Find w, given that -2/17*w**3 + 14/17*w**2 + 18/17 - 30/17*w = 0.
1, 3
Let a(l) be the second derivative of l**6/120 + 3*l**5/40 + 13*l**4/48 + l**3/2 + l**2/2 - 22*l. Factor a(i).
(i + 1)**2*(i + 2)**2/4
Let o be 0/(-4) - 28/16. Let r = -5/4 - o. What is w in r*w**2 + 0 - w = 0?
0, 2
Let d(l) be the third derivative of 1/6*l**5 - 1/3*l**4 + 0*l - 1/3*l**3 + 0 + 2*l**2. Find p such that d(p) = 0.
-1/5, 1
Let d(y) = -y**2 + 3*y - 2. Suppose -b - 3 = 3. Let c(q) = 6*q**2 - 17*q + 11. Let f(z) = b*c(z) - 34*d(z). Factor f(u).
-2*(u - 1)*(u + 1)
Let c(n) = -6*n**2 - 14*n + 36. Let j(t) = -2*t**2 - 5*t + 12. Let w(k) = -3*c(k) + 8*j(k). Factor w(u).
2*(u - 2)*(u + 3)
Suppose 3 = j - 2*j. Let k be ((-18)/(-4))/j*-2. What is s in 0 - 2/3*s**4 + 2/3*s - 2/3*s**k + 2/3*s**2 = 0?
-1, 0, 1
Let p(f) be the third derivative of f**9/10584 + f**8/5880 - f**7/2940 - f**6/1260 - f**3/6 - 2*f**2. Let x(w) be the first derivative of p(w). Factor x(z).
2*z**2*(z - 1)*(z + 1)**2/7
Let c(i) be the second derivative of 0*i**2 - 3/100*i**5 + 0 + 1/20*i**4 + 1/10*i**3 + 4*i - 1/50*i**6. Factor c(j).
-3*j*(j - 1)*(j + 1)**2/5
Let a(f) = 2*f**3 - 6*f**2 - 6*f + 3. Let v be a(5). Let p = v + -364/5. Solve -1/5*l**3 + 0 + 1/5*l**2 + 0*l - p*l**4 + 1/5*l**5 = 0 for l.
-1, 0, 1
Suppose 2*s - 11 = 13. Suppose 3*a + 2*a = -5*g, -5*g = -a - s. Let 3 - 2*p + 0 - 4*p**g - 1 = 0. What is p?
-1, 1/2
Let w(c) be the first derivative of -c**5/35 - c**4/14 - c**3/21 - 3. What is o in w(o) = 0?
-1, 0
Suppose -11*l + 1 + 21 = 0. Find d, given that -2*d**l + 2*d**4 + 0 + 4/3*d**3 - 4/3*d = 0.
-1, -2/3, 0, 1
Factor -5*w**2 - 58*w - 78*w - 845 + 6*w.
-5*(w + 13)**2
Let j(c) be the first derivative of -c**8/3360 + c**6/360 - c**4/48 - c**3/3 + 1. Let z(q) be the third derivative of j(q). Factor z(d).
-(d - 1)**2*(d + 1)**2/2
Let r(q) = 4*q. Let f(k) = k**3 - k**2 - 13*k. Let b(p) = 4*f(p) + 11*r(p). Solve b(h) = 0 for h.
-1, 0, 2
Let o(b) be the third derivative of b**10/100800 - b**8/13440 - b**5/20 - 2*b**2. Let q(x) be the third derivative of o(x). Find l such that q(l) = 0.
-1, 0, 1
Let u be (-6)/(-18) - (-1)/3. Factor -2/3*t**2 + 2/3 + u*t**3 - 2/3*t.
2*(t - 1)**2*(t + 1)/3
Let c(z) be the second derivative of 1/42*z**4 - 1/15*z**6 + 0*z**3 + 4/147*z**7 + 0 + 0*z**2 + 1/35*z**5 + 3*z. Solve c(g) = 0.
-1/4, 0, 1
Let u(l) be the first derivative of -l**6/2 - 3*l**5/5 + 9*l**4/4 + 5*l**3 + 3*l**2 + 1. Let u(p) = 0. What is p?
-1, 0, 2
Let a(k) = 12*k**2 + k. Let m be a(-1). Let d = m - 6. Determine r so that -2/3*r**d + 0 + 2/3*r**4 + 0*r**2 + 0*r**3 + 0*r = 0.
0, 1
Let d(q) be the first derivative of 2*q**5/15 + q**4/6 - 5. Factor d(v).
2*v**3*(v + 1)/3
Let g = 1 - -2. Let l be (-2)/(-21)*g*13. Solve -4/7*z + 18/7*z**4 + l*z**2 + 0 - 40/7*z**3 = 0.
0, 2/9, 1
Suppose 0 = -x + 4*p - 9, -2*p + 21 = -x + 6*x. Let c(s) be the first derivative of 0*s - 2/15*s**x + 2 - 2/5*s**2. Let c(k) = 0. Calculate k.
-2, 0
Let k(s) be the second derivative of -s**7/2520 - s**6/360 - s**5/120 - 2*s**4/3 - 2*s. Let i(z) be the third derivative of k(z). Determine t so that i(t) = 0.
-1
Suppose -2*b + 15 = -9. Find z such that 5*z**4 - 15*z**2 - 2*z**4 + b*z**2 = 0.
-1, 0, 1
Let l(b) be the third derivative of 0*b + 0 + 0*b**3 + 0*b**4 + b**2 - 1/120*b**6 + 1/60*b**5. Factor l(v).
-v**2*(v - 1)
Let x be (2/(-4))/(13/(-234)). Suppose 4*a - x = -a + h, -1 = 2*a - 5*h. What is i in 4/3*i - a - 2/9*i**2 = 0?
3
Let k(a) be the second derivative of a**7/11340 - a**6/1620 + a**4/6 + 2*a. Let t(b) be the third derivative of k(b). Factor t(z).
2*z*(z - 2)/9
Let z = -1 + 3. Let -4*r + 2 + 5*r**3 - z + 6 - r**4 + 2 - 6*r**2 = 0. Calculate r.
-1, 2
Let a(d) be the second derivative of d**6/270 + d**5/180 - d**4/54 - d - 32. Determine i so that a(i) = 0.
-2, 0, 1
Let c(z) = -3*z. Let r be c(0). Factor 0*n**3 + r - 3/2*n**5 + 0*n + 0*n**2 - n**4.
-n**4*(3*n + 2)/2
Let w(x) = x + 7. Let u be w(-3). Determine d so that -1 + 3*d**u - 6*d**2 + 4 + 0 = 0.
-1, 1
Factor 0*p + 0 + 0*p**2 - 2/9*p**5 + 0*p**3 + 4/9*p**4.
-2*p**4*(p - 2)/9
Let q be 238/170 - 4/(-10). Factor 0 - 3/5*x - q*x**2 - 3/5*x**4 - 9/5*x**3.
-3*x*(x + 1)**3/5
Factor -9/8 + 3/4*k - 1/8*k**2.
-(k - 3)**2/8
Let r = 483/5 - 96. Solve r + 3/5*x**2 - 6/5*x = 0 for x.
1
Factor 4/5 + 1/5*u**4 + 3*u**2 - 13/5*u - 7/5*u**3.
(u - 4)*(u - 1)**3/5
Factor -48*i + 5*i**2 + 3 + 53 + 136 - 2*i**2.
3*(i - 8)**2
Suppose 282*t = 289*t - 21. Solve 1/4 + 1/4*p - 1/2*p**t + 1/4*p**4 - 1/2*p**2 + 1/4*p**5 = 0 for p.
-1, 1
Let b = -17 - -8. Let u = 13 + b. Solve 4/7 - 2/7*f**3 + 6/7*f**2 - 2/7*f**u + 10/7*f = 0.
-1, 2
Suppose -3*y - 44 = -2. Let o be 2/(-6) + y/(-6). Solve -4/9*f**o + 0 + 2/9*f + 2/9*f**3 = 0 for f.
0, 1
Factor -4*o + 1 + 4*o**2 - 1.
4*o*(o - 1)
Let m(f) = -f + 4. Let u be m(5). Let s be (0 - (-1 - u))/2. Let 5*t**5 + 10*t**2 + 2 - 3*t - 12*t**4 - 6*t + s*t + 4*t**3 = 0. Calculate t.
-1, 2/5, 1
Let c(x) be the first derivative of -x**4/10 + x**2/5 + 34. Factor c(q).
-2*q*(q - 1)*(q + 1)/5
Let k(w) be the first derivative of w**6/27 - 8*w**5/45 - w**4/9 + 8*w**3/9 + w**2 - 10. Determine p, given that k(p) = 0.
-1, 0, 3
Let h(t) be the third derivative of -t**6/90 + 2*t**5/15 - 2*t**4/3 - 4*t**3/3 - 9*t**2. Let k(o) be the first derivative of h(o). Factor k(a).
-4*(a - 2)**2
Let m(d) be the first derivative of -1/5*d**4 - 2/25*d**5 + 0*d**2 - 2/15*d**3 - 1 + 0*d. Suppose m(t) = 0. What is t?
-1, 0
Let x(i) be the first derivative of -i**5/40 - i**4/8 + i**3/24 + i**2/4 + 3. Find t such that x(t) = 0.
-4, -1, 0, 1
Let u be (-2)/12 + (-93)/(-18). Let c(l) be the second derivative of 0*l**3 + 1/6*l**4 + 0*l**2 + 1/15*l**6 - 1/5*l**u + 0 - 2*l. Suppose c(v) = 0. What is v?
0, 1
Factor -10*k**2 + 0 + 4/3*k - 49/6*k**4 + 21*k**3.
-k*(k - 2)*(7*k - 2)**2/6
Let k(r) be the first derivative of 3*r**5/5 - 21*r**4/2 + 49*r**3 + 20. Factor k(i).
3*i**2*(i - 7)**2
Let s(n) be the third derivative of -n**9/7560 + n**8/1680 - n**6/180 + n**5/60 + n**4/24 - 3*n**2. Let b(y) be the second derivative of s(y). Solve b(t) = 0.
-1, 1
Let p be (7007/(-270))/13 - -2. Let o(z) be the third derivative of 0 + p*z**5 - 4*z**2 + 0*z + 1/108*z**4 + 0*z**3. Factor o(q).
2*q*(q + 1)/9
Let h(x) = -x**2 - 6*x - 6. Let q be h(-4). Suppose -2 - 6 = -q*a. Factor 56/3*w**3 - 98/3*w**a + 0 - 8/3*w**2 + 0*w.
-2*w**2*(7*w - 2)**2/3
Let -2/15*s**4 + 4/15*s + 0 + 2/15*s**2 - 4/15*s**3 = 0. What is s?
-2, -1, 0, 1
Suppose 9*u + 20 - 47 = 0. Let 0*v + 4/9*v**2 - 2/9 + 0*v**u - 2/9*v**4 = 0. What is v?
-1, 1
Let c(s) = s**2 + 3*s. Let v be c(-3). Factor -3*n**3 + 6 - 6*n**2 + 2*n**3 + 3*n + v*n**3 - 2*n**3.
-3*(n - 1)*(n + 1)*(n + 2)
Suppose 8*j = j. Determine a so that 0*a - 1/5*a**5 + 0 + j*a**2 - 2/5*a**4 - 1/5*a**3 = 0.
-1, 0
Let i(u) be the second derivative of -1/60*u**6 - 5/24*u**4 + 0 - 1/6*u**3 + 0*u**2 + 2*u - 1/10*u**5. Find x, given that i(x) = 0.
-2, -1, 0
Let w be ((-1)/1)/((-2)/6). Let t(b) be the third derivative of -2*b**2 + 0*b**4 + 0*b + 1/240*b**6 + 0*b**5 + 0*b**w + 1/420*b**7 + 0. Let t(v) = 0. What is v?
-1, 0
Suppose -4*v - v - 20 = 0. Let p = -4 - v. Determine o, given that -4 - o + p*o + 2*o**2 + 3*o = 0.
-2, 1
Suppose 0 = 3*p - y - 8, 0 = 2*p - 7*p + 4*y + 4. Suppose -4*z = -4*w + z + 12, -3*w - p*z = -9. Suppose 2/9*d - 4/9*d**2 + 4/9 - 2/9*d**w = 0. What is d?
-2, -1, 1
Let a(t) = t + 1. Let n be a(-4). Let u be (63/12)/n*-3. Solve 9/4*r**5 - u*r + 3*r**3 - 6*r**4 + 3/2 + 9/2*r**2 = 0.
-1, 2/3, 1
Let t(y) be the first derivative of -1/6*y**3 - 1/2*y + 1/2*y**2 + 4. Factor t(z).
-(z - 1)**2/2
Let m(k) be the first derivative of k**6/24 - 3*k**5/10 + k**4/2 + k**3 - 6. Let b(j) be the third derivative of m(j). Determine r so that b(r) = 0.
2/5, 2
Let k(f) = -3*f. Let l(v) = 10*v. Let z(m) = 7*k(m) + 2*l(m). Let q be z(-2). Find b such that -2/7*b**q - 4/7*b**3 + 2/7*b + 0 = 0.
-1, 0, 1/2
Let n = 5 - 3. Let g be n + -3 - (-14)/10. Factor -g*x + 0 + 2/5*x**3 - 2/5*x**4 + 2/5*x**2.
-2*x*(x - 1)**2*(x + 1)/5
Let d(w) be the second derivative of -1/2*w**2 + 1/12*w**4 + 0*w**3 + 2*w + 0. Factor d(z).
(z - 1)*(z + 1)
Let f(j) = -j**5 - 4*j**4 + 4*j**3 + 6*j**2 - j. Let h(t) = t**4 - t**3 - t**2 - 1. Let l(s) = 2*f(s) + 4*h(s). Solve l(r) = 0 for r.
-2, -1, 1
Let l be (-570)/(-450) - -2*6/(