FACTOR each problem as demonstrated in class. Show All WORK! 6. x^2-10x+16 8. 8x^2+14x+3 10. 5x^2+6x-8 9. 5x^2-12x+4

Let's factor each quadratic expression step by step.<br /><br />### 6. \( x^2 - 10x + 16 \)<br /><br />To factor this quadratic expression, we need to find two numbers that multiply to 16 (the constant term) and add up to -10 (the coefficient of the linear term).<br /><br />The numbers that satisfy these conditions are -2 and -8 because:<br />- \((-2) \times (-8) = 16\)<br />- \((-2) + (-8) = -10\)<br /><br />So, we can write the quadratic expression as:<br />\[ x^2 - 10x + 16 = (x - 2)(x - 8) \]<br /><br />### 8. \( 8x^2 + 14x + 3 \)<br /><br />To factor this quadratic expression, we need to find two numbers that multiply to \(8 \times 3 = 24\) and add up to 14.<br /><br />The numbers that satisfy these conditions are 12 and 2 because:<br />- \(12 \times 2 = 24\)<br />- \(12 + 2 = 14\)<br /><br />We can then rewrite the middle term (14x) using numbers:<br />\[ 8x^2 + 14x + 3 = 8x^2 + 12x + 2x + 3 \]<br /><br />Next, we factor by grouping:<br />\[ = 4x(2x + 3) + 1(2x + 3) \]<br />\[ = (4x + 1)(2x + 3) \]<br /><br />### 10. \( 5x^2 + 6x - 8 \)<br /><br />To factor this quadratic expression, we need to find two numbers that multiply to \(5 \times -8 = -40\) and add up to 6.<br /><br />The numbers that satisfy these conditions are 10 and -4 because:<br />- \(10 \times (-4) = -40\)<br />- \(10 + (-4) = 6\)<br /><br />We can then rewrite the middle term (6x) using these two numbers:<br />\[ 5x^2 + 6x - 8 = 5x^2 + 10x - 4x - 8 \]<br /><br />Next, we factor by grouping:<br />\[ = 5x(x + 2) - 4(x + 2) \]<br />\[ = (5x - 4)(x + 2) \]<br /><br />### 9. \( 5x^2 - 12x + 4 \)<br /><br />To factor this quadratic expression, we need to find two numbers that multiply to \(5 \times 4 = 20\) and add up to -12.<br /><br />The numbers that satisfy these conditions are -10 and -2 because:<br />- \((-10) \times (-2) = 20\)<br />- \((-10) + (-2) =\)<br /><br />We can then rewrite the middle term (-12x) using these two numbers:<br />\[ 5x^2 - 12x + 4 = 5x^2 - 10x - 2x + 4 \]<br /><br />Next, we factor by grouping:<br />\[ = 5x(x - 2) - 2(x - 2) \]<br />\[ = (5x - 2)(x - 2) \]<br /><br />So, the factored forms are:<br />6. \( x^2 - 10x + 16 = (x - 2)(x - 8) \)<br />8. \( 8x^2 + 14x + 3 = (4x + 1)(2x + 3) \)<br />10. \( 5x^2 + 6x - 8 = (5x - 4)(x + 2) \)<br />9. \( 5x^2 - 12x + 4 = (5x - 2)(x - 2) \)