tive of -n**5/45 + 5*n**4/54 + 11*n**3/27 + 4*n**2/9 - 2*n. Solve k(r) = 0.
-1, -1/2, 4
Let s be (-1 - -2)*(-8)/24. Let k = 0 - s. Factor -1/3*a**3 + 2/3*a**2 - k*a + 0.
-a*(a - 1)**2/3
Suppose -5*k + 16 = -9. Let f = k - 3. Factor -d**4 - d**f + d**5 - 2*d**2 + 4*d**2 - d**3.
d**2*(d - 1)**2*(d + 1)
Let a(s) = 11*s**3 - 18*s**2 + 7*s - 5. Let o(w) = -w - 5*w**3 - w - 2*w + 9*w**2 + 2. Let q(u) = -2*a(u) - 5*o(u). Factor q(r).
3*r*(r - 2)*(r - 1)
Let b(s) = 7*s**4 - 4*s**3 + 2*s**2 + 5*s + 5. Let c(f) = 4*f**4 - 2 + 3*f - 2*f**3 + f**2 + 4 + 1. Let w(r) = -3*b(r) + 5*c(r). What is u in w(u) = 0?
0, 1
Let f(v) be the second derivative of v**7/48 - 3*v**6/80 + v**5/80 - 23*v. Factor f(g).
g**3*(g - 1)*(7*g - 2)/8
Let o(y) be the third derivative of y**7/420 + y**6/60 + y**5/20 + y**4/12 + y**3/3 - 3*y**2. Let g(a) be the first derivative of o(a). Factor g(p).
2*(p + 1)**3
Let w(v) = v**2 - 12*v + 7. Let c be w(9). Let d be 4*(161/c)/(-7). Find n, given that 2/5 + d*n**2 - 3/5*n**3 - 13/5*n - 9/5*n**4 = 0.
-2, 1/3, 1
Let t(n) = n**3 + 8*n**2. Let f = 13 + -7. Let l(j) = 21*j**2 + 6*j**2 - 10*j**2 + 2*j**3. Let i(p) = f*l(p) - 13*t(p). Let i(w) = 0. Calculate w.
-2, 0
Factor 0 + 1/4*c**5 - 1/4*c**3 - 1/4*c**4 + 0*c + 1/4*c**2.
c**2*(c - 1)**2*(c + 1)/4
Let m(o) = -6*o + 1. Let n be m(-2). Let a be (n - 8)*(0 - -1). Factor a*y**4 + 4*y**4 + 0*y**5 - 6*y**5 - 3*y**2.
-3*y**2*(y - 1)**2*(2*y + 1)
Suppose -17*i = -14*i - 9. Let u(z) be the first derivative of -2/5*z**5 + 1 + 5/4*z**4 + 1/2*z**2 + 0*z - 4/3*z**i. Factor u(o).
-o*(o - 1)**2*(2*o - 1)
Let z(g) be the first derivative of -33*g**5/40 + 9*g**4/4 - 15*g**3/8 + 3*g**2/8 + 11. Suppose z(q) = 0. What is q?
0, 2/11, 1
Suppose -w = -0 - 2. Let l be (-6)/12 - 14/(-4). Factor w*z**2 - l + 3.
2*z**2
Let -3/2 - 3/8*n**2 + 15/8*n = 0. Calculate n.
1, 4
Let b be 0/((-14)/(-4)*32/56). Let r(u) be the second derivative of 1/60*u**4 - 1/15*u**3 - 3*u + 1/10*u**2 + b. Solve r(q) = 0 for q.
1
Let j(o) be the third derivative of -1/315*o**7 - 1/90*o**6 + 0*o + 0*o**5 + 1/18*o**4 + 1/9*o**3 + 3*o**2 + 0. Factor j(k).
-2*(k - 1)*(k + 1)**3/3
Solve 8/5*p + 0 + 2/5*p**4 + 0*p**2 - 6/5*p**3 = 0 for p.
-1, 0, 2
Let j(a) be the second derivative of -a**6/165 - a**5/110 + a**4/66 + a**3/33 + 2*a. Factor j(q).
-2*q*(q - 1)*(q + 1)**2/11
Let l be (-280)/(-88) - (-4)/(-22). Let j be (-2)/4 + (-3)/(-6). Let -y**3 + y + j*y**l - 2*y**2 + 2*y**3 = 0. Calculate y.
0, 1
Let b(r) be the second derivative of -7/60*r**6 + 0*r**2 + 0 + 0*r**3 + 1/8*r**5 + 4*r + 1/12*r**4. Factor b(n).
-n**2*(n - 1)*(7*n + 2)/2
Let g(j) = 5*j - 2. Let r be g(2). Let m = -5 + r. Factor -6*c**2 - 1 - 9/2*c - 5/2*c**m.
-(c + 1)**2*(5*c + 2)/2
Let y(h) be the third derivative of -h**7/1365 - h**6/780 + h**5/390 + h**4/156 - 30*h**2. Factor y(n).
-2*n*(n - 1)*(n + 1)**2/13
Let n(j) = -2*j**2 + 4*j - 2. Let o be n(1). Let q(p) be the second derivative of -1/27*p**3 + o*p**2 + 2*p + 0 + 1/54*p**4. Find t such that q(t) = 0.
0, 1
Let q(t) be the second derivative of -t**4/30 + t**2/5 - 4*t. Solve q(n) = 0 for n.
-1, 1
Let a = 9 - 6. Let -7*s**2 - a + 0*s**4 + 9*s**4 + 3 - 2*s = 0. Calculate s.
-2/3, -1/3, 0, 1
Suppose -2 = -4*m + 5*k, -10 = -m - 3*k - 1. Factor -1/2*c**2 + 0 + 1/2*c**4 + 1/2*c**m - 1/2*c.
c*(c - 1)*(c + 1)**2/2
Solve -4/3 + 5/3*x**2 + 8/3*x = 0.
-2, 2/5
Let o = 327/973 - 7/139. Factor -o*l - 2/7*l**2 + 0.
-2*l*(l + 1)/7
Factor 51*t**2 - 27/2*t**3 - 57/2*t - 9.
-3*(t - 3)*(t - 1)*(9*t + 2)/2
Factor -w + 2 - 4*w + 3*w + 5*w - w**3.
-(w - 2)*(w + 1)**2
Let a be (24/(-2))/4 - -4. Let r be 0/(0 - -1)*a. Factor r*q + 0 + 2/5*q**3 + 2/5*q**2.
2*q**2*(q + 1)/5
What is j in 4*j**2 - 8*j**4 - 16*j**3 + 8*j**4 + 7*j**4 = 0?
0, 2/7, 2
Let t(r) = r**3 + r**2 + 1. Let m(o) = 11*o**3 + 11*o**2 - 5*o + 1. Let u(n) = m(n) - 6*t(n). Factor u(v).
5*(v - 1)*(v + 1)**2
Let f be 4/2 + (-48)/(-12). Let g(i) be the second derivative of 0*i**2 + 0 + 1/50*i**5 - 1/105*i**7 - 1/30*i**4 + 1/75*i**f + 3*i + 0*i**3. Factor g(x).
-2*x**2*(x - 1)**2*(x + 1)/5
Solve 16*d**2 - 8*d**4 + 9*d - 24*d**3 - 8 + 3*d**5 + 16*d**5 - 7*d**5 + 3*d = 0 for d.
-1, 2/3, 1
Suppose -5 = -t - 0*t. Let a = t - 5. Factor 0*y**4 - 2*y**2 + a*y**2 + 2*y**4.
2*y**2*(y - 1)*(y + 1)
Let p be 42/(-2)*10/(-15). Let c = -27/2 + p. Factor -1/2*w**3 + 3/2*w**2 - 3/2*w + c.
-(w - 1)**3/2
Let t be (2/(-280))/((-5)/10). Let g(v) be the second derivative of -1/35*v**6 + 0*v**2 - t*v**5 + 0*v**3 + 0 - v + 0*v**4. Factor g(h).
-2*h**3*(3*h + 1)/7
Let b(x) = -x**2 - 7*x - 1. Let l be b(-7). Let v be (-2 - l)/(6/(-30)). Determine w, given that 0*w + 1/4*w**2 - 1/4*w**4 + 0 - 1/4*w**3 + 1/4*w**v = 0.
-1, 0, 1
Suppose -8 = -2*k - 2*k - c, -4*k + 8 = -5*c. Factor -1/4*h**k + 0 + 0*h.
-h**2/4
Let l(f) be the second derivative of -f**5/50 + 7*f**4/30 - f**3 + 9*f**2/5 - 5*f. Factor l(n).
-2*(n - 3)**2*(n - 1)/5
Let p(y) = -9*y**4 - 17*y**3 - 3*y**2 + 5*y + 5. Let f(k) = 28*k**4 + 52*k**3 + 8*k**2 - 16*k - 16. Let w(l) = 5*f(l) + 16*p(l). Factor w(z).
-4*z**2*(z + 1)*(z + 2)
Let j(w) = -36*w**2 + 360*w**2 - 26*w + 70*w. Let d(s) = 59*s**2 + 8*s. Let i(k) = 28*d(k) - 5*j(k). Factor i(y).
4*y*(8*y + 1)
Let i(y) be the first derivative of y**6/2 - 6*y**5/5 - 9*y**4 - 14*y**3 - 15*y**2/2 - 3. Factor i(m).
3*m*(m - 5)*(m + 1)**3
Let w(h) = h**3 + h**2 - h - 1. Let y(g) = -g**4 + 10*g**3 + 12*g**2 - 10*g - 11. Let z(m) = 22*w(m) - 2*y(m). Determine i, given that z(i) = 0.
-1, 0, 1
Let b = 142 + -139. Factor -1/2*v**2 - 1/2*v**b - 1/4*v**5 - 1/4 + 3/4*v + 3/4*v**4.
-(v - 1)**4*(v + 1)/4
Let z = 12 - 9. Let g(m) be the third derivative of 0*m - m**2 + 1/9*m**z + 0*m**4 - 1/90*m**5 + 0. Factor g(s).
-2*(s - 1)*(s + 1)/3
Let a be -7*(1 + 1) - 0. Let y = a - -21. Factor -4*x + 18*x**2 + 8 - 9*x - y*x + x**4 - 7*x**3.
(x - 2)**3*(x - 1)
Suppose -8*d**3 + 4*d**4 - 10*d**2 + 0*d**3 - 2*d**2 = 0. Calculate d.
-1, 0, 3
Let b(w) = 2*w**3 - 14*w**2 - w + 10. Let k be b(7). Let t(j) be the first derivative of 1/2*j**k - 1 + 3/4*j**2 + 1/8*j**4 + 1/2*j. Factor t(c).
(c + 1)**3/2
Let a = 18 - 18. Let d(n) be the first derivative of -1/18*n**4 + 1 - 4/45*n**5 + 0*n + a*n**2 + 2/27*n**3. Factor d(c).
-2*c**2*(c + 1)*(2*c - 1)/9
Let j(n) be the second derivative of n**5/80 + n**4/48 - n**3/24 - n**2/8 + 9*n. Suppose j(z) = 0. What is z?
-1, 1
Let g(v) = 3*v**2 + 3*v + 2. Let u(c) = -c**2 - c - 1. Let w(j) = 2*g(j) + 4*u(j). Determine f, given that w(f) = 0.
-1, 0
Let s(m) be the second derivative of -1/21*m**3 - 1/14*m**5 + 0 + 3*m + 0*m**2 - 1/7*m**4. Factor s(u).
-2*u*(u + 1)*(5*u + 1)/7
Factor 1/4*l**4 - 1/4*l + 1/2*l**3 - 1/2*l**2 - 1/4*l**5 + 1/4.
-(l - 1)**3*(l + 1)**2/4
Let h be 361/114 + (-5)/2. Let f**5 + 1/3*f + h + 4/3*f**4 - 4/3*f**3 - 2*f**2 = 0. What is f?
-1, 2/3, 1
Let i(t) be the second derivative of t**6/120 + t**5/15 + 5*t**4/24 + t**3/3 - 2*t**2 - 2*t. Let a(f) be the first derivative of i(f). Solve a(y) = 0.
-2, -1
Let o(m) = -m + 29. Let y be o(29). Factor y + 1/4*z**5 + 1/4*z**4 - 3/4*z**3 + 1/2*z - 1/4*z**2.
z*(z - 1)**2*(z + 1)*(z + 2)/4
Let p(i) be the second derivative of 0 - 4/21*i**4 - 8/21*i**3 + 0*i**2 + 3*i - 1/35*i**5. Factor p(u).
-4*u*(u + 2)**2/7
Let h(m) be the third derivative of -m**5/30 + m**4/12 + 2*m**3/3 + 15*m**2. Find y, given that h(y) = 0.
-1, 2
Let m be (0/(0 - -1))/2. Let z(t) be the first derivative of 1/4*t**4 + m*t - 2 + 0*t**3 - 1/2*t**2. Determine l so that z(l) = 0.
-1, 0, 1
Let x(y) be the first derivative of -3*y**8/56 + y**7/35 + y**6/12 + y**5/30 + 2*y**2 + 4. Let g(t) be the second derivative of x(t). Factor g(m).
-2*m**2*(m - 1)*(3*m + 1)**2
Factor 8*g**4 + 0*g**3 - 4*g**5 + 0*g**3 - 4*g**3.
-4*g**3*(g - 1)**2
Factor -4/5*q**3 + 0*q**2 - 2/5*q**4 + 0 + 0*q.
-2*q**3*(q + 2)/5
Let b be 1/((-3)/(-9)) + (-5)/5. Suppose 2/3*q**b + 4/3*q + 2/3 = 0. What is q?
-1
Let b(k) = -5*k**3 + 11*k**2 - 11*k - 3. Let t(u) = 3*u**3 - 7*u**2 + 7*u + 2. Let o(g) = -5*b(g) - 8*t(g). Factor o(d).
(d - 1)*(d + 1)**2
Let f(c) = c**4 + c**3 - c**2 + 1. Let n(k) = -6*k**4 - 18*k**3 + 7*k**2 - 7. Let t(a) = 14*f(a) + 2*n(a). Solve t(b) = 0 for b.
0, 11
Let t(l) be the first derivative of -1 - 1/4*l**2 - 1/6*l**3 + 0*l. Find b, given that t(b) = 0.
-1, 0
Let w = -66 + 68. Let f be ((-4)/(-21))/((-1