PLS FACTORISE the polynomial into 2 binomials a2+16a+28
Answers
Answer:
find the missing factors and see the formulae from ncert
16a2-49/a2-1/4a-7/a-1
Final result :
64a4 - a3 - 4a2 - 28a - 196
———————————————————————————
4a2
Step by step solution :
Step 1 :
7
Simplify —
a
Equation at the end of step 1 :
49 1 7
((((16•(a2))-————)-(—•a))-—)-1
(a2) 4 a
Step 2 :
1
Simplify —
4
Equation at the end of step 2 :
49 1 7
((((16•(a2))-————)-(—•a))-—)-1
(a2) 4 a
Step 3 :
49
Simplify ——
a2
Equation at the end of step 3 :
49 a 7
((((16•(a2))-——)-—)-—)-1
a2 4 a
Step 4 :
Equation at the end of step 4 :
49 a 7
(((24a2 - ——) - —) - —) - 1
a2 4 a
Step 5 :
Rewriting the whole as an Equivalent Fraction :
5.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using a2 as the denominator :
24a2 24a2 • a2
24a2 = ———— = —————————
1 a2
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
5.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
24a2 • a2 - (49) 16a4 - 49
———————————————— = —————————
a2 a2
Equation at the end of step 5 :
(16a4 - 49) a 7
((——————————— - —) - —) - 1
a2 4 a
Step 6 :
Trying to factor as a Difference of Squares :
6.1 Factoring: 16a4-49
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 16 is the square of 4
Check : 49 is the square of 7
Check : a4 is the square of a2
Factorization is : (4a2 + 7) • (4a2 - 7)
Polynomial Roots Calculator :
6.2 Find roots (zeroes) of : F(a) = 4a2 + 7
Polynomial Roots Calculator is a set of methods aimed at finding values of a for which F(a)=0
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers a which can be expressed as the quotient of two integers
The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient
In this case, the Leading Coefficient is 4 and the Trailing Constant is 7.
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