Question

Simplify the expression to a polynomial in standard form:
(-4x-3)(2x^2-3x+4)

Answer 1

`y=-8x^3+6x^2-7x-12`

Explanation:

Standard Form of a Polynomial is having an order of numbers with the higher exponents being first and it going lower throughout the order.

ax^2 + bx + c

In this case we have
`(-4x-3)(2x^2-3x+4)`, to get one polynomial all together, multiply the two parenthesis using FOIL.

FOIL

Front, multiply the first numbers in each parenthesis,

-4x * 2x^2

-8x^3

FOIL

Outer, multiply the first number by the rest of the numbers within the second parenthesis,

-4x * -3x

12x^2

-4x * 4

-16x

At this point, we should have,

-8x^3 + 12x^2 - 16x

FOIL

Inner, multiply the second number by the first number within both parenthesis,

-3 * 2x^2

-6x^2

-8x^3 + 12x^2 - 16x - 6x^2

FOIL

Last, multiply the second number by the rest of the numbers within the second parenthesis,

-3 * -3x

9x

-3 * 4

-12

Now that we finished, you should have,

`-8x^2+12x^2-16x-6x^2+9x-12`

Now combine like terms, meaning adding/subtracting/multiplying/dividing numbers that have the same exponent or variable ending only.

`-8x^2+[12x^2]-16x[-6x^2]+9x-12`

`-8x^2+6x^2 -16x+9x-12`

`-8x^2+6x^2 [-16x+9x]-12`

`-8x^2+6x^2 -7x-12`

`[y=-8x^2+6x^2 -7x-12]`

is our answer.