Álgebra preguntas y respuestas

Let \( f(x)=x^{2}+a x+b \) and \( g(x)=x^{2}-2 b x-a \), where \( a \) and \( b \) are constants. Given that the H.C.F. of \( f(x) \) and \( g(x) \) is \( x-1 \), find the values of \( a \) and \( b \). A. \( \quad a=5, b=-2 \) B. \( \quad a=3, b=2 \) C. \( \quad a=-3, b=2 \) D. \( \quad a=-5, b=-2 \)

A telephone company offers a monthly cellular phone plan for \( \$ 34.99 \). It includes 350 anytime minutes plus \( \$ 0.25 \) per minute for additional minutes. The following function is used to compute the monthly cost for a subscriber, where \( x \) is the number of anytime minutes used. \( C(x)=\left\{\begin{array}{ll}34.99 & \text { if } 0<x \leq 350 \\ 0.25 x-52.51 & \text { if } x>350\end{array}\right. \) Compute the monthly cost of the cellular phone for use of the following anytime minutes. \( \begin{array}{ll}\text { (a) } 225 & \text { (b) } 395 \\ \text { (a) } C(225)=\$ \square \text { (Round to the nearest cent as needed.) } \\ \text { (b) } C(395)=\$ \square \text { (Round to the nearest cent as needed.) } \\ \text { (c) } C(351)=\$ \square \text { (Round to the nearest cent as needed.) }\end{array} \)

Which of the following functions has a graph that is symmetric about the \( y \)-axis? Select all that apply. \( \square \) A. \( y=|x| \) \( \square \) B. \( y=\sqrt{x} \) \( \square \) C. \( y=\frac{1}{x} \) \( \square \) D. \( y=x^{3} \)

7. \( \frac{12^{7}}{9^{3} \cdot 2^{10}} \) ifadosinin qiymotini hesablaym. \( \begin{array}{llll}\text { A) } 40 & \text { B) } 42 & \text { C) } 46 & \text { D) } 48\end{array} \) \( \begin{array}{lll}\text { 8. } \frac{4^{5} \cdot 3^{9}}{6^{8}} & \text { ifadosinin qiymotini hesablayın. }\end{array} \)

\( \begin{array}{ll}\text { 3.1 Factorisethe following: } \\ \text { 3.1.1 } & 2 x^{2}-x-15 \\ \text { 3.1.2 } & -a^{2}-5 a-4 \\ \text { 3.1.3 } & x^{3}+8\end{array} \)

2. Two leaking water containers have a total capacity of 760 . If they both leak 204 per hour, find the capacity of each container If one of the containers have 4 times the amount of water than the other after 9 hours.

When a polynomial \( P(x) \) is divided by \( 4 x-1 \), the remainder is \( R \). When \( P(x) \) is divided by \( 1-4 x \), the remainder is \( \begin{array}{ll}\text { A. } 4 R . & \text { B. } \quad R . \\ \text { C. }-\frac{1}{4} R . & \text { D. }-R .\end{array} \)

When \( x^{3}-x+4 \) is divided by a polynomial \( f(x) \), the quotient and the remainder are \( x^{2}+2 x+3 \) and 10 respectively. Find the polynomial \( f(x) \).

1. निम्न द्विघात बहुपदों के शून्यक ज्ञात कीजिए और शून्यकों तथा गुणांकों के बीच के संबंध की सत्यता की जाँच कीजिए : \( \begin{array}{lll}\text { (i) } x^{2}-2 x-8 & \text { (ii) } 4 s^{2}-4 s+1 & \text { (iii) } 6 x^{2}-3-7 x\end{array} \)

б) \( \frac{x}{16}=\frac{x}{4} \);