SAT Polynomial Expressions And Equations Practice Questions (Free + Explanations)

Advanced Math · Polynomial Expressions And Equations

SAT Polynomial Expressions And Equations Practice Questions (Free + Explanations) | Quiz 1

Question 12345 of 5

Question 1 of 5

A garden center models the height of a young plant, in inches, after x weeks with the expression x^{2} + 4 x + 7 . According to the model, what will the plant's height be after 3 weeks?

Explanation Substitute x = 3 into the expression: 3^{2} + 4 (3) + 7 = 9 + 12 + 7 = 28. So the model predicts the plant will be 28 inches tall after 3 weeks. Concept summary To evaluate a polynomial in context, replace the variable with the given value and simplify carefully using order of operations.

Question 2 of 5

A rectangular garden has length x + 3 yards and width x - 2 yards. The area of the garden is represented by the polynomial x^{2} + x - 6 . Which expression is equivalent to x^{2} + x - 6 ?

Explanation The area of a rectangle is found by multiplying its length and width. Since the garden’s length is x + 3 and its width is x - 2, the area expression is (x + 3) (x - 2) . Expanding confirms this: (x + 3) (x - 2) = x^{2} - 2 x + 3 x - 6 = x^{2} + x - 6. So the equivalent expression is (x + 3) (x - 2) . Concept summary To write a polynomial as a product of two binomials, match the factors to the given dimensions or expand each candidate and compare terms.

Question 3 of 5

Which expression is equivalent to x^{2} - 9 ?

Explanation x^{2} - 9 is a difference of squares because 9 = 3^{2} . Using the pattern a^{2} - b^{2} = (a - b) (a + b), we get x^{2} - 9 = (x - 3) (x + 3) . Concept summary A difference of squares factors as a^{2} - b^{2} = (a - b) (a + b) .

Question 4 of 5

The graph of the polynomial y = (x - 4) (x + 1) is shown in the x y -plane. Which coordinate is an x -intercept of the graph?

Explanation An x -intercept is a point where y = 0 . So solve (x - 4) (x + 1) = 0 . This gives x = 4 or x = - 1, so the graph has x -intercepts at (4, 0) and (- 1, 0) . Among the choices, the correct coordinate is (4, 0) . Concept summary For a polynomial graph, x -intercepts occur where the output is 0, so set the factored expression equal to 0 and solve for x .

Question 5 of 5

For the polynomial p (x), it is known that p (2) = 5 and p (x) = x^{2} + b x + c . What is the value of 2 b + c ?

Explanation Substitute x = 2 into p (x) = x^{2} + b x + c . Then p (2) = 2^{2} + 2 b + c = 4 + 2 b + c . Since p (2) = 5, we have 4 + 2 b + c = 5, so 2 b + c = 1. Concept summary When a polynomial value is given, substitute the input and use the resulting equation to isolate the requested combination of coefficients.

Your results

0of 5 correct

Estimated SAT Math band

500-550

Illustrative range from this short quiz—not an official College Board score.

Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.

Download on the App Store Get it on Google Play

More SAT Math practice

Your results

1of 5 correct

Estimated SAT Math band

500-550

Illustrative range from this short quiz—not an official College Board score.

Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.

Download on the App Store Get it on Google Play

More SAT Math practice

Your results

2of 5 correct

Estimated SAT Math band

600-650

Illustrative range from this short quiz—not an official College Board score.

Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.

Download on the App Store Get it on Google Play

More SAT Math practice

Your results

3of 5 correct

Estimated SAT Math band

600-650

Illustrative range from this short quiz—not an official College Board score.

Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.

Download on the App Store Get it on Google Play

More SAT Math practice

Your results

4of 5 correct

Estimated SAT Math band

700+

Illustrative range from this short quiz—not an official College Board score.

Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.

Download on the App Store Get it on Google Play

More SAT Math practice

Your results

5of 5 correct

Estimated SAT Math band

700+

Illustrative range from this short quiz—not an official College Board score.

Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.

Download on the App Store Get it on Google Play

More SAT Math practice

Practice outline (enable JavaScript for interactive mode)

Q1. A garden center models the height of a young plant, in inches, after x weeks with the expression x 2 + 4 x + 7 . According to the model, what will the plant's height be after 3 weeks?

Q2. A rectangular garden has length x + 3 yards and width x − 2 yards. The area of the garden is represented by the polynomial x 2 + x − 6 . Which expression is equivalent to x 2 + x − 6 ?

Q3. Which expression is equivalent to x 2 − 9 ?

Q4. The graph of the polynomial y = ( x − 4 ) ( x + 1 ) is shown in the x y -plane. Which coordinate is an x -intercept of the graph?

Q5. For the polynomial p ( x ) , it is known that p ( 2 ) = 5 and p ( x ) = x 2 + b x + c . What is the value of 2 b + c ?