...numerator. lim *7 — 6 *6 + x Ans. 15. HINT. Make use of the theorem that if a polynomial vanishes when a is substituted for x, then x — a is a factor of the polynomial. The other factor may be found by actual division. 25. lim -4 Ans. — 8. HINT. Put * = // + •_',...

...~ 6 z* + x , , K> 2*' x = l (1-x)' HINT. Make use of the theorem that if a polynomial vanishes when a is substituted for x, then x — a is a factor of the polynomial. The other factor may be found by actual division. 25. /I", _ ?~1= ,4m,. -8. - WT2 - V3 z - 2 HINT....

...which requires demonstration. THE FACTOR THEOREM 96. Tf any expression containing x reduce« to 0 when a is substituted for x, then x — a is a factor of that expression. Let E represent the expression. Divide E by x— a until the remainder does not contain...

...division is exact. That is, x — a is a factor of D. (5) If x = ч does not reduce D to zero, then R is not zero, and the division is not exact. That is,...zero, then x — a is not a factor. This principle is often called the factor theorem. 93. In applying the factor theorem the trial divisor must always be...

...division is exact. That is, x — a is a factor of D. (2) If x = a does not reduce D to zero, then R is not zero, and the division is not exact. That is, x — a is not a factor of D. 93. In applying the factor theorem the trial divisor must always be written in the form x — a. Ex....

...important general theorem, known as the factor theorem : If any polynomial in x assumes the value zero when a is substituted for x, then x — a is a factor of the polynomial. We prove this first for the particular polynomial ж4-3ж3 + 7ж2-2ж-16. By substituting 2 for x we...

...important general theorem, known as the factor theorem : If any polynomial in x assumes the value zero when a is substituted for x, then x — a is a factor of the polynomial. We prove this first for the particular polynomial x* - 3 x3 + 7 x2 - 2 x - 16. By substituting 2 for...

...division is exact. That is, x — a is a factor of D. (2) If x = a does not reduce D to zero, then R is not zero, and the division is not exact. That is,...zero, then x — a is not a factor. This principle is often called the factor theorem. In applying the factor theorem the trial divisor must always be written...

...division is exact. That is, x — a is a factor of D. (2) If x — a does not reduce D to zero, then R is not zero, and the division is not exact. That is,...zero when a particular number a is substituted for ж, then x — a is a factor of the polynomial, and if the substitution of a for x does not reduce...

...ж3-ав. 11. (а + Ь)3-(а- Ь)5. 67. Factor Theorem. If any polynomial in x assumes the value zero when a is substituted for x, then x — a is a factor of the polynomial. For example, substitute 2 for x in the polynomial : Then, 24 - 3 - 2' + 7 . 22 - 2 - 2 - 16 = 16 -...