Algebraic Functions - Quadratic to Sum and Product (Level 1) - Mobius Math Academy

Algebraic Functions

Quadratic to Sum and Product (Level 1)

This math topic focuses on understanding quadratic expressions and their factors. It involves identifying the sum and product of the roots of quadratic equations, expressed in the standard form \(x^2 + px + q = (x+a)(x+b)\). Each problem presents a quadratic expression, asking to determine the correct values of 'a' and 'b' such that the sum \(a+b\) equals the middle coefficient (p) and the product \(ab\) equals the constant term (q). The problems are designed to enhance skills in polynomial factorization and algebraic manipulations within the broader context of polynomials and quadratics.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Algebraic Functions - Quadratic to Sum and Product Worksheet

Algebraic Functions - Quadratic to Sum and Product

What is true about 'a' and 'b' for this quadratic?

$A LaTex expression showing x to the power of 2 + 12x + 32\\=(x+a)(x+b)$

a $A LaTex expression showing a + b = 32\\a multiplied by b = 12$

b $A LaTex expression showing a + b = 12\\a multiplied by b = 32$

c $A LaTex expression showing a + b = 24\\a multiplied by b = 32$

d $A LaTex expression showing a + b = 12\\a multiplied by b = 64$

What is true about 'a' and 'b' for this quadratic?

$A LaTex expression showing x to the power of 2 + 10x + 24\\=(x+a)(x+b)$

a $A LaTex expression showing a + b = 24\\a multiplied by b = 10$

b $A LaTex expression showing a + b = 10\\a multiplied by b = 24$

c $A LaTex expression showing a + b = 10\\a multiplied by b = 48$

d $A LaTex expression showing a + b = 20\\a multiplied by b = 24$

What is true about 'a' and 'b' for this quadratic?

$A LaTex expression showing x to the power of 2 + 5x + 6\\=(x+a)(x+b)$

a $A LaTex expression showing a + b = 5\\a multiplied by b = 6$

b $A LaTex expression showing a + b = 6\\a multiplied by b = 5$

c $A LaTex expression showing a + b = 10\\a multiplied by b = 6$

d $A LaTex expression showing a + b = 5\\a multiplied by b = 12$

What is true about 'a' and 'b' for this quadratic?

$A LaTex expression showing x to the power of 2 + 9x + 18\\=(x+a)(x+b)$

a $A LaTex expression showing a + b = 18\\a multiplied by b = 9$

b $A LaTex expression showing a + b = 9\\a multiplied by b = 18$

c $A LaTex expression showing a + b = 18\\a multiplied by b = 18$

d $A LaTex expression showing a + b = 9\\a multiplied by b = 36$

What is true about 'a' and 'b' for this quadratic?

$A LaTex expression showing x to the power of 2 + 13x + 42\\=(x+a)(x+b)$

a $A LaTex expression showing a + b = 42\\a multiplied by b = 13$

b $A LaTex expression showing a + b = 13\\a multiplied by b = 42$

c $A LaTex expression showing a + b = 13\\a multiplied by b = 84$

d $A LaTex expression showing a + b = 26\\a multiplied by b = 42$

What is true about 'a' and 'b' for this quadratic?

$A LaTex expression showing x to the power of 2 + 7x + 6\\=(x+a)(x+b)$

a $A LaTex expression showing a + b = 7\\a multiplied by b = 12$

b $A LaTex expression showing a + b = 14\\a multiplied by b = 6$

c $A LaTex expression showing a + b = 6\\a multiplied by b = 7$

d $A LaTex expression showing a + b = 7\\a multiplied by b = 6$

What is true about 'a' and 'b' for this quadratic?

$A LaTex expression showing x to the power of 2 + 6x + 5\\=(x+a)(x+b)$

a $A LaTex expression showing a + b = 6\\a multiplied by b = 10$

b $A LaTex expression showing a + b = 12\\a multiplied by b = 5$

c $A LaTex expression showing a + b = 5\\a multiplied by b = 6$

d $A LaTex expression showing a + b = 6\\a multiplied by b = 5$

What is true about 'a' and 'b' for this quadratic?

$A LaTex expression showing x to the power of 2 + 2x + 0\\=(x+a)(x+b)$

a $A LaTex expression showing a + b = 4\\a multiplied by b = 0$

b $A LaTex expression showing a + b = 0\\a multiplied by b = 2$

c $A LaTex expression showing a + b = 2\\a multiplied by b = 0$