When factoring x^2 + bx + c, we look for two binomial factors in the form (x + m)(x + n) that, when multiplied together, give the original quadratic expression. The coefficients b and c are directly used to determine the values of m and n.
Factoring a quadratic expression ax^2 + bx + c, where a ≠ 1, is different from factoring x^2 + bx + c due to the presence of the leading coefficient "a".
On the other hand, when factoring ax^2 + bx + c, where a ≠ 1, factoring becomes more complex because the leading coefficient "a" affects the factorization. To factor such a quadratic expression, we need to find two binomial factors in the form (px + m)(qx + n) that, when multiplied together, give the original quadratic expression.
Factoring quadratics with a leading coefficient of a requires finding two sets of factors for "a" and "c" that combine in different ways to give "b". This involves considering factors of "a" and "c", as well as their combinations, to determine the appropriate values for p, q, m, and n.
In summary, factoring ax^2 + bx + c, where a ≠ 1, involves additional considerations and calculations due to the presence of the leading coefficient "a", making the factorization process more intricate compared to factoring x^2 + bx + c.
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21x² - 2x + 1/2 =0
find the following quadratic equation by factorization method
PLESE SOMEONE HELP
Step-by-step explanation:
21x²-2x +1/2 = 0
x² - 2x ×21 + 1/2× 21 = 0
Can someone help me please? ASAP
Answer:
triangle XYZ is similar to triangle RPQ
scale factor = 2/5
Step-by-step explanation:
Angles X and R are given as congruent.
Angles Z and Q are right angles, so they are congruent.
Then, angles Y and P must be congruent.
The similarity statement is
triangle XYZ is similar to triangle RPQ
To find the scale factor, divide the length of a side of the image by the length of the corresponding side in the original.
10/25 = 2/5
The scale factor is 2/5.
Write an equation for the function graphed below
The rational function graphed in this problem is defined as follows:
y = -2(x - 1)/(x² - x - 2).
How to define the rational function?The vertical asymptotes of the rational function for this problem are given as follows:
x = -1 and x = 2.
Hence the denominator of the function is given as follows:
(x + 1)(x - 2) = x² - x - 2.
The intercept of the function is given as follows:
x = 1.
Hence the numerator of the function is given as follows:
a(x - 1)
In which a is the leading coefficient.
Hence:
y = a(x - 1)/(x² - x - 2).
When x = 0, y = -1, hence the leading coefficient a is obtained as follows:
-1 = a/2
a = -2.
Thus the function is given as follows:
y = -2(x - 1)/(x² - x - 2).
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