Question

Tony factors the quadratic x^2-7x+12 by listing all the numbers that add to -7. Then he finds a pair that multiplies to 12. Sasha has another way. She looks at all the numbers that multiply to 12. Then she finds a pair that adds to -7. Which quadratic expressions are easier to factor with Sasha's method? With Tony's method? Explain.
1a) x^2-2x-35
1b) x^2-13x+36
1c) x^2+13x-36
1d) x^2+32x-185
1e) x^2+30x+189
1f) x^2+19x-34

Answer 1

sorry don't know

Answer 2

ok thx anyway

Answer 3

please help @allay

Answer 4

Factor quadratic expression ax^2 + bx + c
Sacha's method. Compose factor pairs of c, then find the pair that add up to b.
1a ; 1b ; 1d; 1e ; These expression are easier to factor using Sacha's method
1a: x^2 - 2x - 35. Compose factor pairs of c = -35. They are (5, -7). Their sum is -2 = b.
1b: x^2 - 13x + 36.
Compose factor pairs of c = 36. They are...(-4, -9). The sum is -13 = b.
1d: x^2 + 32x - 185
Compose factor pairs of -185 = c. They are ..(-5, 37). The sum is 37 - 5 = 32 = b.
1e: x^2 + 30x + 189.
Compose factor pairs of c = 189. They are (9, 21). The sum is 9 + 21 = 30 = b.
Tony's method: Find the pairs of 2 numbers that add up to b. Then find the pair among them that multiplies to c.
1c: x^2 + 13x - 36. Pairs that add up to 13. Proceeding (1, 12)(2, 11)...(4, 9). This pair (4, 9) multiplies to 36.
1f: x^2 + 19x - 34. Not factorable.

Answer 5

Correction:
1c) Tony finds the pair (4, 9) that add up to b = 13 and multiplies to 36. However, this is wrong, because c = -36.
1f) Tony finds the pair (2, 17) that add up to b = 19 and multiplies to 34. This method is wrong, because c = -34.

Answer 6

@thu1935 thanks for the helpful answer!