Factor each expression. Please show me how to do it. Thanx
8x^2-10x+3
15X^2-x-2
8X^2-18X-5
2x^2-5x-88
3x^2+43x-30
3x^2+7x-2
10^2-89x+156
4x^2+11x+13
3x^2-42x+147
5x^2-20x+20
Break the coefficeint of the x^2 term and the constant both into prime number factors (a*b) and (c*d), and then try various combinations of (ax+c)(bx+d) until you find one that works.
For 8x^2-10x+3, choose 4 and 2 for the factors of 8 and 3 and 1 for the factors of 3.
(4x - 3)(2x - 1) works!
The pair of minus signs before 3 and 1 is needed to make the 3 positive and -10 negative in the final product
To factor each expression, we need to find two binomials whose product equals the given expression. The process of factoring involves finding the common factors and then applying different factoring methods like factoring by grouping or the quadratic formula. Let's go through each expression one by one:
1. 8x^2 - 10x + 3:
To factor this expression, we need to find two binomials whose product equals 8x^2 - 10x + 3. Since the coefficient of the x^2 term is not 1, we need to use factoring by grouping or the quadratic formula. However, this expression cannot be factored further using integers. Therefore, the factored form of 8x^2 - 10x + 3 is: (8x - 1)(x - 3).
2. 15x^2 - x - 2:
Similarly, the factored form of 15x^2 - x - 2 is: (3x - 2)(5x + 1).
3. 8x^2 - 18x - 5:
The factored form of 8x^2 - 18x - 5 is: (4x + 1)(2x - 5).
4. 2x^2 - 5x - 88:
The factored form of 2x^2 - 5x - 88 is: (2x + 11)(x - 8).
5. 3x^2 + 43x - 30:
The factored form of 3x^2 + 43x - 30 is: (3x - 2)(x + 15).
6. 3x^2 + 7x - 2:
The factored form of 3x^2 + 7x - 2 is: (x + 2)(3x - 1).
7. 10x^2 - 89x + 156:
The factored form of 10x^2 - 89x + 156 is: (2x - 13)(5x - 12).
8. 4x^2 + 11x + 13:
The factored form of 4x^2 + 11x + 13 is: This expression cannot be factored further using integers.
9. 3x^2 - 42x + 147:
The factored form of 3x^2 - 42x + 147 is: (x - 3)(3x - 49).
10. 5x^2 - 20x + 20:
The factored form of 5x^2 - 20x + 20 is: 5(x - 2)(x - 2).
Please note that factored forms may vary, but the expressions provided above are one possible way to factor each given expression.