Question

SUBTRACTING VERTICALLY Use a vertical format to subtract the second polynomial from the first polynomial. $$4 x^{3}+3 x^{2}+8 x+6,2 x^{3}-3 x^{2}-7 x$$

Short answer

After subtracting the second polynomial from the first polynomial, the result is \(2 x^{3} + 6 x^{2}+ x + 6\).

Step-by-step solution

Aligning Polynomials

Write the first and second polynomials vertically and align terms according to the degree of each term. \[\begin{array}{c}4 x^{3}+3 x^{2}+8 x+6 \- (2 x^{3}-3 x^{2}-7 x)\\end{array}\]

Distribute Negative Sign

First distribute the negative sign to each term in the second polynomial: \[\begin{array}{c}4 x^{3}+3 x^{2}+8 x+6 \-2 x^{3}+3 x^{2}+7 x\\end{array}\]

Subtract Term by Term

Now, subtract each term in the second polynomial from the corresponding term in the first polynomial. This gives: \( (4 x^{3} - 2 x^{3})+ (3 x^{2} + 3 x^{2})+ (8 x - 7 x) + 6 = 2 x^{3} + 6 x^{2}+ x + 6 \)