MAT1503-Exam OCt/Nov 2024 Assume that \( A \) is a \( 2 \times 2 \) matrix with integer entries. If \( B \) is the inverse of \( A \) and \( B \) has integer entries, then choose the correct statement: \( \operatorname{det}(A)= \pm 1 \) and \( \operatorname{det}(B)= \pm 1 \) \( \operatorname{det}(A)=-1 \) or \( \operatorname{det}(A)=0 \) \( \operatorname{det}(A)=1 \) or \( \operatorname{det}(A)=0 \) and \( B \) has integer \( \operatorname{entries} \) None of the given options det \( (A)=-1 \) and \( \operatorname{det}(A)=0 \)

e. \( a+b \) es divisor de \( a^{4}+b^{4} \). ( ) f. \( a-b \) es divisor de \( a^{5}+b^{5} \). ( ) g. \( \quad \) El grado del polinomio cociente entre \( x^{5}+y^{5} y \) \( x+y \) es 4. ( ) h. La cantidad de términos del polinomio co- ciente entre \( x^{7}-y^{7} y x-y \) es 7 . ( )

Expand. Your answer should be a polynomial in standard form. \( (6 f-7)(8 f-9)=\square \)

What is a proportional relationship?

Expand. Your answer should be a polynomial in standard form. \( (3 b-4)(b+2)=\square \)

138. Hallar el resto de la división \( \frac{[(x+4)(x+3)(x+2)(x+1)+3]^{4}}{x^{2}+5 x+5} \) \( \begin{array}{lllll}\text { a. } 25 & \text { b. } 34 & \text { c. } 43 & \text { d. } 27 & \text { e. } 6\end{array} \)