SAT Question for January 27th

If4x²+ 7x+ 1is multiplied by3x+ 5, what is the coefficient ofxin the resulting polynomial?

Difficulty:Medium

Category:Passport to Advanced Math / Exponents

Strategic Advice:When multiplying polynomials, carefully multiply each term in the first factor by each term in the second factor. This question doesn’t ask for the entire product, so check to make sure you answered the right question (the coefficient ofx).

Getting to the Answer:After performing the initial multiplication, look for thex-terms and add their coefficients. To save time, you do not need to simplify the other terms in the expression.

\begin{matrix} (4 x^{2} + 7 x + 1) (3 x + 5) \\ = 4 x^{2} (3 x + 5) + 7 x (3 x + 5) + 1 (3 x + 5) \\ = 12 x^{3} + 20 x^{2} + 21 x^{2} + \underline{35 x + 3 x} + 5 \end{matrix}

The coefficient ofxis 35 + 3 = 38.

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SAT Question for January 27th

If4x²+ 7x+ 1is multiplied by3x+ 5, what is the coefficient ofxin the resulting polynomial?

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SAT Question for January 27th

If4x2+ 7x+ 1is multiplied by3x+ 5, what is the coefficient ofxin the resulting polynomial?

WANT ANOTHER PRACTICE QUESTION?

READY FOR A HIGHER SCORE ON THE SAT?

EASE INTO PREP WITH AN SAT^® QUESTION A DAY

If4x²+ 7x+ 1is multiplied by3x+ 5, what is the coefficient ofxin the resulting polynomial?