, only (4) 9 and 25

Explanation:

Step1: Apply the distributive property (FOIL method)

Multiply each term in the first binomial by each term in the second binomial:
$$(5x - 3)(-2x + 7) = 5x \cdot (-2x) + 5x \cdot 7 - 3 \cdot (-2x) - 3 \cdot 7$$

Step2: Simplify each product

Calculate each term:
$$5x \cdot (-2x) = -10x^2$$
$$5x \cdot 7 = 35x$$
$$-3 \cdot (-2x) = 6x$$
$$-3 \cdot 7 = -21$$

Step3: Combine like terms

Combine the \(x\)-terms:
$$-10x^2 + (35x + 6x) - 21 = -10x^2 + 41x - 21$$

Answer:

\(-10x^2 + 41x - 21\)