How to multiply a monomial by a polynomial

Help Questions

ACT Math › How to multiply a monomial by a polynomial

Questions 1 - 3

1

Multiply: $2x\ast(4x+3)$

$8x^{2}+6x$

$6x^{2}+8x$

$8x^{2}+6$

Explanation

To solve you must multiply by both terms in

$2x\ast4x=8x^{2}$

$2x\ast3=6x$

$8x^{2}+6x$

2

Multiply:

$4x\cdot(5x+7)$

$20x^{2}+28x$

$9x^{2}+28x$

$9x^{2}+28$

Explanation

Multiply by both terms in

$4x\cdot5x=20x^{2}$

$4x\cdot7=28x$

$20x^{2}+28x$

3

Multiply $\left (7x^{2}-12x+4 \right ) \cdot 3x$

$21x^{3}-36x^{2}+12x$

$21x^{3}+36x^{2}+12x$

$21x^{2}-36x+12$

$7x^{3}-12x^{2}+4x$

None of the other answers

Explanation

When multiplying a polynomial by a monomial, each term in the polynomial gets multiplied by the monomial. Calculate each term one at a time, then add the results to get the final answer. In this case, we start by multiplying $7x^{2}\cdot3x$ . $7\cdot3=21$ and $x^{2}\cdot x=x^{3}$ , thus we get $21x^{3}$ . For the second term of the polynomial, we multiply $-12\cdot3=-36$ and $x\cdot x= x^{2}$ , resulting in $-36x^{2}$ . Finally, we multiply $4\cdot3 = 12$ and $1\cdot x = x$ , resulting in . Adding the three terms that we just found, we come to the answer of $21x^{3}-36x^{2}+12x$ .

Return to subject