8. Suppose 0 = -3*y - 0 + j. Factor 5*g**2 + 2*g + y*g**2 - 2 + 0*g**3 - 6*g**2 - 2*g**3.
-2*(g - 1)**2*(g + 1)
Let v be (-15)/50 + 1/3. Let p(a) be the second derivative of 0 + 0*a**2 + v*a**4 - a - 1/15*a**3. Factor p(w).
2*w*(w - 1)/5
Determine b, given that -3/5*b**2 + 1/5*b**4 - 1/5*b + 1/5*b**3 + 2/5 = 0.
-2, -1, 1
Let n(f) be the third derivative of 0 - 3*f**2 + 2/45*f**3 + 1/450*f**6 + 0*f - 1/90*f**5 + 1/180*f**4. Find s such that n(s) = 0.
-1/2, 1, 2
Let y = 15 + 23. Let v = -36 + y. Factor 3/2*w - 3/2*w**3 - 3/4*w**4 + 0*w**v + 3/4.
-3*(w - 1)*(w + 1)**3/4
Let t(f) = -3*f + f + 0*f**3 + 3*f**2 - 2 - f**3 + 8*f. Let w be t(4). Let w*i**2 + 0*i**2 - 3*i**2 = 0. What is i?
0
Let u be 180/72*(-16)/(-10). Suppose 0 + 2/5*g**2 + 0*g - 1/5*g**5 + 0*g**u + 3/5*g**3 = 0. What is g?
-1, 0, 2
Factor 9 + 21/2*c + 0*c**2 - 3/2*c**3.
-3*(c - 3)*(c + 1)*(c + 2)/2
Let o(n) = 12*n**3 - 15*n**2 + 15*n - 3. Let g(w) = 1 + 14*w**2 + 2 - 16*w - 4*w**3 + w**3 - 9*w**3 - w**4. Let z(i) = -3*g(i) - 4*o(i). Factor z(k).
3*(k - 1)**4
Let f be -2 - -4 - (0 + 8/(-6)). Suppose 0 = -5*b + 5 + 5. Factor -8/3 + 8*j - f*j**b.
-2*(j - 2)*(5*j - 2)/3
Let c(d) be the third derivative of -d**6/360 - d**5/60 - d**3/2 - 8*d**2. Let i(p) be the first derivative of c(p). Suppose i(r) = 0. What is r?
-2, 0
Let h(k) be the second derivative of -2*k**7/21 + 4*k**6/15 - k**5/5 + 26*k. Factor h(w).
-4*w**3*(w - 1)**2
Let l(h) = 11*h**4 - 7*h**3 - 53*h**2 - 24*h + 11. Let f(z) = -4*z**4 + 2*z**3 + 18*z**2 + 8*z - 4. Let k(u) = 17*f(u) + 6*l(u). What is s in k(s) = 0?
-1
Let q(r) = -r**3 - r**2 - r + 1. Let h(c) = c**2 + c - 1. Let n(i) = h(i) + q(i). Let f(a) = 12*a**3 - 4*a**2 - 6*a + 4. Let s(j) = -f(j) - 6*n(j). Factor s(m).
-2*(m - 1)*(m + 1)*(3*m - 2)
Let 0*x - 10*x**5 + 16/5*x**2 + 12*x**4 + 72/5*x**3 + 0 = 0. What is x?
-2/5, 0, 2
Let b(k) be the first derivative of -5*k**3/3 - 15*k**2/2 + 20*k + 31. Factor b(h).
-5*(h - 1)*(h + 4)
Let p(r) = -1. Let u(x) = x**2 + 3*x + 5. Let s(f) = -3*p(f) - u(f). Factor s(v).
-(v + 1)*(v + 2)
Let c be (-13)/(-4) + 7/28. Let n(i) be the first derivative of -10/3*i**3 + i**2 + c*i**4 - 1 - 6/5*i**5 + 0*i. Determine x so that n(x) = 0.
0, 1/3, 1
Let y(i) be the first derivative of -1/3*i**5 - 1/6*i**6 + 0*i**3 - 5 + 0*i**2 - 1/6*i**4 + 0*i. Factor y(d).
-d**3*(d + 1)*(3*d + 2)/3
Let i(l) be the third derivative of 0*l**6 - 1/1344*l**8 + 5*l**2 + 0*l + 0 - 1/420*l**7 + 0*l**3 + 1/120*l**5 + 1/96*l**4. Find w, given that i(w) = 0.
-1, 0, 1
Let u(z) be the third derivative of -2*z**7/105 + z**6/30 + 9*z**2. Find m, given that u(m) = 0.
0, 1
Let h(y) be the third derivative of 0*y**3 + 2*y**2 + 1/40*y**5 + 1/24*y**4 + 0 + 1/240*y**6 + 0*y. Factor h(z).
z*(z + 1)*(z + 2)/2
Let t = 5 - 2. Let o = -70 - -70. Factor 0*l**2 + 0*l - 2/13*l**4 - 2/13*l**t + o.
-2*l**3*(l + 1)/13
Suppose -6*z + x = -2*z - 5, -4*x - 20 = -z. Let s(g) be the third derivative of z*g - 1/21*g**4 - g**2 - 4/21*g**3 + 0 - 1/210*g**5. Factor s(t).
-2*(t + 2)**2/7
Let 21*q**3 - 6 + 64*q - 69*q**3 - 16*q**5 - 73*q**2 + 68*q**4 - 6 + 17*q**2 = 0. Calculate q.
-1, 1/4, 1, 3
Suppose 0 = -2*k - 3 + 11. Suppose k*n = -0*n + 8. Solve 0 + 2*b**2 - n*b**3 - 1/2*b = 0 for b.
0, 1/2
Let s be ((-20)/25)/(1/(-5)). Suppose 4*b - 5 = 5*w, 0 = -4*w + s*b - 0 - 8. Suppose -5*n**4 - n**5 + 2*n**5 + 6*n**4 - n**2 - n**w = 0. Calculate n.
-1, 0, 1
Suppose -6 = -2*t - 0. Factor t*w**2 + w**2 - 1 - 2*w**3 + 1.
-2*w**2*(w - 2)
Find m, given that 12/5*m**2 - 2/5 - 3/5*m - 7/5*m**3 = 0.
-2/7, 1
Let w(d) be the first derivative of -27*d**5/20 + 117*d**4/8 - 28*d**3 + 75*d**2/4 - 21*d/4 - 2. Suppose w(y) = 0. Calculate y.
1/3, 1, 7
Let d = -6 + 10. Let p(z) be the second derivative of 1/60*z**5 + 0 + 1/36*z**d - 2*z - 1/6*z**2 - 1/18*z**3. Factor p(q).
(q - 1)*(q + 1)**2/3
Let l(w) be the first derivative of -w**5/15 - w**4/12 + w**3/3 + 5*w**2/6 + 2*w/3 - 5. Find m, given that l(m) = 0.
-1, 2
Let q(r) = -r**3 - 4*r**2 + 4*r + 1. Let x(f) = -f**3 - 5*f**2 + 5*f + 1. Let g(o) = -4*q(o) + 3*x(o). Factor g(h).
(h - 1)*(h + 1)**2
Let r(z) = -z**3 - 14*z**2 - 14*z - 8. Let p be r(-13). Suppose -a**p - a + 18*a**3 - 4*a**3 - 12*a**3 = 0. What is a?
-1, 0, 1
Let y = 49 + -49. Let d(u) be the second derivative of 1/18*u**4 + 2/9*u**3 - 3*u + y*u**2 + 0. Factor d(h).
2*h*(h + 2)/3
Let b(u) be the first derivative of 4/15*u**3 - 1 + 1/5*u**2 - 1/5*u**4 - 2/5*u - 2/25*u**5 + 1/15*u**6. Find q such that b(q) = 0.
-1, 1
Let u(y) be the first derivative of 2*y**5/5 - 2*y**3/3 - 5. Factor u(v).
2*v**2*(v - 1)*(v + 1)
Let l(t) be the second derivative of 1/3*t**3 - 3/14*t**4 - 2/7*t**2 + 1/14*t**5 - 3*t - 1/105*t**6 + 0. Factor l(a).
-2*(a - 2)*(a - 1)**3/7
Suppose 0 = 2*i - 0*i - 6. Suppose 2*d + 2*x = x + 3, -5*d + 2*x + 30 = 0. Factor -9*l**4 - 2*l**2 + 10*l**d - 2*l**3 + i*l**2.
l**2*(l - 1)**2
Let s(l) be the third derivative of -l**6/600 + l**5/100 - l**4/40 + l**3/30 - 11*l**2. Find w such that s(w) = 0.
1
Let s(m) = -m**4 - m**3 + m**2 - m. Let i(j) = 3*j**5 - 40*j**4 + 149*j**3 - 2*j**2 + 2*j. Let y(q) = i(q) + 2*s(q). Determine z, given that y(z) = 0.
0, 7
Determine h, given that 2/7*h**3 + 4/7*h**2 + 0 + 0*h = 0.
-2, 0
Let l(q) be the third derivative of q**5/60 + q**4/6 - 5*q**3/6 + 42*q**2. Factor l(g).
(g - 1)*(g + 5)
Let u(b) be the first derivative of -3*b**5 + 21*b**4/4 + 8*b**3 - 6*b**2 + 13. Find k such that u(k) = 0.
-1, 0, 2/5, 2
Suppose -5*p + 104 = -2*c, -74 = -4*p + c + 11. Let t = p - 18. What is a in -a**2 - 3/5*a**5 + 0 + 2/5*a + a**t + 1/5*a**3 = 0?
-1, 0, 2/3, 1
Let d(c) be the second derivative of -c**6/90 - c**5/60 + c**4/36 + c**3/18 + 7*c. Find h, given that d(h) = 0.
-1, 0, 1
Solve 5/2*u**2 + 9/2*u - 1 = 0 for u.
-2, 1/5
Let v(i) be the third derivative of i**6/720 - i**4/48 + i**3/18 - 8*i**2. Suppose v(t) = 0. What is t?
-2, 1
Suppose 10*k + 4*j = 5*k + 29, -5*k + 65 = -5*j. Let n = k + -7. Suppose 0*t - 3*t**n + 0*t + 6*t = 0. What is t?
0, 2
Let c(q) = -q - 3. Let u be c(-5). Let z(x) be the second derivative of -x + 0 + 0*x**u + 1/42*x**4 + 0*x**3. Factor z(s).
2*s**2/7
Let j = -12 - -6. Let r = -4 - j. Factor -4*n**3 + 2*n**2 + r*n**4 - 4*n + 4*n.
2*n**2*(n - 1)**2
Let f(i) be the third derivative of 0 - 1/240*i**5 + 0*i**3 + 0*i**4 + 4*i**2 + 0*i. Factor f(m).
-m**2/4
Determine a, given that -8/3*a**2 + 0 + 4/3*a + 4/3*a**3 = 0.
0, 1
Suppose -3*g + 23 = -5*q, -g + 6 = g - q. Suppose -10 = -3*t - g. Factor -2/7*f**2 + 2/7 - 2/7*f**t + 2/7*f.
-2*(f - 1)*(f + 1)**2/7
Let x(z) be the first derivative of z**5/10 + z**4/2 + z**3 + z**2 - 4*z - 3. Let q(d) be the first derivative of x(d). Solve q(v) = 0 for v.
-1
Find o such that -1/3*o**3 + 0*o + 0 - o**2 = 0.
-3, 0
Let c(u) be the third derivative of 3*u**2 + 0*u + 0 - 1/40*u**5 + 0*u**4 + 1/4*u**3. Suppose c(l) = 0. Calculate l.
-1, 1
Let f = -13 - -11. Let w be -2 + 5 + 0/f. Find l, given that -5/3*l**2 + 0 - l**w - 2/3*l = 0.
-1, -2/3, 0
Let l(o) = -o**2 - 4*o + 3. Let x be l(-4). Let j(c) be the first derivative of -1 - 1/2*c**2 - 2*c + 1/3*c**x. Factor j(u).
(u - 2)*(u + 1)
What is f in -1/3*f**3 - 4/3*f + 5/3*f**2 + 0 = 0?
0, 1, 4
Let h = -13/12 + 115/84. Factor 0*w + 8/7 - h*w**2.
-2*(w - 2)*(w + 2)/7
Let h(j) = -j**3 - 11*j**2 - j - 13. Let i be h(-11). Let x(b) = -b**2 - b. Let r(f) = -f**3 - 6*f**2 - 7*f. Let t(d) = i*r(d) + 14*x(d). Solve t(u) = 0.
0, 1
Let o(j) = -5*j**2 + 7*j**2 + j**2 + 7 - 2*j. Let s(m) = m**2 - m + 1. Let d(c) = o(c) - 4*s(c). What is h in d(h) = 0?
-1, 3
Let d(v) = v**2 - v - 1. Suppose -7 = -2*h - 13. Let f(a) = 9*a + 6. Let n(w) = h*d(w) - f(w). Solve n(o) = 0.
-1
Let g(y) = -2 + 2*y**3 + y**2 - 3*y**3 - 2*y**3 + 2*y**2. Let a(m) = 7*m**3 - 7*m**2 + 5. Let t(v) = -2*a(v) - 5*g(v). Suppose t(c) = 0. Calculate c.
0, 1
Let m(h) be the third derivative of 2*h**2 - 1/60*h**5 + 0 + 0*h**3 + 1/12*h**4 + 0*h. Factor m(s).
-s*(s - 2)
Suppose -32/7*h**5 + 0 + 2/7*h - 16/7*h**4 + 30/7*h**3 + 16/7*h**2 = 0. Calculate h.
-1, -1/4, 0, 1
Let n(q) = -q**3. Let a(h) = -4*h**3 - h**2 - 2*h. Let p(v) = 2*a(v) - 10*n(v). Factor p(m).
2*m*(m - 2)*(m + 1)
Let u be -1 + (80/7)/2. Let t = 211/21 - u. Factor -t - 140/3*z**2 - 50/3*z**3 - 88/3*z.
-2*(z + 2)*(5*z + 2)**2/3
Let r(l) be the third derivative of -l**5/450