(i).
-2*(i + 1)*(i + 3)
Suppose 4*h - 17 = 3*f, 3*h + f - 3 = -0*f. Suppose h*n**3 - 2 + 3 + 3*n + n**2 + 2*n**2 - n**3 = 0. Calculate n.
-1
Let x be (-2)/(-11) + (-40)/(-22). Let m = 4 - x. Factor 1/2*w**3 - 1/2*w**m + 0*w + 0.
w**2*(w - 1)/2
Let m(w) = -w**2 + 8*w + 4. Let h = -16 + 24. Let k be m(h). Let i**4 - 2*i**5 + 0*i**k - 3*i**4 = 0. What is i?
-1, 0
Let a(n) be the second derivative of -n**7/7560 + n**6/1080 - n**5/360 + 5*n**4/12 + 5*n. Let g(f) be the third derivative of a(f). Find i such that g(i) = 0.
1
Let d(q) be the third derivative of -q**5/80 - 7*q**4/32 - 3*q**3/4 + 38*q**2. Factor d(z).
-3*(z + 1)*(z + 6)/4
Let u(k) = 2*k + 22 - 3*k - 12. Let v be u(7). Factor -2 - 4*l + 2*l - l**3 - l**2 + v + 3*l.
-(l - 1)*(l + 1)**2
Let c = -15 - -17. Let -6/7 - 9/7*x**3 + 12/7*x**c + 3/7*x = 0. Calculate x.
-2/3, 1
Let m(y) be the third derivative of -y**5/120 + y**3/3 + y**2. Determine l, given that m(l) = 0.
-2, 2
Let g = 7 + -7. Let k(i) be the third derivative of 0 + 0*i - 1/120*i**6 + g*i**3 + 1/24*i**4 + 0*i**5 + i**2. Factor k(j).
-j*(j - 1)*(j + 1)
Let l(f) be the first derivative of 2/25*f**5 + 0*f**2 + 3 - 1/10*f**4 + 1/15*f**6 - 2/15*f**3 + 0*f. Factor l(v).
2*v**2*(v - 1)*(v + 1)**2/5
Let w(g) be the second derivative of -g**7/840 + g**3/6 + g. Let a(k) be the second derivative of w(k). Suppose a(b) = 0. Calculate b.
0
Let y be (132/605 + (-2)/(-11))/1. What is i in 0 + 4/5*i + y*i**2 - 2/5*i**3 = 0?
-1, 0, 2
Let i(f) be the second derivative of -65*f**4/12 - 20*f**3 + 10*f**2 + 12*f. Factor i(p).
-5*(p + 2)*(13*p - 2)
Let v(q) be the first derivative of 3/2*q**2 - 2 + 1/6*q**5 + 0*q - 7/12*q**4 + 2/3*q**3. Let b(l) be the second derivative of v(l). Let b(t) = 0. What is t?
2/5, 1
Let h be (-3)/9 - 2432/90. Let w = h + 139/5. Factor 0 + 2/9*y**3 + 2/9*y**2 - w*y.
2*y*(y - 1)*(y + 2)/9
Let i(j) = -j**4 + j**3 - j**2 + j + 1. Let r(c) = c**4 + c**2 - 5 - 7*c**3 + 1 - 5*c + 2*c**4. Let o(f) = 4*i(f) + r(f). Factor o(a).
-a*(a + 1)**3
Let a(h) = h + 7. Let i be a(0). Factor -y**3 + i*y**3 - 3*y**4 + 0*y**4.
-3*y**3*(y - 2)
Find x such that -8/7*x + 12/7*x**4 + 0 - 32/7*x**3 + 4*x**2 = 0.
0, 2/3, 1
Let m(a) = a**2 + a. Let q be m(2). Let l(c) be the third derivative of -1/15*c**5 + 0*c + 1/60*c**q - c**2 - 1/12*c**4 + 0 + 2/3*c**3. What is b in l(b) = 0?
-1, 1, 2
Let t = -257483/458337 + 3/8041. Let x = 2/19 - t. Solve -2/3*s + 0 + 4/3*s**2 - x*s**3 = 0 for s.
0, 1
Let l be (-8 - 826/(-105)) + 23/60. Determine i, given that 0 - 1/4*i - l*i**2 = 0.
-1, 0
Let h(r) be the second derivative of 3*r**5/50 - 3*r**4/20 + 3*r**2/10 - 23*r. Solve h(d) = 0 for d.
-1/2, 1
Let b be 10/(-8) - ((-3861)/88)/27. Factor b*c**4 - 3/4 + 3/8*c**2 - 9/8*c + 9/8*c**3.
3*(c - 1)*(c + 1)**2*(c + 2)/8
Let w(z) be the second derivative of z**6/6 + 7*z**5/4 + 15*z**4/2 + 50*z**3/3 + 20*z**2 + 12*z + 3. Suppose w(p) = 0. What is p?
-2, -1
Let x(m) = -m**2 + 2*m + 15. Let p be x(5). Let i(u) be the first derivative of p*u**2 + 0*u**5 + 1/4*u**4 - 1/6*u**6 + 0*u + 0*u**3 - 1. Factor i(n).
-n**3*(n - 1)*(n + 1)
Let u(p) = -p + 1. Let a be u(-2). Factor -2 + 3*q**5 - 4*q**3 - 51*q**2 + 53*q**2 - 2*q**5 + a*q.
(q - 1)**3*(q + 1)*(q + 2)
Let t(h) be the first derivative of -h**6/900 - h**5/100 - h**4/30 - 2*h**3/3 - 1. Let l(m) be the third derivative of t(m). Factor l(o).
-2*(o + 1)*(o + 2)/5
Let k(b) be the first derivative of -5*b**4/4 + 5*b**2/2 - 7. Factor k(h).
-5*h*(h - 1)*(h + 1)
Let k(p) be the second derivative of -1/10*p**5 + 1/6*p**4 + 4*p + 1/3*p**3 - p**2 + 0. Let k(i) = 0. Calculate i.
-1, 1
Let p(a) be the third derivative of a**8/50400 + a**7/12600 - a**5/60 + 4*a**2. Let q(b) be the third derivative of p(b). Factor q(j).
2*j*(j + 1)/5
Factor 1/6 - 1/12*c - 1/6*c**2 + 1/12*c**3.
(c - 2)*(c - 1)*(c + 1)/12
Let m(b) be the third derivative of -b**9/68040 + b**7/11340 - b**4/6 + 4*b**2. Let n(x) be the second derivative of m(x). Find y such that n(y) = 0.
-1, 0, 1
Suppose 4*s + 4 = -8, 3*k + 3*s = 27. Let d be k/(-6) - 10/(-4). Let -9/4*x**2 - 11/4*x**4 + 0 + 3/4*x**5 + d*x + 15/4*x**3 = 0. What is x?
0, 2/3, 1
Let s(b) = b**2 + 2*b - 5. Let l be s(-4). Solve -9*t**4 - 9*t**l + 6 + 15*t - 8*t**4 + 6*t**2 - 3*t**3 + 5*t**4 - 3*t**5 = 0 for t.
-2, -1, 1
Let u(n) be the second derivative of n**7/630 + n**6/180 - n**5/15 + n**4/12 + 8*n. Let r(f) be the third derivative of u(f). Solve r(h) = 0 for h.
-2, 1
Determine c, given that 0 + 2/5*c**2 - 2/5*c = 0.
0, 1
Let q(v) be the first derivative of 4*v**5/5 + v**4 - 4*v**3/3 - 2*v**2 + 10. Factor q(x).
4*x*(x - 1)*(x + 1)**2
Let w(x) be the third derivative of -x**5/12 + 16*x**2. Factor w(f).
-5*f**2
Let w(q) be the second derivative of -q**6/50 + q**4/10 - 3*q**2/10 - 19*q. Let w(j) = 0. Calculate j.
-1, 1
Let c(r) = 6*r. Let u(p) = p**2 + 11*p. Let o(d) = 5*c(d) - 3*u(d). Factor o(t).
-3*t*(t + 1)
Suppose 7*r = 10*r - 12. Let k(n) be the third derivative of 0*n - 1/90*n**5 - 4/315*n**7 - 1/36*n**6 + 0 + 0*n**3 + 0*n**r + 2*n**2. Solve k(s) = 0 for s.
-1, -1/4, 0
Let d(c) be the second derivative of -c**6/195 - c**5/65 + 20*c. Factor d(q).
-2*q**3*(q + 2)/13
Factor -33*a**3 + 7*a**2 - 34*a**2 + 3 - 3*a + 0 - 6*a**4 - 6*a**4.
-3*(a + 1)**3*(4*a - 1)
Suppose 2*c = 4*t + 2, -2*t + 20 + 4 = 4*c. Factor 3*v**2 + 2*v - 2*v**2 - 1 + 2*v**t - 4*v**2.
-(v - 1)**2
Factor -34/15*x**2 - 8/15 + 8/3*x + 8/15*x**3.
2*(x - 2)**2*(4*x - 1)/15
Let f(b) be the second derivative of b**9/22680 + b**4/12 + 2*b. Let s(p) be the third derivative of f(p). Factor s(x).
2*x**4/3
Let c(p) = 4*p**4 - 9*p**3 + 5*p**2 + 23*p - 9. Let u(z) = 2*z**4 - 4*z**3 + 2*z**2 + 12*z - 4. Let h(g) = -4*c(g) + 7*u(g). Suppose h(m) = 0. Calculate m.
-1, 1, 2
Factor 0 - 4/3*y + 14/9*y**2.
2*y*(7*y - 6)/9
Let x(l) = -11*l**4 + l**3 + 11*l**2 - 11*l. Let b(g) = 6*g**4 - 6*g**2 + 6*g. Let z(v) = 5*b(v) + 3*x(v). Factor z(q).
-3*q*(q - 1)**2*(q + 1)
Let b = 16/21 + 4/7. Let x(r) be the first derivative of 2*r + 9/2*r**2 + 4 + b*r**3. Factor x(j).
(j + 2)*(4*j + 1)
Let x(u) be the first derivative of -u**7/700 + u**6/450 + u**5/100 - u**4/30 - 2*u**3 - 6. Let j(l) be the third derivative of x(l). Let j(k) = 0. Calculate k.
-1, 2/3, 1
Suppose 6*a - 8 = 3*i + 2*a, 5*i + 4 = 2*a. Factor i + 12/7*n - 44/7*n**2 - 16/7*n**3.
-4*n*(n + 3)*(4*n - 1)/7
Let k(x) be the second derivative of -1/5*x**2 - 5*x + 0 - 1/10*x**4 - 4/15*x**3. Factor k(o).
-2*(o + 1)*(3*o + 1)/5
Let i = 382/189 + -16/27. Suppose 4/7 + 8/7*y**2 - i*y - 2/7*y**3 = 0. Calculate y.
1, 2
Solve 0*o - o**4 + 0 + 0*o**2 + 1/2*o**3 = 0.
0, 1/2
Suppose 0 = 4*k - 3*s - 13, 0 = -3*k + 4*k + 3*s - 7. Let -108*w**2 - 294*w**5 + 922/3*w**3 + 16/3 + 308/3*w**k - 40/3*w = 0. What is w?
-1, -2/9, 2/7, 1
Let h be -1*1/(-1)*5. Suppose -h*w = 4*d - 8, w + 3*w = 0. Determine n, given that -n**2 - n**2 + 2*n**4 + 2*n - 2*n**3 + 0*n**d = 0.
-1, 0, 1
Let w be (5/2 + (-48)/16)/(-1). Solve 0 + w*k**2 - 1/4*k**3 - 1/4*k = 0.
0, 1
Suppose -14*f = -3*f. Factor 0 - 1/5*b**3 - 1/5*b**2 + f*b.
-b**2*(b + 1)/5
Let k(p) be the first derivative of -p**6/6 - p**5/3 - p**4/12 + p**3/9 + 26. Suppose k(c) = 0. What is c?
-1, 0, 1/3
Let z be 4 + (1 + 2 - 0) - 3. Factor -2/9*b**3 + 10/9*b - 2/3*b**2 - 4/9 + 2/9*b**z.
2*(b - 1)**3*(b + 2)/9
Find f such that 125*f**3 - f + f - 122*f**3 - 3*f**5 = 0.
-1, 0, 1
Factor -8/5 + 0*m**2 + 4/5*m**3 - 12/5*m.
4*(m - 2)*(m + 1)**2/5
Factor -4*w**2 - 9 - w**2 - w**2 + 9*w**2 + 6*w.
3*(w - 1)*(w + 3)
Let y be 0*(-1)/(-3) + 2. Factor 2*s**y - 4*s**2 + 2*s**2 + 12 - 3*s**2.
-3*(s - 2)*(s + 2)
Solve -c**2 - c + 7*c**2 + 7 - 9 = 0 for c.
-1/2, 2/3
Let f(w) be the third derivative of -w**6/24 + 7*w**5/60 - w**4/12 - 8*w**2. Factor f(a).
-a*(a - 1)*(5*a - 2)
Let b(x) be the second derivative of x**9/30240 + x**8/13440 + x**4/3 + x. Let p(g) be the third derivative of b(g). Factor p(a).
a**3*(a + 1)/2
Let c(r) be the first derivative of r**4/4 + 9. Factor c(b).
b**3
Let s(t) be the first derivative of t**6/360 - t**5/60 + t**4/24 + t**3 - 3. Let n(f) be the third derivative of s(f). Solve n(q) = 0.
1
Factor -1/7*i**5 + 1/7*i**2 + 0*i + 3/7*i**4 - 3/7*i**3 + 0.
-i**2*(i - 1)**3/7
Solve 10/9*o**3 + 0*o + 2/9*o**5 + 8/9*o**4 + 4/9*o**2 + 0 = 0 for o.
-2, -1, 0
Let l = -14 + 20. Let g be 4/(l/(-3)) + 4