Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

${:[P(x)=1.3x^(2)-5.2 x-3],[Q(x)=0.7x^(2)+3.8 x-5.2]:} If P(x)-Q(x)=0.6x^(2)+bx+2.2 for all values of x where b is a constant, then what is the value of b ? Choose 1 answer: (A) -9 (B) -1.4 (C) 1.4 (D) 9$

$\begin{array}{l} P(x)=1.3 x^{2}-5.2 x-3 \\ Q(x)=0.7 x^{2}+3.8 x-5.2 \end{array}$ $\newline$ If $\newline$ $P(x)-Q(x)=0.6 x^{2}+b x+2.2$ $\newline$ for all values of $x$ where $b$ is a constant, then what is the value of $b$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $-9$ $\newline$ (B) $-1$ . $4$ $\newline$ (C) $1$ . $4$ $\newline$ (D) $9$

View step-by-step help

Home

Math Problems

Algebra 1

Compare linear, exponential, and quadratic growth

Full solution

\begin{array}{l} P(x)=1.3 x^{2}-5.2 x-3 \\ Q(x)=0.7 x^{2}+3.8 x-5.2 \end{array}

\newline

\newline

P(x)-Q(x)=0.6 x^{2}+b x+2.2

\newline

for all values of

x

where

b

is a constant, then what is the value of

b

\newline

Choose

1

answer:

\newline

(A)

-9

\newline

(B)

-1

4

\newline

(C)

1

4

\newline

(D)

9

Write down polynomials and equation: Write down the given polynomials and the equation for $P(x) - Q(x)$ . $\newline$ We have: $\newline$ $P(x) = 1.3x^2 - 5.2x - 3$ $\newline$ $Q(x) = 0.7x^2 + 3.8x - 5.2$ $\newline$ And we are given that: $\newline$ $P(x) - Q(x) = 0.6x^2 + bx + 2.2$ $\newline$ We need to find the value of $b$ .
Subtract Q(x) from P(x): Subtract $Q(x)$ from $P(x)$ to find the expression for $P(x) - Q(x)$ . $\newline$ $P(x) - Q(x) = (1.3x^2 - 5.2x - 3) - (0.7x^2 + 3.8x - 5.2)$ $\newline$ Now, we will perform the subtraction by combining like terms.
Perform the subtraction: Perform the subtraction. $\newline$ $P(x) - Q(x) = (1.3x^2 - 0.7x^2) - (5.2x - 3.8x) - (3 + 5.2)$ $\newline$ $P(x) - Q(x) = 0.6x^2 - 1.4x - 8.2$ $\newline$ Now we have the expression for $P(x) - Q(x)$ in terms of $x$ .
Compare coefficients of x term: Compare the coefficients of the x term in the expression we found with the given expression for P(x) - Q(x). $\newline$ We found that P(x) - Q(x) = $0.6x^2 - 1.4x - 8.2$ $\newline$ The given expression is P(x) - Q(x) = $0.6x^2 + bx + 2.2$ $\newline$ By comparing the coefficients of the x term, we can see that $b$ must be equal to $-1.4$ .
Confirm coefficients of other terms: Confirm that the coefficients of the other terms also match. $\newline$ The coefficient of $x^2$ is $0.6$ in both the expression we found and the given expression, which matches. $\newline$ The constant term in the expression we found is $-8.2$ , which does not match the given constant term of $2.2$ . This indicates that there is a mistake in our calculation.