*u(z). Find f, given that k(f) = 0.
33
Let z(o) be the second derivative of -o**5/40 - o**4/12 + 5*o**3/12 + 3*o**2/2 - 6*o - 2. Suppose z(x) = 0. Calculate x.
-3, -1, 2
Let r(x) be the third derivative of -x**6/60 - x**5/15 - x**4/12 - x**2 - 5*x. Factor r(t).
-2*t*(t + 1)**2
Let f(c) be the third derivative of -c**10/15120 - c**9/1890 - c**8/1120 + 2*c**4/3 - 43*c**2. Let z(q) be the second derivative of f(q). Solve z(y) = 0.
-3, -1, 0
Suppose 4*d - 3 = -n + 5, 5 = 3*d + n. Let h be (d/(-60))/((-1)/4). Factor h*l**3 + 1/5 + 3/5*l + 3/5*l**2.
(l + 1)**3/5
Let l(x) = -7*x**2 + 66*x + 73. Let s(f) = 3*f**2 - 33*f - 36. Let o(h) = 6*l(h) + 13*s(h). Find k, given that o(k) = 0.
-10, -1
Suppose 1/7*d**4 + 1/7*d**5 + 0*d**2 + 0*d + 0 - 6/7*d**3 = 0. What is d?
-3, 0, 2
Let d = -4194 - -8391/2. Find m such that 0*m - d*m**3 + 0 - 3/4*m**2 - 3/4*m**4 = 0.
-1, 0
Suppose 2*c + 5*p = -515, -2*p = 2*c - 3*p + 545. Let g be (-5 - -1)/(-20) - 246/c. Factor -g*k**2 + 4/9*k + 0 - 2/9*k**4 + 8/9*k**3.
-2*k*(k - 2)*(k - 1)**2/9
Factor 13*d - 1/5*d**3 - 13/5*d**2 - 51/5.
-(d - 3)*(d - 1)*(d + 17)/5
Suppose 846 = -53*y + 952. Determine u, given that -1/7*u**y - 6/7*u - 8/7 = 0.
-4, -2
Let k = 13 - 7. Let o(z) = -z**3 + 5*z**2 + 5*z + 8. Let q be o(6). Factor -2*m**3 + q*m - 8 + 2 + k.
-2*m*(m - 1)*(m + 1)
Find n such that 11258/7*n**2 - 2040*n + 504 - 512/7*n**3 + 6/7*n**4 = 0.
1/3, 1, 42
Let a(g) be the second derivative of 7/60*g**5 + 0*g**3 + 0*g**2 + 0 - 1/90*g**6 + 0*g**4 + 4*g. Factor a(q).
-q**3*(q - 7)/3
Suppose 15*l = -2*w + 12*l - 3, -12 = w + 5*l. Factor 14*o - 3*o - 5*o**2 + 5*o**w - 21*o.
5*o*(o - 2)*(o + 1)
Let g(w) = -2*w + 31. Let y be g(17). Let v be (4 + -6 - y)*0. Suppose -4/3*a + v + 2/3*a**2 = 0. What is a?
0, 2
Let w(l) be the first derivative of l**5/15 + l**4 + 16*l**3/3 + 32*l**2/3 + 18. Find v such that w(v) = 0.
-4, 0
Let b(l) be the third derivative of 0*l + 1/200*l**6 + 0*l**3 + 1/150*l**7 - 1/336*l**8 + 0 - 7/300*l**5 + 1/60*l**4 + 4*l**2. Suppose b(u) = 0. What is u?
-1, 0, 2/5, 1
Solve -24/5*l**4 + 44/5*l**3 + 0 + 168/5*l**2 + 98/5*l + 2/5*l**5 = 0.
-1, 0, 7
Let o(r) = 2*r**2 - 7*r - 4. Let h(l) = -3*l**2 + 13*l + 8. Let x = 61 - 58. Let j(a) = x*h(a) + 5*o(a). Factor j(q).
(q + 2)**2
Let v = -681 + 683. Factor -1/7*d**4 + 3/7*d**3 - 3/7*d + 2/7 - 1/7*d**v.
-(d - 2)*(d - 1)**2*(d + 1)/7
Let j = -747 + 749. Let n(q) be the third derivative of -4*q**j - 1/20*q**5 - 8*q**3 + q**4 + 0 + 0*q. Factor n(w).
-3*(w - 4)**2
Let j(l) be the second derivative of -l**4/21 - 20*l**3/3 - 238*l. Find i such that j(i) = 0.
-70, 0
Let x(r) = -74 - r**3 + 585*r - 575*r + 8*r**2 + 0*r**3. Let w(a) = -a**3 - a**2 - a - 1. Let m(f) = -6*w(f) + 3*x(f). Factor m(h).
3*(h - 2)*(h + 6)**2
Let f(b) = -b**2 - 88*b - 909. Let z be f(-76). Factor 2*y + 2*y**2 + 2/3*y**z + 2/3.
2*(y + 1)**3/3
Let h(b) be the third derivative of b**5/60 + b**4/3 + b**3 + 6*b**2. Let u be h(-8). Find k, given that 3*k + 14*k + 9*k + u*k + 64 + 4*k**2 = 0.
-4
Let c = -566 - -568. Let g(s) be the first derivative of -46/15*s**5 + 7/9*s**6 + 9/2*s**4 + 8 + 0*s - 26/9*s**3 + 2/3*s**c. Determine j so that g(j) = 0.
0, 2/7, 1
Let y(h) be the first derivative of h**3/12 + h**2 - 33*h/4 - 234. Factor y(t).
(t - 3)*(t + 11)/4
Factor -12/7*i - 16/7 + 6/7*i**2 + 2/7*i**3.
2*(i - 2)*(i + 1)*(i + 4)/7
Let t = 1857 - 1857. Factor t*d + 0 - 2/3*d**2 + 8/3*d**3 - 2*d**4.
-2*d**2*(d - 1)*(3*d - 1)/3
Let u = 118 - 110. Let -5*t**2 + 8*t + u*t - 4*t - 2*t - 5 = 0. Calculate t.
1
Let 4*c**2 + 0*c - 10/3*c**3 + 0 - 2/3*c**4 = 0. What is c?
-6, 0, 1
Let a(h) = -6*h - 84. Let w be a(-14). Let i be (-8)/(-12) - (1 + -1). Let w - 5/3*k**4 + i*k**3 - 7/3*k**5 + 0*k**2 + 0*k = 0. What is k?
-1, 0, 2/7
Let g(h) = h**3 - 3*h**2 - 2*h - 6. Let z be g(4). Factor 10*l - 33 + 29 + 6*l**2 + 0*l**z.
2*(l + 2)*(3*l - 1)
Let u be 3864/414 - (-14)/(-6). Let k(m) be the first derivative of 0*m + m**3 + 13/16*m**4 + 1/24*m**6 + 3/10*m**5 + 1/2*m**2 - u. What is h in k(h) = 0?
-2, -1, 0
Let h(r) = -r**4 + r**3 + r**2 + 5*r. Let b(s) = -5*s**4 + 6*s**3 + 5*s**2 + 27*s. Let o(y) = 6*b(y) - 33*h(y). Suppose o(g) = 0. Calculate g.
-1, 0, 1
Let k(b) be the first derivative of -b**3/4 + 9*b**2 + 75*b/4 - 165. Find y, given that k(y) = 0.
-1, 25
Let c = -587 - -589. Let r(o) be the second derivative of -1/10*o**c - 1/60*o**4 - o + 0 - 1/15*o**3. What is s in r(s) = 0?
-1
Let r(o) be the second derivative of -o**7/168 + o**6/60 + 9*o**5/40 + 2*o**4/3 + 23*o**3/24 + 3*o**2/4 - 22*o. Factor r(m).
-(m - 6)*(m + 1)**4/4
Let r(f) be the first derivative of -10 - 1/3*f**4 - f**2 - 4/3*f**3 - 1/30*f**5 + 0*f. Let x(w) be the second derivative of r(w). Factor x(v).
-2*(v + 2)**2
Let l(y) be the first derivative of y**5/150 - y**4/30 - 4*y**2 + 23. Let x(r) be the second derivative of l(r). Factor x(k).
2*k*(k - 2)/5
Suppose o - 4*w - 6 = 0, -2*w + 7 = 2*o - 5*w. Factor o*m**2 - m**3 + 3*m**5 - 11 - 7*m**2 + 5*m**4 - 2*m + 11.
m*(m - 1)*(m + 1)**2*(3*m + 2)
Let n = 33 + 83. Factor 2*r**3 - 115*r**5 + 0*r**4 + n*r**5 + 3*r**4.
r**3*(r + 1)*(r + 2)
Let r(b) be the third derivative of 0 - 1/6*b**3 + 1/480*b**6 + 1/60*b**5 - 5*b**2 + 0*b - 1/96*b**4. Factor r(l).
(l - 1)*(l + 1)*(l + 4)/4
Let k(g) be the second derivative of -3*g**5/4 - 13*g**4/24 + 5*g**3/6 + g + 105. Factor k(a).
-a*(5*a - 2)*(6*a + 5)/2
Let g(z) = 15*z + 0*z**3 - 2*z**3 - 100*z**2 + 93*z**2 + 18. Let y(h) = -h**3 + h**2. Let p(b) = g(b) + y(b). Solve p(i) = 0.
-3, -1, 2
Let z = 1794 - 1790. Let a(j) be the second derivative of 1/10*j**5 + 0 - 10*j + 0*j**2 + 1/30*j**6 + 0*j**3 + 1/12*j**z. Find k, given that a(k) = 0.
-1, 0
Let f(k) be the second derivative of -k**7/12 + k**6/12 + 13*k**5/8 + 95*k**4/24 + 25*k**3/6 + 2*k**2 + 9*k + 2. Solve f(u) = 0.
-1, -2/7, 4
Let o be (-3)/2*2222/132. Let b = o + 917/36. Suppose -1/3*i + 5/9*i**2 - b = 0. Calculate i.
-2/5, 1
Let w(i) be the first derivative of i**5/20 - 17*i**4/8 + 107*i**3/4 - 68*i**2 + 64*i - 41. What is n in w(n) = 0?
1, 16
Suppose 0*g - 103 = -2*g + 5*r, 5*g - 300 = 4*r. Let d be (g/24)/((-2)/(-3)). Factor w - 1/2 + 0*w**2 + 1/2*w**d - w**3.
(w - 1)**3*(w + 1)/2
Factor -y**3 + 4*y**3 + 4*y**4 + 3*y - 1625 - 15*y - 18*y**2 - y**4 + 1649.
3*(y - 2)*(y - 1)*(y + 2)**2
Let y(d) be the second derivative of -4*d**5/35 + 26*d**4/7 - 51*d**3/14 + 19*d**2/14 + 2*d + 33. Find w, given that y(w) = 0.
1/4, 19
Factor -13/4 - 7/2*t - 1/4*t**2.
-(t + 1)*(t + 13)/4
Let d(z) be the third derivative of -z**6/30 - 7*z**5/15 - 4*z**4/3 + 32*z**3/3 + 57*z**2. Let d(u) = 0. What is u?
-4, 1
Suppose 5*x - 100 = -4*y, 4*x + 3*y - 100 = -x. Let o be 9/x - ((-18)/(-8) + -2). Factor o*u**2 - 2/5*u**3 + 1/5*u**4 + 0 + 0*u.
u**2*(u - 1)**2/5
Let t(y) = -y**3 - 11*y**2 + 22*y. Let s(f) = -f**3 - 13*f**2 + 24*f. Let u(m) = 2*s(m) - 3*t(m). Factor u(w).
w*(w - 2)*(w + 9)
Let g(l) be the first derivative of 1/24*l**4 - 1/3*l**3 - 37 + 5/12*l**2 + 0*l. Suppose g(i) = 0. What is i?
0, 1, 5
Let v(h) = -h**2 + 8*h + 11. Let z be v(9). Factor -4*i**z + 4*i**4 - 3*i - i + 5*i**3 - i**3.
4*i*(i - 1)*(i + 1)**2
Let v(l) = -2*l**2 - 42*l. Let u be v(-21). Let k(b) be the first derivative of -8/45*b**5 - 4/27*b**3 - 3 + u*b + 1/27*b**6 + 0*b**2 + 5/18*b**4. Factor k(t).
2*t**2*(t - 2)*(t - 1)**2/9
Factor 25*b**2 - 317*b**3 + 165*b**3 + 157*b**3 + 35 - 65*b.
5*(b - 1)**2*(b + 7)
What is m in 2/3*m**3 - 352/3 - 38/3*m**2 + 208/3*m = 0?
4, 11
Let l(i) be the third derivative of i**7/840 + i**6/80 + i**5/20 + 13*i**4/24 + 8*i**2. Let j(w) be the second derivative of l(w). Factor j(q).
3*(q + 1)*(q + 2)
Factor -1/5*p - 5 + 1/5*p**3 + 5*p**2.
(p - 1)*(p + 1)*(p + 25)/5
Suppose -4*o + 4*h = -56, -3*o + 30 = 2*o + 5*h. Suppose 5*v + o = 10*v. Determine f, given that 0*f**v + 0 + 3/7*f**3 + 0*f = 0.
0
Let a(i) = 58*i**3 + 80*i**4 + 0*i**2 + 3*i + 2*i**5 - 14*i**5 + 3 + 47*i**5 + 7*i**2. Let q(w) = -w**3 + w**2 - w - 1. Let r(b) = -a(b) - 3*q(b). Factor r(y).
-5*y**2*(y + 1)**2*(7*y + 2)
What is j in 28*j**2 + 17*j**2 - 5*j**3 + 68*j + 55 + 37*j = 0?
-1, 11
Suppose 9*g = -83 + 101. Let s be (0 + -1)/((-4)/12). Factor s*a + 4*a + 7*a + 4*a**2 - g*a.
4*a*(a + 3)
Factor -5703*i + 0*i**3 + 36 + 5679*i + 7*i**3 - 4*i**3 - 3*i**2.
3*(i - 2)**2*(i + 3)
Let c(r) be th