7.2E: Exercises
- Page ID
- 30552
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Factor Trinomials of the Form \(x^2+bx+c\)
In the following exercises, factor each trinomial of the form \(x^2+bx+c\)
\(x^2+4x+3\)
- Answer
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\((x+1)(x+3)\)
\(y^2+8y+7\)
\(m^2+12m+11\)
- Answer
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\((m+1)(m+11)\)
\(b^2+14b+13\)
\(a^2+9a+20\)
- Answer
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\((a+4)(a+5)\)
\(m^2+7m+12\)
\(p^2+11p+30\)
- Answer
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\((p+5)(p+6)\)
\(w^2+10w+21\)
\(n^2+19n+48\)
- Answer
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\((n+3)(n+16)\)
\(b^2+14b+48\)
\(a^2+25a+100\)
- Answer
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\((a+5)(a+20)\)
\(u^2+101u+100\)
\(x^2−8x+12\)
- Answer
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\((x−2)(x−6)\)
\(q^2−13q+36\)
\(y^2−18y+45\)
- Answer
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\((y−3)(y−15)\)
\(m^2−13m+30\)
\(x^2−8x+7\)
- Answer
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\((x−1)(x−7)\)
\(y^2−5y+6\)
\(p^2+5p−6\)
- Answer
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\((p−1)(p+6)\)
\(n^2+6n−7\)
\(y^2−6y−7\)
- Answer
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\((y+1)(y−7)\)
\(v^2−2v−3\)
\(x^2−x−12\)
- Answer
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\((x−4)(x+3)\)
\(r^2−2r−8\)
\(a^2−3a−28\)
- Answer
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\((a−7)(a+4)\)
\(b^2−13b−30\)
\(w^2−5w−36\)
- Answer
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\((w−9)(w+4)\)
\(t^2−3t−54\)
\(x^2+x+5\)
- Answer
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prime
\(x^2−3x−9\)
\(8−6x+x^2\)
- Answer
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\((x−4)(x−2)\)
\(7x+x^2+6\)
\(x^2−12−11x\)
- Answer
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\((x−12)(x+1)\)
\(−11−10x+x^2\)
Factor Trinomials of the Form \(x^2+bxy+cy^2\)
In the following exercises, factor each trinomial of the form \(x^2+bxy+cy^2\)
\(p^2+3pq+2q^2\)
- Answer
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\((p+q)(p+2q)\)
\(m^2+6mn+5n^2\)
\(r^2+15rs+36s^2\)
- Answer
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\((r+3s)(r+12s)\)
\(u^2+10uv+24v^2\)
\(m^2−12mn+20n^2\)
- Answer
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\((m−2n)(m−10n)\)
\(p^2−16pq+63q^2\)
\(x^2−2xy−80y^2\)
- Answer
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\((x+8y)(x−10y)\)
\(p^2−8pq−65q^2\)
\(m^2−64mn−65n^2\)
- Answer
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\((m+n)(m−65n)\)
\(p^2−2pq−35q^2\)
\(a^2+5ab−24b^2\)
- Answer
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\((a+8b)(a−3b)\)
\(r^2+3rs−28s^2\)
\(x^2−3xy−14y^2\)
- Answer
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prime
\(u^2−8uv−24v^2\)
\(m^2−5mn+30n^2\)
- Answer
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prime
\(c^2−7cd+18d^2\)
Mixed Practice
In the following exercises, factor each expression.
\(u^2−12u+36\)
- Answer
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\((u−6)(u−6)\)
\(w^2+4w−32\)
\(x^2−14x−32\)
- Answer
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\((x+2)(x−16)\)
\(y^2+41y+40\)
\(r^2−20rs+64s^2\)
- Answer
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\((r−4s)(r−16s)\)
\(x^2−16xy+64y^2\)
\(k^2+34k+120\)
- Answer
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\((k+4)(k+30)\)
\(m^2+29m+120\)
\(y^2+10y+15\)
- Answer
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prime
\(z^2−3z+28\)
\(m^2+mn−56n^2\)
- Answer
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\((m+8n)(m−7n)\)
\(q^2−29qr−96r^2\)
\(u^2−17uv+30v^2\)
- Answer
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\((u−15v)(u−2v)\)
\(m^2−31mn+30n^2\)
\(c^2−8cd+26d^2\)
- Answer
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prime
\(r^2+11rs+36s^2\)
Everyday Math
Consecutive integers Deirdre is thinking of two consecutive integers whose product is 56. The trinomial \(x^2+x−56\) describes how these numbers are related. Factor the trinomial.
- Answer
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\((x+8)(x−7)\)
Consecutive integers Deshawn is thinking of two consecutive integers whose product is 182. The trinomial \(x^2+x−182\) describes how these numbers are related. Factor the trinomial describes how these numbers are related. Factor the trinomial.
Writing Exercises
Many trinomials of the form \(x^2+bx+c\) factor into the product of two binomials \((x+m)(x+n)\). Explain how you find the values of \(m\) and \(n\).
- Answer
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Answers may vary
How do you determine whether to use plus or minus signs in the binomial factors of a trinomial of the form \(x^2+bx+c\) where \(b\) and \(c\) may be positive or negative numbers?
Will factored \(x^2−x−20\) as \((x+5)(x−4)\). Bill factored it as \((x+4)(x−5)\). Phil factored it as \((x−5)(x−4)\). Who is correct? Explain why the other two are wrong.
- Answer
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Answers may vary
Look at Example, where we factored \(y^2+17y+60\). We made a table listing all pairs of factors of 60 and their sums. Do you find this kind of table helpful? Why or why not?
Self Check
a. After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.
b. After reviewing this checklist, what will you do to become confident for all goals?