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Exercises Polynomials and factoring

Example 10.9 from Prealgebra, 10.1 Add and Subtract Polynomials

Add and Subtract Polynomials: example 10.9

Evaluate $3 x^{2} - 9 x + 7$ when

ⓐ $x = 3$
ⓑ $3 \cdot 9 - 9 (3) + 7$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution

ⓐ $x = 3$

$3 x^{2} - 9 x + 7$

Substitute 3 for $x$ $3 {(3)}^{2} - 9 (3) + 7$

Simplify the expression with the exponent. $3 \cdot 9 - 9 (3) + 7$

Multiply. $27 - 27 + 7$

Simplify. $7$

ⓑ $x = −1$

$3 x^{2} - 9 x + 7$

Substitute −1 for $x$ $3 {(−1)}^{2} - 9 (−1) + 7$

Simplify the expression with the exponent. $3 \cdot 1 - 9 (−1) + 7$

Multiply. $3 + 9 + 7$

Simplify. $19$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Evaluate: $2 x^{2} + 4 x - 3$ when

ⓐ $x = 2$
ⓑ $x = −3$

How did it go?

PreviousAdd and Subtract Polynomials: example 10.8 Next Add and Subtract Polynomials: example 10.10

From Prealgebra (1st edition) by OpenStax (Rice University), section 10.1, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.