{"id":172,"date":"2022-04-13T10:13:55","date_gmt":"2022-04-13T10:13:55","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=172"},"modified":"2025-01-21T11:30:11","modified_gmt":"2025-01-21T11:30:11","slug":"i-3-factorise-quadratics-with-leading-coefficient-1","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/i-3-factorise-quadratics-with-leading-coefficient-1\/","title":{"rendered":"I.3 Factorise quadratics with leading coefficient 1"},"content":{"rendered":"\n

Factorise quadratics with leading coefficient 1<\/strong><\/h2>\n\n\n\n

key notes:<\/p>\n\n\n\n

To factorize a quadratic of the form x2<\/sup>+bx+c, write it as<\/p>\n\n\n\n

(x+r1<\/sub>)(x+r2<\/sub>)<\/p>\n\n\n\n

where c=r1<\/sub> . r2<\/sub> and b=r1<\/sub>+r2<\/sub>.<\/p>\n\n\n\n

Learn with an example<\/strong><\/p>\n\n\n\n

\n
\n

Factorise.<\/p>\n\n\n\n

y2<\/sup>+24y+23=_______________<\/p>\n<\/div><\/div>\n\n\n\n

Look at the given quadratic:<\/p>\n\n\n\n

y2<\/sup>+24y+23<\/p>\n\n\n\n

The c term is 23, so you need to find a pair of factors with a product of 23. The b term is 24, so you need to find a pair of factors with a sum of 24. Since the product is positive (23) and the sum is positive (24), you need both factors to be positive.<\/p>\n\n\n\n

Make a list of the possible factor pairs with a product of 23, and then find the one with a sum of 24.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

The factors 1 and 23 have a sum of 24. Use those numbers to factorise y2<\/sup>+24y+23.<\/p>\n\n\n\n

y2<\/sup>+24y+23<\/p>\n\n\n\n

(y+1<\/strong>)(y+23<\/strong>)<\/p>\n\n\n\n

Finally, check your work.<\/p>\n\n\n\n

(y+1)(y+23)<\/p>\n\n\n\n

y2<\/sup>+y+23y+23 Apply the distributive property (FOIL)<\/p>\n\n\n\n

y2<\/sup>+24y+23<\/p>\n\n\n\n

Yes, y2<\/sup>+24y+23=(y+1)(y+23).<\/p>\n<\/div><\/div>\n\n\n\n

\n
\n

Factorise.<\/p>\n\n\n\n

j2<\/sup>+24j+23=_______________<\/p>\n<\/div><\/div>\n\n\n\n

Look at the given quadratic:<\/p>\n\n\n\n

j2<\/sup>+24j+23<\/p>\n\n\n\n

The c term is 23, so you need to find a pair of factors with a product of 23. The b term is 24, so you need to find a pair of factors with a sum of 24. Since the product is positive (23) and the sum is positive (24), you need both factors to be positive.<\/p>\n\n\n\n

Make a list of the possible factor pairs with a product of 23, and then find the one with a sum of 24.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

The factors 1 and 23 have a sum of 24. Use those numbers to factorise j2<\/sup>+24j+23.<\/p>\n\n\n\n

j2<\/sup>+24j+23<\/p>\n\n\n\n

(j+1<\/strong>)(j+23<\/strong>)<\/p>\n\n\n\n

Finally, check your work.<\/p>\n\n\n\n

(j+1)(j+23)<\/p>\n\n\n\n

j2+j+23j+23Apply the distributive property (FOIL)<\/p>\n\n\n\n

j2<\/sup>+24j+23<\/p>\n\n\n\n

Yes, j2<\/sup>+24j+23=(j+1)(j+23).<\/p>\n<\/div><\/div>\n\n\n\n

\n
\n

Factorise.<\/p>\n\n\n\n

n2<\/sup>+6n+8=_______________<\/p>\n<\/div><\/div>\n\n\n\n

Look at the given quadratic:<\/p>\n\n\n\n

n2+6n+8<\/p>\n\n\n\n

The c term is 8, so you need to find a pair of factors with a product of 8. The b term is 6, so you need to find a pair of factors with a sum of 6. Since the product is positive (8) and the sum is positive (6), you need both factors to be positive.<\/p>\n\n\n\n

Make a list of the possible factor pairs with a product of 8, and then find the one with a sum of 6.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

The factors 2 and 4 have a sum of 6. Use those numbers to factorise n2+6n+8.<\/p>\n\n\n\n

n2<\/sup>+6n+8<\/p>\n\n\n\n

(n+2<\/strong>)(n+4<\/strong>)<\/p>\n\n\n\n

Finally, check your work.<\/p>\n\n\n\n

(n+2)(n+4)<\/p>\n\n\n\n

n2<\/sup>+2n+4n+8 Apply the distributive property (FOIL)<\/p>\n\n\n\n

n2<\/sup>+6n+8<\/p>\n\n\n\n

Yes, n2<\/sup>+6n+8=(n+2)(n+4).<\/p>\n<\/div><\/div>\n\n\n\n

let’s practice!<\/p>\n\n\n\n

\n
\n
\"\"<\/a><\/figure>\n<\/div>\n\n\n\n
\n
\"\"<\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Factorise quadratics with leading coefficient 1 key notes: To factorize a quadratic of the form x2+bx+c, write it as (x+r1)(x+r2) where c=r1 . r2 and b=r1+r2. Learn with an example Factorise. y2+24y+23=_______________ Look at the given quadratic: y2+24y+23 The c term is 23, so you need to find a pair of factors with a product of 23. The b term is 24, so you need to find a pair of factors with a sumContinue reading “I.3 Factorise quadratics with leading coefficient 1”<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-172","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/172","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=172"}],"version-history":[{"count":18,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/172\/revisions"}],"predecessor-version":[{"id":17429,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/172\/revisions\/17429"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=172"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}