Factor the following quadratics. Notice you have a number in front of $x^{2}$
$3 x^{2} + 22 x + 7$

Question

Factor the following quadratics. Notice you have a number in front of x2  3x2+22x+7

David Clayton · Accepted Answer

Step 1  Given: 3x2+22x=7  =3x2+21x+x+7  =3x(x+7)+1(x+7)  =(3x+1)(x+7)  ∴3x2+22x+7=(3x+1)(x+7)

Jim Hunt · Accepted Answer

Step 1  Given: 3x2+22x+7  Quadratic polynomial can be factored using the transformation ax2+bx+c=a(x−x1)(x−x2) where x1 and x2 are the solutions of the quadratic equation ax2+bx+c=0  3x2+22x+7=0  All equations of the form ax2+bx+c=0 can be solved using the quadratic formula: −b±b2−4ac2a  The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.  x=−22±222−4×3×72×3  Square 22.  x=−22±484−4×3×72×3  Multiply -4 times 3  x=−22±484−12×72×3  Multiply -12 times 7  x=−22±484−842×3  Add 484 to -84  x=−22±4002×3  Take the square root of 400.  x=−22±202×3  Multiply 2 times 3.  x=−22±206  Now solve the equation x=−22±206 when ± is plus. Add -22 to 20  x=−26  Reduce the fraction −26 to lowest terms by extracting and canceling out 2  x=−13  Now solve the equation x=−22±206 when ± is minus. Subtract 20 from -22  x=−426 Divide -42 by 6  x=−7  Factor the original expression using ax2+bx+c=a(x−x1)(x−x2) Substitute −13 for x1 and -7 for x2  3x2+22x+7=3(x−(−13))(x−(−7))  Simplify all the expressions of the form p−(−q) to p+q

Factor the following quadratics. Notice you have a number in

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