Elementary Algebra 2e

# Review Exercises

Elementary Algebra 2eReview Exercises

### Review Exercises

##### 7.1 Greatest Common Factor and Factor by Grouping

Find the Greatest Common Factor of Two or More Expressions

In the following exercises, find the greatest common factor.

363.

$42,6042,60$

364.

$450,420450,420$

365.

$90,150,10590,150,105$

366.

$60,294,63060,294,630$

Factor the Greatest Common Factor from a Polynomial

In the following exercises, factor the greatest common factor from each polynomial.

367.

$24x−4224x−42$

368.

$35y+8435y+84$

369.

$15m4+6m2n15m4+6m2n$

370.

$24pt4+16t724pt4+16t7$

Factor by Grouping

In the following exercises, factor by grouping.

371.

$ax−ay+bx−byax−ay+bx−by$

372.

$x2y−xy2+2x−2yx2y−xy2+2x−2y$

373.

$x2+7x−3x−21x2+7x−3x−21$

374.

$4x2−16x+3x−124x2−16x+3x−12$

375.

$m3+m2+m+1m3+m2+m+1$

376.

$5x−5y−y+x5x−5y−y+x$

##### 7.2 Factor Trinomials of the form $x2+bx+cx2+bx+c$

Factor Trinomials of the Form $x2+bx+cx2+bx+c$

In the following exercises, factor each trinomial of the form $x2+bx+cx2+bx+c$.

377.

$u2+17u+72u2+17u+72$

378.

$a2+14a+33a2+14a+33$

379.

$k2−16k+60k2−16k+60$

380.

$r2−11r+28r2−11r+28$

381.

$y2+6y−7y2+6y−7$

382.

$m2+3m−54m2+3m−54$

383.

$s2−2s−8s2−2s−8$

384.

$x2−3x−10x2−3x−10$

Factor Trinomials of the Form $x2+bxy+cy2x2+bxy+cy2$

In the following examples, factor each trinomial of the form $x2+bxy+cy2x2+bxy+cy2$.

385.

$x2+12xy+35y2x2+12xy+35y2$

386.

$u2+14uv+48v2u2+14uv+48v2$

387.

$a2+4ab−21b2a2+4ab−21b2$

388.

$p2−5pq−36q2p2−5pq−36q2$

##### 7.3 Factoring Trinomials of the form $ax2+bx+cax2+bx+c$

Recognize a Preliminary Strategy to Factor Polynomials Completely

In the following exercises, identify the best method to use to factor each polynomial.

389.

$y2−17y+42y2−17y+42$

390.

$12r2+32r+512r2+32r+5$

391.

$8a3+72a8a3+72a$

392.

$4m−mn−3n+124m−mn−3n+12$

Factor Trinomials of the Form $ax2+bx+cax2+bx+c$ with a GCF

In the following exercises, factor completely.

393.

$6x2+42x+606x2+42x+60$

394.

$8a2+32a+248a2+32a+24$

395.

$3n4−12n3−96n23n4−12n3−96n2$

396.

$5y3+25y2−70y5y3+25y2−70y$

Factor Trinomials Using the “ac” Method

In the following exercises, factor.

397.

$2x2+9x+42x2+9x+4$

398.

$3y2+17y+103y2+17y+10$

399.

$18a2−9a+118a2−9a+1$

400.

$8u2−14u+38u2−14u+3$

401.

$15p2+2p−815p2+2p−8$

402.

$15x2+x−215x2+x−2$

403.

$40s2−s−640s2−s−6$

404.

$20n2−7n−320n2−7n−3$

Factor Trinomials with a GCF Using the “ac” Method

In the following exercises, factor.

405.

$3x2+3x−363x2+3x−36$

406.

$4x2+4x−84x2+4x−8$

407.

$60y2−85y−2560y2−85y−25$

408.

$18a2−57a−2118a2−57a−21$

##### 7.4 Factoring Special Products

Factor Perfect Square Trinomials

In the following exercises, factor.

409.

$25x2+30x+925x2+30x+9$

410.

$16y2+72y+8116y2+72y+81$

411.

$36a2−84ab+49b236a2−84ab+49b2$

412.

$64r2−176rs+121s264r2−176rs+121s2$

413.

$40x2+360x+81040x2+360x+810$

414.

$75u2+180u+10875u2+180u+108$

415.

$2y3−16y2+32y2y3−16y2+32y$

416.

$5k3−70k2+245k5k3−70k2+245k$

Factor Differences of Squares

In the following exercises, factor.

417.

$81r2−2581r2−25$

418.

$49a2−14449a2−144$

419.

$169m2−n2169m2−n2$

420.

$64x2−y264x2−y2$

421.

$25p2−125p2−1$

422.

$1−16s21−16s2$

423.

$9−121y29−121y2$

424.

$100k2−81100k2−81$

425.

$20x2−12520x2−125$

426.

$18y2−9818y2−98$

427.

$49u3−9u49u3−9u$

428.

$169n3−n169n3−n$

Factor Sums and Differences of Cubes

In the following exercises, factor.

429.

$a3−125a3−125$

430.

$b3−216b3−216$

431.

$2m3+542m3+54$

432.

$81x3+381x3+3$

##### 7.5 General Strategy for Factoring Polynomials

Recognize and Use the Appropriate Method to Factor a Polynomial Completely

In the following exercises, factor completely.

433.

$24x3+44x224x3+44x2$

434.

$24a4−9a324a4−9a3$

435.

$16n2−56mn+49m216n2−56mn+49m2$

436.

$6a2−25a−96a2−25a−9$

437.

$5r2+22r−485r2+22r−48$

438.

$5u4−45u25u4−45u2$

439.

$n4−81n4−81$

440.

$64j2+22564j2+225$

441.

$5x2+5x−605x2+5x−60$

442.

$b3−64b3−64$

443.

$m3+125m3+125$

444.

$2b2−2bc+5cb−5c22b2−2bc+5cb−5c2$

Use the Zero Product Property

In the following exercises, solve.

445.

$(a−3)(a+7)=0(a−3)(a+7)=0$

446.

$(b−3)(b+10)=0(b−3)(b+10)=0$

447.

$3m(2m−5)(m+6)=03m(2m−5)(m+6)=0$

448.

$7n(3n+8)(n−5)=07n(3n+8)(n−5)=0$

In the following exercises, solve.

449.

$x2+9x+20=0x2+9x+20=0$

450.

$y2−y−72=0y2−y−72=0$

451.

$2p2−11p=402p2−11p=40$

452.

$q3+3q2+2q=0q3+3q2+2q=0$

453.

$144m2−25=0144m2−25=0$

454.

$4n2=364n2=36$

Solve Applications Modeled by Quadratic Equations

In the following exercises, solve.

455.

The product of two consecutive numbers is $462462$. Find the numbers.

456.

The area of a rectangular shaped patio $400400$ square feet. The length of the patio is $99$ feet more than its width. Find the length and width.