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Q. 104

Expert-verifiedFound in: Page 832

Book edition
2nd

Author(s)
Lynn Marecek, MaryAnne Anthony-Smith

Pages
1240 pages

ISBN
9780998625713

In the following exercises, factor each trinomial of the form ${x}^{2}+bxy+c{y}^{2}$

${p}^{2}-8pq-65{q}^{2}$

The factorization of ${p}^{2}-8pq-65{q}^{2}$ is $(p+5q)(p-13q)$

Given expression is ${p}^{2}-8pq-65{q}^{2}$

The factors of the expression:

The factor of -65 | Sum of factor |

5, -13 | 5 + (-13) = -8 |

13, -5 | 13 +(-5) = 8 |

Use $5$and $-13$as the last terms of the trinomials.

${p}^{2}-8pq-65{q}^{2}=(p+5q)(p-13q)$

$(p+5q)(p-13q)={p}^{2}+5pq-13pq-65{q}^{2}\phantom{\rule{0ex}{0ex}}={p}^{2}-8pq-65{q}^{2}$

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