Table of Integrals

2 + bx + c BY GROUPING (the a • c Method) Step 1: Look for a GCF and factor it out first Step 2: Multiply the coefficient of the leading term a by the constant term c List the factors of this product (a • c) to find the pair of factors, f 1 and f 2, that sums to b, the coefficient of the middle term

Factoring Trinomials of the Form ax2 + bx + c, a = 1

Factoring Trinomials of the Form ax2 + bx + c, a = 1 When trinomials factor, the resulting terms are binomials Trinomials in the form of ax2 + bx + c where a = 1 will fall into one of three patterns for factoring Pattern 1: ax2 + bx + c In this pattern, the coefficient a is positive and both of the operators are addition This will result

FACTORING TRINOMIALS OF THE FORM: AX2 + BX + C

Put in standard quadratic form: Ax2 + Bx + C Factor out a GCF if possible Step 1 Find A•C (Ax2 + Bx + C) Step 2 Find 2 factors of the product A•C whose algebraic sum is B Same sign binomials--correct factors must ADD to B Different signs--correct factors must have a DIFFERENCE of B Step 3 Re-write middle term as the algebraic sum of the two

8th Grade

Factoring ax2 + bx + c A-SSE A 1a Interpret parts of an expression, such as Obiective To factor trinomials of the form ax2 + bx + c X+3 Getting Ready An array of three rectangular solar panels has area 3x2 + 21x + 36 The height of the array is x + 3 What is the length of the array? You did this for Explain your reasoning one panel in

8-6 ax^2+bx+c

ax2 + bx + c when a 1 different from factoring a trinomial when a I ? How is it similar? Open-Ended Find two different values that complete each expression so that the trinomial can be factored into the product of two binomials Factor your trinomi 32 + x 4 Answers may vary Sample: 19, 16: (4x + + 4); 35 8n2 4 n - 10 Answers may vary Sample:

Factoring

(continued) Form K Factoring ax2 1 bx 1 c Open-Ended Find two diff erent values that complete each expression so that the trinomial can be factored into the product of two binomials Factor your trinomials 19 4n2 1 u n 2 3 20 12r2 1 u1 6 21 24a2 1 u a 2 15 22 18b2 1 u b 1 8 23 A parallelogram has an area of 8x2 2 2x 2 45 Th e height of

2 QUADRATIC EQUATIONS

2 3 3 To Solve Quadratic Equations : ax2 + bx + c = 0 II Method of completing the square - by expressing ax2 + bx + c in the form a(x + p)2 + q [a = 1, but involving fractions when completing the square] EXAMPLE EXERCISE C3 Solve x2 – 3x – 2 = 0 by method of ‘completing the square’ Give your answer correct to 4 significant figures

Table of Basic Integrals Basic Forms

ax2 + bx+ c dx= 1 2a lnjax2+bx+cj b a p 4ac 2b2 tan 1 2ax+ b p 4ac b Integrals with Roots (17) Z p x adx= 2 3 (x a)3=2 (18) Z 1 p x a dx= 2 p x a (19) Z 1 p a x dx= 2