Exercise 5A
Question 1
Answer whether each of the following expressions is a polynomial or not.
(a) 5x2 – 3x + 1
Sol : Polynomial
(b) 3√x – 5x – 11
Sol : Not a Polynomial
(c) √3 x3 + 8
Sol : Polynomial
(d) 2m-1 + m + 1
Sol : Not a Polynomial
(e) 5x
Sol : Polynomial
(f) 59
Sol : Polynomial
(g) $\frac{x}{2}+3$
Sol : Polynomial
(h) $\frac{9}{x}-2x^2+13$
Sol : Not a Polynomial
(i) $\frac{3}{2x+1}$
Sol : Not a Polynomial
(j) πx2 – 2
Sol : Polynomial
Question 2
Identify each polynomial as a monomial, binomial, trinomial or as neither of these. Then give the coefficients of the polynomial and if the polynomial is in simple form, give its degree.
(a) 2p2 + 5p3 + p
Sol : Trinomial , coefficient: 2,5,1 ,
Degree : 3
(b) 7a2 + 5a + (-7)a4
Sol : Trinomial , coefficient: 7,5,-7 ,
Degree : 4
(c) a2 – b2
Sol : Binomial , coefficient: 1,-1
Degree : 2
(d) 8x5 + 3x3y – 2x2y2 + y6
Sol : Neither ; , coefficient: 8,3,-2,1; ,
Degree: 6
(e) -18x6
Sol : Monomial , coefficient: -18 ;
Degree: 6
(f) xy + yz + zx
Sol :
Trinomial , coefficient: 1,1,1 ;
Degree: 2
Question 3
Pick out like terms in each polynomial.
(a) ab + ac + 3ab + 3ac
Sol : ab+3ab+ac+3ac
=ab ,3ab & ac,3ac
(b) 3xy + xz + 5xy – 7xz
Sol :
=3xy, 5xy, & xz ,-7x
(c) -8 + x2y + 5 + 3x2y
Sol :
=x2y ,3x2y & -8 ,5
(d) ab + 2a2b2 + 4ab + 3a2b2
Sol :
=ab ,4ab ,& 2a2b2 ,3a2b2
(e) xyz + x2yz3 + x3yz – xy3z2
Sol : None
(f) 23x2y + 25x2y – 32x2y + 26xy2
Sol :
= 23x2y ,25x2y ,– 32x2y
Question 4
Simplify:
(a) 15b + 8b
Sol :
=23b
(b) 7p + p + 21p – 8p
Sol :
=21p
(c) 5x2+ 8x + 7 + 9x2 – 2x – 12
Sol :
=5x2+9x2+8x– 2x+7–12
=14x2+6x-5
(d) 59 + 20y4 + 30y4
Sol :
=59+50y4
(e) (7x3 + 5x2 + 3x + 8) + (9x3 – 2x2 + 9 – 7x)
Sol :
=7x3 + 5x2 + 3x + 8+9x3 – 2x2 + 9 – 7x
=16x3+3x2-4x+17
Question 5
Find the sum of the given polynomials.
(a) (3x + 4) + (7x – 1)
Sol :
$\begin{aligned}3x+4&\\+7x-1&\\ \hline 10x+3&\end{aligned}$
(b) (3y2 + 4y – 7) + (y2 + y + 12)
Sol :
$\begin{aligned}3y^2+4y-7 &\\+y^2+y+12&\\ \hline 4y^2+5y+5&\end{aligned}$(c) (x4 – x2y + 3y2) + (-x4 + 2x2y + y2)
Sol :
$\begin{aligned}x^4-x^2y+3y^2 &\\-x^4+2x^2y+y^2 &\\ \hline x^2y+4y^2&\end{aligned}$
Question 6
Subtract:
(a) (7y2+5x2)–(2y2–3x2)
Sol :
$\begin{aligned}7y^2+5x^2 &\\2y^2-3x^2 &\\(-)\phantom{2y^2}(+)\phantom{3x^2} &\\ \hline 5y^2+8x^2&\end{aligned}$(b) (5ab+6bc–7ca)–(-2ab+4bc+2ca)
Sol :
$\begin{aligned}5ab+6bc-7ca&\\-2ab+4bc+2ca&\\(+)\phantom{-2ab}(-)\phantom{4bc}(-)\phantom{2ca}&\\ \hline 7ab+2bc-9ca&\end{aligned}$(c) (4a–3b–9c)–(-2a–5b–10c)
Sol :
$\begin{aligned}4a-3b-9c&\\-2a-5b-10c&\\(+)\phantom{2a}(+)\phantom{5b}(+)\phantom{10c}&\\ \hline 6a+2b+c&\end{aligned}$
Question 7
Find:
(a) The sum of the given polynomials.
(b) The difference of the given polynomials (2nd from the 1st).
(i) -5x + 9; 2x + 3
(ii) 7q + p; q – p
(iii) y4 – 9, y4 + 3
(iv) 5m2 + 3m + 8; 6m2 + 2m + 10
(v) x2 – xy – y2; -x2 + xy – y2
(vi) 3m2 – 5mn + 7n2; 2mn – 5n2 – m2
Sol :
Question 8
Subtract the second polynomial from the first:
(a) 5m2 – 4n2; 5m2+ 6mn + 6n2
(b) a2 + 2ab – b2; 4a2 – 2ab + 4b2
Sol :
Question 9
Simplify
(3x2 + 5x + 4) + (x2 + 6) – (3 – 7x)
Sol :
=3x2+5x+4+x2+6–3+7x
=3x2+x2+5x+7x+4-3+6
=4x2+12x+7
Question 10
(x2+y2–z2)–(3z2–2x2–4y2)+(4y2+x2+z2)
Sol :
=x2+y2–z2–3z2+2x2+4y2+4y2+x2+z2
=x2+2x2+x2+y2+4y2+4y2–z2–3z2+z2
=4x2+9y2–3z2
All solutions are very good
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