To solve the question [tex]\( A - B \)[/tex], where [tex]\( A \)[/tex] and [tex]\( B \)[/tex] are given polynomials, we proceed by subtracting polynomial [tex]\( B \)[/tex] from polynomial [tex]\( A \)[/tex] term by term.
Given:
[tex]\[ A = 7x^2 - 3x + 10 \][/tex]
[tex]\[ B = -4x^2 + 6x - 4 \][/tex]
Now, let's subtract [tex]\( B \)[/tex] from [tex]\( A \)[/tex]:
1. Identify the coefficients of similar powers of x:
- For [tex]\( x^2 \)[/tex] terms: [tex]\( 7x^2 \)[/tex] (from [tex]\( A \)[/tex]) and [tex]\( -4x^2 \)[/tex] (from [tex]\( B \)[/tex]).
- For [tex]\( x \)[/tex] terms: [tex]\( -3x \)[/tex] (from [tex]\( A \)[/tex]) and [tex]\( 6x \)[/tex] (from [tex]\( B \)[/tex]).
- For constant terms: [tex]\( 10 \)[/tex] (from [tex]\( A \)[/tex]) and [tex]\( -4 \)[/tex] (from [tex]\( B \)[/tex]).
2. Subtract the corresponding coefficients:
- For [tex]\( x^2 \)[/tex] terms:
[tex]\[ 7x^2 - (-4x^2) = 7x^2 + 4x^2 = 11x^2 \][/tex]
- For [tex]\( x \)[/tex] terms:
[tex]\[ -3x - 6x = -3x - 6x = -9x \][/tex]
- For constant terms:
[tex]\[ 10 - (-4) = 10 + 4 = 14 \][/tex]
3. Combine the results:
[tex]\[ A - B = 11x^2 - 9x + 14 \][/tex]
So, the polynomial in standard form after subtracting [tex]\( B \)[/tex] from [tex]\( A \)[/tex] is:
[tex]\[ 11x^2 - 9x + 14 \][/tex]
