Multiply Polynomial By Monomial

Example 1

Let's multiply the polynomial (3x⁶+2x+5) by the monomial (5x)

You should be comfortable combining like terms and using the laws of exponents.

Video Tutorial on Multiplying Monomials by Polynomials

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Problem1 ) Multiply the polynomial (3x³ + 4x² − 5) by the monomial (7x)

Step 1

This problem is similar to example 1.

Step 1) Distribute by multiplying the monomial with every term in the polynomial

Step 2

Step 2) Simplify using the formula for multiplying exponents

21x4+ 28x3 - 35x

Problem 2 ) Multiply the polynomial (5x⁴− 4x¹² + 12) by the monomial (9x)

Step 1

Step 1) Distribute by multiplying the monomial with every term in the polynomial

Step 2

Step 2) Simplify using the formula for multiplying exponents

45x5− 36x12+108x

Problem 3 ) Multiply the polynomial (2x¹¹− 9x¹⁰+4x³) by the monomial (5x)

Step 1

Step 1) Distribute by multiplying the monomial with every term in the polynomial

Step 2

Step 2) Simplify using the formula for multiplying exponents

10x12 − 45x11 + 20x4

Problem 4 ) Multiply the polynomial (3x⁷− 9x⁵ + 4) by the monomial (-2x)

Step 1

Step 1) Distribute by multiplying the monomial with every term in the polynomial

Step 2

Step 2) Simplify using the formula for multiplying exponents

-6x8 − 18x6 − 8x

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