d(7). Find a, given that 7*a**3 + 1/4*a**2 + 0 - z*a**4 - 1/4*a - 48*a**5 = 0.
-1/3, -1/4, 0, 1/4
Let d = 9492/11 + -862. Suppose -d*n + 10/11*n**3 - 4/11 + 4/11*n**2 = 0. Calculate n.
-1, -2/5, 1
Let q(s) be the first derivative of s**6/90 - s**5/60 - 9*s - 1. Let m(c) be the first derivative of q(c). Suppose m(k) = 0. What is k?
0, 1
Factor 4*g**3 + 2*g**2 + 2 - 3*g**4 - g**4 - 2*g**5 + 3*g**5 - 5*g.
(g - 2)*(g - 1)**3*(g + 1)
Let i(z) be the first derivative of z**3 - 9*z**2 + 15*z - 33. Find h, given that i(h) = 0.
1, 5
Factor 3*m**4 + 0*m**4 + 12*m**3 + 6*m**3 + 27*m**2.
3*m**2*(m + 3)**2
Let d(o) be the third derivative of 0*o**3 + 2*o**2 + 1/840*o**8 + 0 + 0*o**4 + 0*o**7 + 0*o + 0*o**5 - 1/300*o**6. Find g, given that d(g) = 0.
-1, 0, 1
Let m(r) be the third derivative of -r**6/480 - r**5/80 + 3*r**2. Find t such that m(t) = 0.
-3, 0
Let n(t) = -7*t**4 - 3*t**3 + 3*t**2 - t - 4. Let y(g) = 6*g**4 + 3*g**3 - 3*g**2 + 3. Let s(j) = 3*n(j) + 4*y(j). Determine l, given that s(l) = 0.
-1, 0, 1
Suppose 4*d + m - 21 = 0, 2*d - 4*m - 4 + 16 = 0. Suppose -d*r + 2*r = 0. Determine b so that 2/7*b**4 + r - 2/7*b**2 + 2/7*b**5 - 2/7*b**3 + 0*b = 0.
-1, 0, 1
Let n(y) be the second derivative of -1/100*y**5 + 2*y + 0*y**2 + 0 + 1/60*y**4 + 0*y**3. Find a such that n(a) = 0.
0, 1
Let n(s) be the third derivative of s**5/35 + 5*s**4/42 - 4*s**3/21 - 11*s**2. Factor n(t).
4*(t + 2)*(3*t - 1)/7
Let r(n) = -4*n**2 + 17*n - 13. Let g(j) = -2*j**2 + 8*j - 6. Suppose 0 = -2*s - 3*h + 2, s + 2*h + 20 = 5*s. Let w(i) = s*r(i) - 10*g(i). Factor w(u).
4*(u - 2)*(u - 1)
Suppose -2*y**2 + 0*y - 4 + 2*y + 4*y = 0. Calculate y.
1, 2
Let r(i) be the third derivative of i**6/160 + i**5/80 + 8*i**2. Factor r(l).
3*l**2*(l + 1)/4
Suppose -36 = -4*g - 4*n, 4*n = 4*g - 0*g - 60. Let u be 3/(-1) - (-39)/g. Factor 0*o + 1/4*o**4 + 1/4*o**3 - 1/4*o**2 + 0 - u*o**5.
-o**2*(o - 1)**2*(o + 1)/4
Let x be (-46)/(-160) - (-16)/40. Let t(c) be the first derivative of 1/2*c**2 - 4/3*c**3 + x*c**4 - 5/8*c**6 + 0*c + 1 + 4/5*c**5. Find n, given that t(n) = 0.
-1, 0, 2/5, 2/3, 1
Let s(l) = l**3 - 9*l**2 + 9*l - 5. Suppose 1 = -y + 9. Let j be s(y). Factor 0 + 2/5*c**4 + 0*c + 0*c**2 - 2/5*c**j.
2*c**3*(c - 1)/5
Let o be ((-6)/(-27))/((-72)/(-108)). Find n, given that -4/3 - 4/3*n - o*n**2 = 0.
-2
Suppose 2/3*n**2 - 8/3*n - 10/3 = 0. What is n?
-1, 5
Suppose 0*w - 9 = -3*h + 3*w, -34 = -2*h - 5*w. Suppose 0 = -3*b + h*b. Determine y, given that -1/4*y**4 + b*y + 0*y**2 + 0*y**3 + 1/4*y**5 + 0 = 0.
0, 1
Suppose c = 2*b + 3*b + 31, -b - 1 = 0. Let m = -24 + c. Find t such that t - 3/2*t**m + 1/2 = 0.
-1/3, 1
Let y(o) be the first derivative of 1/3*o**3 + 3/4*o**4 - o - 2 - 3/2*o**2. Factor y(w).
(w - 1)*(w + 1)*(3*w + 1)
Let p(y) = y**2 + 9*y + 10. Let z be p(-7). Let o = -2 - z. Factor 4*l**2 - 3*l**2 - 2*l**3 - l**3 + o*l**2.
-3*l**2*(l - 1)
Let u(r) be the first derivative of -1/9*r**2 - 4/9*r**3 + 4/9*r + 1 + 2/9*r**4 + 8/45*r**5 - 1/9*r**6. Suppose u(s) = 0. Calculate s.
-1, -2/3, 1
Let c = 0 - 0. Let h(m) be the first derivative of c*m - 2/45*m**5 + 1 - 2/27*m**3 - 1/9*m**4 + 0*m**2. Factor h(x).
-2*x**2*(x + 1)**2/9
Suppose 5 + 180*c - 36 - 605*c**4 - 104*c**2 + 11 - 990*c**3 - 81*c**2 = 0. What is c?
-1, 2/11
Let v be 1 + (-2 - 4/(-4)). Let o(j) be the second derivative of 0*j**3 + 1/48*j**4 + v*j**2 + 0 + 3*j. Solve o(r) = 0 for r.
0
Let g(v) = v**2 - 9*v + 5. Let h(j) = -j**2 + 10*j - 6. Let t(f) = 6*g(f) + 5*h(f). What is d in t(d) = 0?
0, 4
Let x = 43/14 + -79/28. Suppose 1/2*o**5 - 1/2*o**2 + 1/4*o**4 - o**3 + x + 1/2*o = 0. Calculate o.
-1, -1/2, 1
Suppose -5 = -3*k + 1. Let z(d) = -d**3 - 2*d**2 + 2. Let h be z(-2). Suppose 7*l**k + l**4 - l**h + 1 + 0*l**3 + 4*l + 4*l**3 = 0. What is l?
-1
Let w = -4 - -3. Let b = w - -3. Solve 1/3*f**4 + 0*f**b - 1/3*f**3 + 0 + 0*f = 0 for f.
0, 1
Let h = 16 - 12. Let x(g) = -5*g**2 + 5*g. Let b(m) = -2*m**2 + 2*m. Let a(o) = h*x(o) - 9*b(o). Let a(v) = 0. What is v?
0, 1
Let y(i) be the third derivative of -1/80*i**5 + 0*i**4 - 1/80*i**6 + 0*i**3 + 0 - 1/280*i**7 + 0*i - 2*i**2. Solve y(d) = 0.
-1, 0
Let j = 46 + -46. Let g be ((-4)/(-3))/((-10)/(-3)). Determine a so that 2/5*a + j + g*a**2 = 0.
-1, 0
Let u(s) be the second derivative of 0 + 7/4*s**4 - 1/10*s**5 + 2*s - 2*s**2 - 4/3*s**3 - 7/30*s**6. What is p in u(p) = 0?
-2, -2/7, 1
Let n(x) = x**2. Let t(v) = -2*v**3 - 5*v**2 + 2*v. Let p(h) = -10*n(h) - 2*t(h). Let p(b) = 0. What is b?
-1, 0, 1
Factor 0 + 2/13*w**5 + 4/13*w**3 + 0*w + 0*w**2 + 6/13*w**4.
2*w**3*(w + 1)*(w + 2)/13
Let m be (-1)/(3 + (-30)/4). Let s be 2/3 - (-7)/3. Determine h so that -2/9*h**s + 2/9*h - m + 2/9*h**2 = 0.
-1, 1
Let g = -7 - -5. Let p be 8 + 1 + -3 + g. Solve 0*u + 2/7*u**3 + 2/7*u**2 - 2/7*u**p + 0 - 2/7*u**5 = 0.
-1, 0, 1
Let 8/5*j**3 - 6/5*j**2 + 0*j + 0 - 2/5*j**4 = 0. What is j?
0, 1, 3
Factor 3*n**5 - 7*n**3 + 2*n**5 + 4*n - n**3 - n**5.
4*n*(n - 1)**2*(n + 1)**2
Let l(p) = -p + 2. Let r(g) = -5*g**2 + g + 3. Let a(n) = -n**2 + 1. Let x(k) = 4*a(k) - r(k). Let c(q) = -2*l(q) + 2*x(q). Factor c(o).
2*(o - 1)*(o + 1)
Suppose 2*h + 1 = p, -5*p - 4 = -3*h - 23. Let b(f) be the first derivative of -h*f**3 + 2 - 6*f**2 - 1/4*f**4 - 8*f. What is v in b(v) = 0?
-2
Let m(a) = -2*a**2 + 3*a - 1. Let l(u) = -6*u**2 + 8*u - 3. Let x(b) = -6*l(b) + 17*m(b). Factor x(q).
(q + 1)*(2*q + 1)
Let m(w) = 2*w. Let f be m(1). Let 2*x**f + 5*x - 2*x**3 + 6*x - 11*x = 0. What is x?
0, 1
Let d(r) be the first derivative of 1/60*r**4 - 3*r + 1/10*r**2 - 1/15*r**3 - 3. Let o(f) be the first derivative of d(f). Find w such that o(w) = 0.
1
Let l(k) be the second derivative of -k**7/630 + k**6/360 + k**5/180 - k**4/72 + 2*k**2 + 4*k. Let m(v) be the first derivative of l(v). Factor m(c).
-c*(c - 1)**2*(c + 1)/3
Let h(q) be the third derivative of q**5/420 + q**4/84 - 14*q**2. Factor h(r).
r*(r + 2)/7
Let n(x) be the third derivative of -x**8/840 - 4*x**7/525 - x**6/60 - x**5/75 + 33*x**2. Factor n(g).
-2*g**2*(g + 1)**2*(g + 2)/5
Let o(g) = -16*g**2 + 30*g - 8. Let i(d) = 31*d + 9 + 7 + 19*d**2 + 13*d**2 - 90*d. Let f(n) = 6*i(n) + 13*o(n). Determine p so that f(p) = 0.
1/4, 2
Let r(u) be the third derivative of -u**5/45 + 8*u**3/9 - 11*u**2. Find t such that r(t) = 0.
-2, 2
Let i(g) = -g**3 - g**2 - g + 2. Let m be i(0). Suppose -4 = -d - m. Factor 4*v**2 + 3*v - 3*v**3 + v**2 - 3*v**4 - 2*v**d.
-3*v*(v - 1)*(v + 1)**2
Let t = 43 - 41. Let f(m) be the first derivative of -10/9*m**3 + 2/3*m**4 - 2/15*m**5 + 1 + 2/3*m**t + 0*m. Find y such that f(y) = 0.
0, 1, 2
Let u(a) be the second derivative of 1/14*a**7 - 2*a + 3/10*a**5 + 0 + 1/2*a**4 + 3/2*a**2 - 3/2*a**3 - 3/10*a**6. Determine w so that u(w) = 0.
-1, 1
Let i = 47 - 177. Let a = 394/3 + i. Factor -a*x + 0 + 2/3*x**2.
2*x*(x - 2)/3
Factor -5 - 2*p**2 + 3*p**2 + 1 - 5*p - 2*p**2.
-(p + 1)*(p + 4)
Let j(w) = 10*w - 30. Let d be j(3). Find a such that -2/5*a**3 + d + 0*a**2 + 2/5*a = 0.
-1, 0, 1
Let r be (-33)/(-77) - 18/(-7). Factor -2*d**2 + 2 - 7*d**r - 2 - d + 6*d**3.
-d*(d + 1)**2
Let n(p) be the second derivative of p**6/30 + p**4/12 + p**2/2 + p. Let d(f) = -8*f**4 - 2*f**3 - 8*f**2 - 7. Let w(i) = 2*d(i) + 14*n(i). Factor w(m).
-2*m**2*(m + 1)**2
Let x = 18 - 37/2. Let z = 9/10 + x. Suppose -2/5*o**5 + 0*o + 0 + z*o**2 + 2/5*o**3 - 2/5*o**4 = 0. What is o?
-1, 0, 1
Let z(u) be the second derivative of u**6/90 - u**5/20 + u**4/12 - u**3/18 - 15*u. Solve z(l) = 0 for l.
0, 1
Let o(y) be the second derivative of -y**6/270 - y**5/60 - y**4/108 + y**3/18 + y**2/9 - 4*y. Factor o(f).
-(f - 1)*(f + 1)**2*(f + 2)/9
Solve -6/5*f + 12/5*f**4 - 24/5*f**3 + 0 - 2/5*f**5 + 4*f**2 = 0.
0, 1, 3
What is l in -8 + 4*l**2 + 4*l**3 - 12*l + 9*l**4 + 0*l**3 + 8*l**3 - 5*l**4 = 0?
-2, -1, 1
Suppose 0 = -3*t - 3*r + 66, -4*t + 2*r + 103 = r. Suppose 4*m = -m + t. Determine s, given that 10*s**4 - 7*s**5 + 2*s - 18*s**3 + 2*s + 21*s**m - 10*s**2 = 0.
-1, 0, 2/7, 1
Solve -12*h - 4*h**5 + 83*h**2 + 8 - 91*h**2 + 16*h**3 + 0*h**5 = 0.
-2, -1, 1
Factor 0 + 2/5*l - 1/5*l**4 - l**2 + 4/5*l**3.
-l*(l - 2)*(l - 1)**2/5
Suppose -5*r = -3*r. Let q(u) be the third derivative of 3*u**2 - 1/16*u**4 + 0*u**3 + 0 - 1/80*u**6 + r*u + 1/20*u**5. Find w, given that q(w) = 0.
0, 1
Let l be (8/3)/4 +