To detrmine factor: a) r2−5r−14 b) 3m2+5m−2 c) 6p2+13pq−5q2

Question

To detrmine factor:  a) r2−5r−14  b) 3m2+5m−2  c) 6p2+13pq−5q2

ol3i4c5s4hr · Accepted Answer

Step 1  a) Given equation: r2−5r−14  To find integers b and d such that  r2−5r−14=(r+b)(r+d)  =r2+dr+br+bd  r2−5r−14=r2+(b+d)r+bd  Since:  must have bd=−14, b and d are factors of -14  Similarly: b+d=−5  Table show the possibilities  Factors b, d of -14Sum b+d=−52(−7)2−7=−51(−14)1−14=−13  So, r2−5r−14=(r+2)(r−7)  To check:  (r+2)(r−7)=r(r−7)+2(r−7)  =r2−7r+2r−14  =r2−5r−14

Lynne Trussell · Accepted Answer

Step 1  b) 3m2+5m−2  To find integers  3m2+5m−2=(am+b)(cm+d)  =acm2+adm+bcm+bd  3m2+5m−2=acm2+(ad+bc)m+bd  Step 2  Since:  ac=3  bd=−2  (3m−2)(m+1)=3m(m+1)−2(m+1)  =3m2+3m−2m−2  =3m2+m−2  (3m−1)(m+2)=3m(m+2)−1(m+2)  =3m2+6m−m−2  =3m2+5m−2  Answer: The last trial gives the correct factorization.

user_27qwe · Accepted Answer

Step 1c)6p2+13pq−5q2Formula:(x+4)(x−2)=x(x−2)+4(x−2)=x2−2x+4x−8=x2+2x−8Step 2To find integers a, b, c, and d6p2+13pq−5q2=(ap+b)(cp+d)=acp2+adp+bcp+bd6p2+13pq−5q2=acp2+(ad+dc)p+bdStep 3Since:ac=6, bd=−5q2(3p+q)(2p−5q)=3p(2p−5q)+q(2p−5q)=6p2−15pq+2pq−5q2=6p2−13pq−5q2(3p−q)(2p+5q)=3p(2p+5q)−q(2p+5q)=6p2+15pq−2pq−5q2=6p2+13pq−5q2

To detrmine factor: a) r2−5r−14 b) 3m2+5m−2 c) 6p2+13pq−5q2

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