Proplem with a polinimial

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marywendy

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Hi, I'm not sure how to solve this clearly simple problem and it's driving me mad. Here it is: Given that -5x-21+6x^2=(ax+b)(cx+d) what is the value of bd? A. -21; B. -5; C. 6; D. 11. I know the correct answer should be A. -21, but I don't know how to get it. Please help. Thanks.
 
marywendy said:
Hi, I'm not sure how to solve this clearly simple problem and it's driving me mad. Here it is: Given that -5x-21+6x^2=(ax+b)(cx+d) what is the value of bd? A. -21; B. -5; C. 6; D. 11. I know the correct answer should be A. -21, but I don't know how to get it. Please help. Thanks.
Click to expand...

Can you factorize the quadratic function

y = 6x^2 - 5x - 21
 
marywendy said:
Hi, I'm not sure how to solve this clearly simple problem and it's driving me mad. Here it is: Given that -5x-21+6x^2=(ax+b)(cx+d) what is the value of bd? A. -21; B. -5; C. 6; D. 11. I know the correct answer should be A. -21, but I don't know how to get it. Please help. Thanks.
Click to expand...
As a different approach:
(ax+b)(cx+d) = ac x2 + (bc+ad) x + bd = 6 x2 - 5 x - 21
so
ac = ?
bc+ad = ?
bd = ?
 
marywendy said:
Hi, I'm not sure how to solve this clearly simple problem and it's driving me mad. Here it is: Given that -5x-21+6x^2=(ax+b)(cx+d) what is the value of bd? A. -21; B. -5; C. 6; D. 11. I know the correct answer should be A. -21, but I don't know how to get it. Please help. Thanks.
Click to expand...
You need to understand at all times that a, b, c and d are just numbers--like 7 or 25 or -3/4 or pi. We just do not know their values yet. If you were multiply out (ax+b)(cx+d) the constant would come from multiply the two constants, b and d giving us bd. Any other product would give us an x term or x^2 term. Now bd is the constant on the right hand side of your equation and -21 is the constant on the left hand side of the equation. Now what do you think the value of bd is?
 
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