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JAMB Mathematics Past Questions & Answers - Page 251

1,251.

Which of the following is a factor of rs + tr - pt - ps?

(p - s)

(s - p)

(r - p)

(r + p)

View answer & explanation

Correct answer is C

rs + tr - pt - ps = rs - ps - tr - pt = (r - p)s + (r - p)t = (r - p)(s + t), hence r - p is a factor

1,252.

Factorize 1 - (a - b)²

(1 - a - b)(1 - a + b)

(1 + a - b)(1 - a + b)

(1 - a + b)(1 - a + b)

(1 + a + b)(1 + a + b)

View answer & explanation

Correct answer is B

1 - (a - b)² = [1 + (a - b)][1 - a + b]

= (1 + a - b)(1 - a + b)

1,253.

Factorize m3 - 2m2 - m + 2

(m² + 1)(m - 2)

(m - 1)(m + 1)(m + 2)

(m - 2)(m + 1)(m - 1)

(m² + 2)(m - 1)

View answer & explanation

Correct answer is C

m3 - 2m2 - m + 2

Let f(m) = m3 - 2m2 - m2 + 2

= f(1)

= 1 - 2 - 2 + 2 = 0

∴ m - 1 is factor $\frac{m^3 - 2m^2 - m^2 + 2}{m - 1}$

= m2 - m - 2

= (m - 1)m2 - m - 2

= (m - 1)(m + 1)(m - 2)

1,254.

If g(x) = x² + 3x + 4, find g(x + 1) - g(x)

(x + 2)

2(x + 2)

(2x + 1)

(x² + 4)

View answer & explanation

Correct answer is B

g(x) = x² + 3x + 4

= g(x + 1) = (x + 1)^2 + 3(x + 1) + 4

= x² + 1 + 2x + 3x + 3 + 4

= x² + 5x + 8

g(x + 1) - g(x) = x² + 5x + 8 - (x² + 3x + 4)

= x² + 5x + 8 - x² + 3x + 4

= 2x + 4

= 2(x + 2)

1,255.

If w varies inversely as $\frac{uv}{u + v}$ and is equal to 8 when

u = 2 and v = 6, find a relationship between u, v, w.

uvw = 16(u + v)

16ur = 3w(u + v)

uvw = 12(u + v)

12uvw = u + v

View answer & explanation

Correct answer is C

W $\alpha$ $\frac{\frac{1}{uv}}{u + v}$

∴ w = $\frac{\frac{k}{uv}}{u + v}$

= $\frac{k(u + v)}{uv}$

w = $\frac{k(u + v)}{uv}$

w = 8, u = 2 and v = 6

8 = $\frac{k(2 + 6)}{2(6)}$

= $\frac{k(8)}{12}$

k = 12