iven that l(k) = 0.
-4
Let n(a) = -8*a**3 - 40*a**2 - 60*a + 104. Let b(k) = -9*k**3 - 41*k**2 - 60*k + 105. Let v(m) = -4*b(m) + 5*n(m). Solve v(j) = 0 for j.
-5, 1
Let k(v) be the third derivative of -v**6/540 - v**5/90 - v**4/36 + v**3/6 + v**2. Let h(f) be the first derivative of k(f). Factor h(j).
-2*(j + 1)**2/3
Let q(s) = 2*s**3 - 26*s**2 + 24*s - 10. Let v(h) = h**3 - 9*h**2 + 8*h - 3. Let m(y) = -3*q(y) + 10*v(y). Suppose m(u) = 0. Calculate u.
0, 1, 2
Let v(c) be the first derivative of 1 + 2/9*c - 2/27*c**3 + 0*c**2. Factor v(q).
-2*(q - 1)*(q + 1)/9
Let m = 44 + -44. Let f(b) be the first derivative of -2 + 1/8*b**4 + 0*b - 1/6*b**3 + m*b**2. Factor f(v).
v**2*(v - 1)/2
Let h be 23/(-5) + (-30)/(-6). Factor 0 + h*i**2 - 4/5*i.
2*i*(i - 2)/5
Let t(p) be the second derivative of 5*p**4/12 - 20*p**3/3 + 40*p**2 + 9*p. Suppose t(h) = 0. Calculate h.
4
Let k(p) be the second derivative of -3*p**5/80 - p**4/8 + p**3/8 + 3*p**2/4 + 10*p + 1. Determine l so that k(l) = 0.
-2, -1, 1
Factor -2/5*a**5 + 8/5 + 2/5*a**2 - 2/5*a**4 + 2*a**3 - 16/5*a.
-2*(a - 1)**3*(a + 2)**2/5
Let v(y) = 14*y**2 + 50*y + 23. Let d(g) = 5*g**2 + 17*g + 8. Let t(h) = -17*d(h) + 6*v(h). Let x be t(11). Factor -x*s + 5*s + s - 2*s + 2*s**2.
2*s*(s + 1)
Let c(x) be the first derivative of 1/2*x**2 - 1/2*x - 1/6*x**3 + 3. Suppose c(q) = 0. Calculate q.
1
Let d(m) = -3*m**3 + m**2 + 5*m. Let p(n) = -n**3 + n**2 + n. Let o(x) = 2*d(x) - 10*p(x). Let o(j) = 0. What is j?
0, 2
Suppose -s + 2*x + 8 = -2*s, -5*s = 5*x + 40. Let d = s + 11. Factor 3*h**d - 2*h**3 + 0*h**2 - 3*h**2 + 2*h.
h*(h - 2)*(h - 1)
Let l(o) = o + 14. Let n be l(-10). Suppose 0*c + 2/5*c**n - 4/5*c**3 + 0 + 2/5*c**2 = 0. What is c?
0, 1
Let h(o) be the first derivative of 5*o**4/4 - 5*o**2/2 - 26. Factor h(f).
5*f*(f - 1)*(f + 1)
Factor -60*o**3 - 140*o + 0*o**2 + 178*o**2 + 45 - 6*o**4 - 28*o**2 + 11*o**4.
5*(o - 9)*(o - 1)**3
Suppose r - 4*a = -5*a - 1, 3*a - 3 = -5*r. Let q be (2 - 1) + 1/(-1). Find b such that 0*b + q - 2/9*b**r + 2/9*b**2 = 0.
0, 1
Let g = 3 + -5. Let f = 1 - g. Factor 5*u**3 - 4*u**4 + 0*u**3 + 2*u**5 - f*u**3.
2*u**3*(u - 1)**2
Let o(b) be the third derivative of 1/1008*b**8 - 3*b**2 + 0*b**3 + 0*b + 0*b**5 - 1/180*b**6 + 1/72*b**4 + 0*b**7 + 0. Factor o(m).
m*(m - 1)**2*(m + 1)**2/3
Let d(p) = -p**4 - p**2 - p - 1. Let a(u) = -2*u**5 + 10*u**4 + 4*u**3 + 10*u**2 + 8*u + 10. Let o(y) = -a(y) - 10*d(y). Factor o(b).
2*b*(b - 1)**2*(b + 1)**2
Let c be (-9)/(6/2) + 5. Let p be c/7 + (-8)/(-28). Solve -6/7*h - 2/7 - 4/7*h**2 + p*h**3 + 2/7*h**5 + 6/7*h**4 = 0.
-1, 1
Let s(j) = -2*j - 9. Let w be s(-6). Let r be 15/(-10)*(-14)/w. Factor -2*z**2 - z**3 + 8*z + 2*z**2 - r*z.
-z*(z - 1)*(z + 1)
Determine g, given that -2/5*g**2 + 0 + 0*g**3 + 0*g + 2/5*g**4 = 0.
-1, 0, 1
Determine s, given that 12/5*s**2 - 2/5*s**3 + 16/5 - 24/5*s = 0.
2
Let v(i) = i + 6. Let h be v(0). Let r(c) be the first derivative of 4*c - 7*c**2 - 3 - 5/2*c**4 + h*c**3 + 2/5*c**5. What is m in r(m) = 0?
1, 2
Find t such that 0*t + 0*t + 25*t**2 - 26*t**2 + 1 = 0.
-1, 1
Suppose -g = 32 - 7. Let t be 10/g*(2 - 3). Suppose -2/5*z**3 + 0*z - 2/5*z**4 + t*z**2 + 0 + 2/5*z**5 = 0. Calculate z.
-1, 0, 1
Suppose -2*i = -5*c + 2*i + 22, 3*i = -9. Suppose -5*v + 4 = -j + 17, 4*j + 3*v = 6. Factor 2/5*l + 0*l**c - 2/5*l**j + 0.
-2*l*(l - 1)*(l + 1)/5
Suppose 125*q**4 - q + q**2 - 123*q**4 + q**5 - 3*q**2 = 0. What is q?
-1, 0, 1
Let o(w) be the second derivative of w**7/357 - 2*w**6/85 + 4*w**5/85 + w**4/51 - 3*w**3/17 + 4*w**2/17 + 25*w. Solve o(r) = 0 for r.
-1, 1, 4
Suppose -t + 5 = 4*d, -4*t = -2*d + 2 + 14. Let h(j) be the first derivative of -2 - 1/3*j + 1/3*j**d + 1/15*j**5 - 1/6*j**4 + 0*j**3. What is k in h(k) = 0?
-1, 1
Suppose -w + 5*m = 3*w - 5, 5*w - 4 = 4*m. Suppose 4*v = 5*p + 77 - 83, -2*v = -5*p + 8. What is r in 0 + w*r - 1/6*r**3 + 1/6*r**p = 0?
0, 1
Let f(h) be the second derivative of -h**5/5 - h**4 + 18*h. Factor f(s).
-4*s**2*(s + 3)
Let u(t) be the first derivative of t**6/40 - 3*t**4/8 - t**3 + 5*t**2/2 + 2. Let g(j) be the second derivative of u(j). Let g(v) = 0. What is v?
-1, 2
Let z(v) = 3*v - 1. Let r be z(2). Suppose 2*p + 6 = r*p. Factor -l + l**3 + 0*l**2 - l**2 - l**4 + 2*l**p.
-l*(l - 1)**2*(l + 1)
Let b(d) be the second derivative of d**6/150 + d**5/50 - d**4/20 + 15*d. Factor b(v).
v**2*(v - 1)*(v + 3)/5
Let s(z) be the first derivative of -3/5*z**5 + 1/4*z**4 + 7/3*z**3 - 1/6*z**6 - 4*z + 0*z**2 + 2. Factor s(n).
-(n - 1)**2*(n + 1)*(n + 2)**2
Let z(s) be the first derivative of -3*s**4/4 - 12*s**3 - 72*s**2 - 192*s + 6. Let z(i) = 0. Calculate i.
-4
Suppose 0 = -5*s + 2*w - 2, s + 0*w + w - 1 = 0. Suppose 4*n + 9 = 5*u, -2*u + 4*u + 5*n - 30 = 0. Factor 2/9*x**u + 2/3*x**4 + 0*x + s - 8/9*x**2 + 0*x**3.
2*x**2*(x - 1)*(x + 2)**2/9
Let r(w) be the second derivative of 3*w**5/20 - 6*w. Suppose r(v) = 0. What is v?
0
Let f(d) be the first derivative of -18*d**5/25 + 3*d**4/20 + 31*d**3/15 - 19*d**2/10 + 3*d/5 - 35. Determine p so that f(p) = 0.
-3/2, 1/3, 1
Let w(c) be the first derivative of -1 + 0*c**4 - 1/2*c**2 + 2/5*c**5 + 1/6*c**6 - 2/3*c**3 + 0*c. Solve w(m) = 0.
-1, 0, 1
Let p(k) be the second derivative of k**7/42 - k**6/15 + k**5/20 - 6*k. Factor p(o).
o**3*(o - 1)**2
Suppose -5*m - 4*i + 6 = 0, -5*i = -3*m + 9 + 2. Let o(j) be the first derivative of 2/15*j**3 + 0*j**2 + 0*j + 1/10*j**4 - m. Suppose o(b) = 0. Calculate b.
-1, 0
Suppose 4*n + 16 = 3*o, -5*n - 18 = -5*o + 2. Let k(x) be the second derivative of -1/6*x**3 + 1/12*x**4 + 0 + 3*x + o*x**2. Suppose k(w) = 0. Calculate w.
0, 1
Suppose d = -0*d. Let a(s) be the third derivative of 0 - 1/420*s**7 + 0*s - 1/40*s**5 + 1/48*s**4 + d*s**3 - s**2 + 1/80*s**6. What is o in a(o) = 0?
0, 1
Factor -7*j**4 - 2*j**5 - 2*j**2 + 0*j**4 - 6*j**3 + j**4.
-2*j**2*(j + 1)**3
Let t be (192/252)/(-8) + 8/21. Factor 6/7*m**2 - 8/7*m + 8/7*m**3 + t*m**4 - 8/7.
2*(m - 1)*(m + 1)*(m + 2)**2/7
Suppose 2/5*f**3 - 1/5*f**2 + 0*f + 0 - 1/5*f**4 = 0. Calculate f.
0, 1
Let s(r) be the third derivative of 0*r + 0*r**5 + 1/40*r**6 + 0*r**3 - 5*r**2 + 1/28*r**8 + 2/35*r**7 + 0*r**4 + 0. Factor s(x).
3*x**3*(2*x + 1)**2
Let i(z) = 2*z - 8. Let b be i(8). Let g be (-2 - b/(-6))*-6. Suppose -17/2*d**3 - 1 - 11/2*d - 21/2*d**2 - 5/2*d**g = 0. What is d?
-1, -2/5
Let y be 44/6 + -4 - 3. Factor 0 + 1/3*z - y*z**4 - z**2 + z**3.
-z*(z - 1)**3/3
Let j be 4*1*206/(-24). Let t = -33 - j. Factor k**3 + 2/3 - 1/3*k - t*k**2.
(k - 1)**2*(3*k + 2)/3
Let o = -1395/2 + 6589/10. Let w = o - -39. Factor -2/5*r + w*r**4 + 2/5*r**3 - 2/5*r**2 + 0.
2*r*(r - 1)*(r + 1)**2/5
Suppose 2*b - 3*q = 5, 5*q - 27 = -3*b - 10. Suppose d + 8 = -b*s, -4*s = -d - 6*s - 4. Factor 5/4*c**4 - 1/2*c**3 + 0*c**2 + 0 + d*c + 7/4*c**5.
c**3*(c + 1)*(7*c - 2)/4
Let n(j) be the third derivative of 2*j**2 + 0*j**3 + 1/1512*j**8 - 1/270*j**6 + 0*j**7 + 1/108*j**4 + 0 + 0*j**5 + 0*j. Factor n(u).
2*u*(u - 1)**2*(u + 1)**2/9
Factor -2/7*i**5 - 2/7*i + 4/7*i**3 + 2/7*i**4 - 4/7*i**2 + 2/7.
-2*(i - 1)**3*(i + 1)**2/7
Let b be 0 + 2/(-7) - 1292/(-798). Factor -2/3*a**4 + 2*a**2 - 8/3 + 8/3*a - b*a**3.
-2*(a - 1)**2*(a + 2)**2/3
Let z(n) = -23*n**4 - 28*n**3 + 18*n**2 + 28*n + 8. Let r(w) = 47*w**4 + 57*w**3 - 37*w**2 - 57*w - 17. Let j(u) = 3*r(u) + 7*z(u). Let j(y) = 0. Calculate y.
-1, -1/4, 1
Factor 0 + 1/2*b - 3/4*b**2 + 1/4*b**3.
b*(b - 2)*(b - 1)/4
Let l(i) be the first derivative of i**3/2 - 3*i**2/2 + 2. Factor l(d).
3*d*(d - 2)/2
Let m(v) be the first derivative of 0*v**2 - 1/14*v**4 + 0*v + 2 - 6/35*v**5 + 4/21*v**3. Determine y, given that m(y) = 0.
-1, 0, 2/3
Suppose -2*o = -4*o, -5*z + 30 = 2*o. Suppose -2*a**2 + 10*a**3 + z*a - 2*a - 9*a**2 - 3*a**2 = 0. Calculate a.
0, 2/5, 1
Suppose 0 = 3*t - 6, -w - 5*t + 22 = 2*w. Solve n + w*n**4 + 16*n**3 + 4 + 24*n**2 + 15*n + 0*n**3 + 0 = 0 for n.
-1
Let q = 43/14 + -3. Let x(a) be the first derivative of -1/7*a**2 + 3 - 2/7*a + q*a**4 + 2/21*a**3. Let x(d) = 0. Calculate d.
-1, 1
Let q(y) be the second derivative of -y**7/378 - y**6/270 + y**5/36 + y**4/108 - 4*y**3/27 + 2*y**2/9 - 4*y. Determine b so that q(b) = 0.
-2, 1
Let m(l) be the first derivative of 2*l**3/27 + 9. What is w in m(w) = 0?
0
Factor 7*w**4 - 3*w**4 - 3*w**3 + 3*w**5 - 6*