2. Let n(v) = v**2 + v. Let d(y) = 4*n(y) + p(y). Let g(c) = -5*c**2 + 6*c - 1. Let l(r) = -4*d(r) + 3*g(r). Let l(k) = 0. What is k?
1
Let g = 87 - 85. Let n(x) = 2*x**2 - 4*x + 6. Let i be n(g). Solve 525/4*v**3 + i + 51*v + 285/2*v**2 = 0 for v.
-2/5, -2/7
Let d(n) be the second derivative of 18*n - 1/30*n**6 + 1/3*n**3 - 3/28*n**7 + 0*n**2 - 1 + 27/40*n**5 + n**4. What is x in d(x) = 0?
-1, -2/9, 0, 2
Find z, given that 3*z**3 - 5*z**3 + 60*z + 131 - 8*z**2 - 2*z**3 + 43 - 30 = 0.
-3, 4
Suppose -18591*r = -18593*r + 10. Determine y, given that -7/3*y**4 + 0*y**2 + 0*y + 0 - 3*y**r + 2/3*y**3 = 0.
-1, 0, 2/9
Let r(g) be the first derivative of -1/9*g**3 + 4*g + 3 - 1/45*g**6 + 1/30*g**5 + 0*g**2 + 1/18*g**4. Let w(a) be the first derivative of r(a). Factor w(l).
-2*l*(l - 1)**2*(l + 1)/3
Find p, given that -382*p**2 - 2/3*p**4 - 1352/3 - 100/3*p**3 + 2600/3*p = 0.
-26, 1
Let i(z) = z**3 - 15*z**2 + 6. Let q(o) = 90*o**2 - 1 + 2 - 36 - 5*o**3. Let b(p) = -35*i(p) - 6*q(p). Factor b(a).
-5*a**2*(a + 3)
Let i(x) be the second derivative of -x**4/66 - 182*x**3/33 - 8281*x**2/11 + 771*x. Suppose i(m) = 0. What is m?
-91
Let g(m) = -2*m**4 - 7*m**3 - 19*m**2 - 5*m + 3. Let o(q) = -7*q + q + 3*q**4 - 18*q**2 - 5*q**4 - 8*q**3 + 2. Let a(w) = -2*g(w) + 3*o(w). Factor a(c).
-2*c*(c + 1)*(c + 2)**2
Factor -216*v**3 - 211*v**3 - 210*v**3 - 213*v**3 - 90*v + 848*v**3 - 92*v**2.
-2*v*(v + 1)*(v + 45)
Let b(f) be the second derivative of -f**4/36 + 7*f**3/6 - 10*f**2/3 - 50*f. Factor b(x).
-(x - 20)*(x - 1)/3
Factor 3*l - l**2 + 7*l**2 - 6*l**3 + 4*l**3 - l - 6*l.
-2*l*(l - 2)*(l - 1)
Find m, given that -224/17*m - 222/17 - 2/17*m**2 = 0.
-111, -1
Suppose 0*p + 0 - 2/3*p**2 + 0*p**3 + 2/3*p**4 = 0. Calculate p.
-1, 0, 1
Let b(k) = k - 27. Let i be b(-8). Let a = 37 + i. Factor 0 - 3/2*r**3 + 0*r**4 + 0*r + 1/2*r**5 + r**a.
r**2*(r - 1)**2*(r + 2)/2
Let n be (-21)/14 + 50/30. Let -1/3 + n*b**2 + 1/6*b = 0. Calculate b.
-2, 1
Let a(t) = 5*t - 3. Let g be a(3). Suppose 2*p + p = g. Factor 7*z**3 - 2*z**3 + p*z**2 - 3*z**3 - 3*z**4 + z**4.
-2*z**2*(z - 2)*(z + 1)
Let q be 13/520*-15 - (-74)/112. Factor -1/7*k**2 + q - 1/7*k.
-(k - 1)*(k + 2)/7
Let o(u) = 36*u + 12. Let b be o(4). Let 156*i - i**2 - b*i = 0. Calculate i.
0
Let m = -105 + 109. Suppose m*y + 4*r - 20 = 0, y = 5*r - r - 20. Factor y*c**3 + 1/3*c**2 + 0 - 1/6*c**5 + 1/6*c - 1/3*c**4.
-c*(c - 1)*(c + 1)**3/6
Let s(n) be the third derivative of -n**5/90 - n**4/4 - 8*n**3/9 - 112*n**2. Determine f so that s(f) = 0.
-8, -1
Let d(i) = -9*i**4 + 402*i**3 - 1189*i**2 + 11*i - 11. Let j(s) = -2*s**4 + 101*s**3 - 297*s**2 + 3*s - 3. Let m(t) = 3*d(t) - 11*j(t). Factor m(u).
-5*u**2*(u - 15)*(u - 4)
Let b be (-2)/(-3) - 916/(-3). Solve 6*u**2 + 306 + 14*u**3 + 2*u**5 - b + 10*u**4 = 0.
-3, -1, 0
Let c(x) be the first derivative of -19/2*x**3 + 6*x - 15/2*x**2 + 7 + 45/4*x**5 + 195/16*x**4. Solve c(o) = 0 for o.
-1, -2/3, 2/5
Solve 35*t**4 + 50*t**5 - 70*t**3 - 101*t**5 + 46*t**5 + 40*t**2 = 0 for t.
0, 1, 2, 4
Let u(y) = -38*y + 192. Let z be u(5). Let b(o) be the third derivative of -1/21*o**3 + 0 - 1/84*o**4 - 7*o**z + 0*o + 1/105*o**5. Solve b(v) = 0 for v.
-1/2, 1
Suppose -2*p - 4*o = -20, 2*o = -0*o + 2. Suppose -p*n - 2 = -34. What is h in -4/9*h**3 + 2/9*h**5 + 16/9*h**2 - 4/9*h**n - 14/9*h + 4/9 = 0?
-2, 1
Let v(m) = m**2 - 5*m - 4. Let p be v(6). Let x = -18 + 20. Factor 0*b**3 + 2*b**x - 1 - b**3 - p + 5*b - 3*b**2.
-(b - 1)**2*(b + 3)
Let j(r) be the first derivative of -2*r**5/5 - 17*r**4 - 634*r**3/3 - 416*r**2 + 1536*r - 251. Determine s so that j(s) = 0.
-16, -3, 1
Determine i, given that 52/7*i + 4/7*i**2 - 120/7 = 0.
-15, 2
Let s be (-77)/(-12)*(-12)/(-28). Factor -s*t - 25/4*t**3 + 1/4 + 35/4*t**2.
-(t - 1)*(5*t - 1)**2/4
Let n(v) be the second derivative of 0*v**2 + 0*v**4 - 5/12*v**3 + 0*v**6 - 5/84*v**7 + 1/4*v**5 - 6*v + 0. Factor n(u).
-5*u*(u - 1)**2*(u + 1)**2/2
Suppose -3*t + 6 = 3*f, -5*f = -4*t + 2*t - 38. Let i(a) = a**2 - 4*a - 10. Let d be i(f). Factor 2/3*b + 0 + 2/9*b**d.
2*b*(b + 3)/9
Suppose -49 + 33 = 2*p. Let y be 0*(1 + 10/p). Let 0*u**4 + 0*u - 3/4*u**5 + 3/4*u**3 + y*u**2 + 0 = 0. What is u?
-1, 0, 1
Let d(k) be the first derivative of 21*k**5/5 + 25*k**4/2 + 11*k**3 - 4*k - 27. Determine m, given that d(m) = 0.
-1, -2/3, 2/7
Let c be 0*(4 + -3)*1. Let q be (6/108)/(18/8 - 2). Factor -2/9 + q*u**2 + c*u.
2*(u - 1)*(u + 1)/9
Let p(y) be the first derivative of -y**8/5880 + y**7/2940 + y**6/1260 - y**5/420 - y**3/3 - 7. Let d(c) be the third derivative of p(c). Solve d(w) = 0 for w.
-1, 0, 1
Suppose -5*r + 6*p - p + 100 = 0, -53 = -3*r - 4*p. Let v = 23 - r. Determine z, given that 0*z - 1/3*z**3 + 1/3*z**2 + 0 - z**5 - 5/3*z**v = 0.
-1, 0, 1/3
Let u(m) be the third derivative of m**8/84 + 26*m**7/105 - 29*m**6/30 + m**5 - 114*m**2 + 4. Factor u(n).
4*n**2*(n - 1)**2*(n + 15)
Determine v so that 2/5*v**2 + 36/5 - 38/5*v = 0.
1, 18
Let d(h) be the third derivative of -h**5/210 + 5*h**4/7 - 300*h**3/7 + 230*h**2. Solve d(j) = 0.
30
Let o be 2/(-2)*(-72 + -3). Solve 0*r**2 + 2*r**2 - o - 30*r - 8*r**2 + 3*r**2 = 0.
-5
Let b(v) be the third derivative of -v**6/40 + 3*v**5/5 - 4*v**4 + 3*v**2 - 87*v. Find o such that b(o) = 0.
0, 4, 8
Let p(d) be the third derivative of -d**6/60 - 97*d**5/30 - 200*d**4 - 768*d**3 + 5*d**2 - 3. Factor p(n).
-2*(n + 1)*(n + 48)**2
Let o(d) be the second derivative of d**7/336 + d**6/720 + d**3/6 + 3*d**2 + 26*d. Let q(n) be the second derivative of o(n). Factor q(p).
p**2*(5*p + 1)/2
Let t = 40 - 61. Let u be (-3)/t - 13/(-7). Factor 4/7 - 6/7*y + 2/7*y**u.
2*(y - 2)*(y - 1)/7
Factor -2*k**2 - 5/2*k + 1 + 3/2*k**3.
(k - 2)*(k + 1)*(3*k - 1)/2
Let i be (-9795)/(-75)*(2 - 0). Let q = 262 - i. Let 1/5*p**2 + q - 4/5*p = 0. What is p?
2
Let f(d) be the first derivative of 0*d + 1/18*d**2 - 1/36*d**4 + 1 + 0*d**3. Find u, given that f(u) = 0.
-1, 0, 1
Let g(k) be the first derivative of k**6/60 - k**5/10 + k**4/6 + 6*k**2 - 12. Let p(j) be the second derivative of g(j). Solve p(h) = 0 for h.
0, 1, 2
Let l be 0/(-3 - 2) - 4. Let a be (((-45)/l)/(-3))/(1134/(-432)). Factor -4/7 + a*k - 6/7*k**2.
-2*(k - 1)*(3*k - 2)/7
Let u be (-141)/9 + 1 + -3. Let b = u + 18. Find l such that -1/3 + 0*l + b*l**2 = 0.
-1, 1
Let n = 335/12 + -83/3. Let o(f) be the second derivative of -4*f + 0 - 17/12*f**4 - 8/3*f**3 - n*f**5 - 2*f**2. Find a, given that o(a) = 0.
-2, -1, -2/5
Let r(t) = t**3 - 9*t**2 - 16*t + 25. Let s(a) = a**2 + a - 1. Let l(h) = -2*r(h) - 14*s(h). Factor l(v).
-2*(v - 3)*(v - 2)*(v + 3)
Factor -4/3*j**3 - 2/3*j**4 + 2/3*j**2 + 1/3*j**5 + 0 + j.
j*(j - 3)*(j - 1)*(j + 1)**2/3
Factor 24*l**2 - 576*l + 4608 - 1/3*l**3.
-(l - 24)**3/3
Let y(m) be the third derivative of -m**8/42 - m**7/14 + m**6/60 + 4*m**5/15 + m**4/4 - m**3/6 - 41*m**2. Determine j, given that y(j) = 0.
-1, 1/8, 1
Let t be ((-6)/(-63))/(80/120). Let o(x) be the second derivative of -t*x**2 + 0 - 5/42*x**3 - 6*x - 1/28*x**4. Suppose o(l) = 0. Calculate l.
-1, -2/3
Let z(f) be the third derivative of -f**8/3024 - 29*f**7/1890 + 7*f**6/60 - 97*f**5/270 + 131*f**4/216 - 11*f**3/18 - 140*f**2. Let z(j) = 0. Calculate j.
-33, 1
Let h(d) be the third derivative of d**7/1260 - d**6/36 - 11*d**5/60 - 5*d**4/3 + 29*d**2. Let n(v) be the second derivative of h(v). Factor n(i).
2*(i - 11)*(i + 1)
Let r(o) be the first derivative of 4*o**3 + 5 + 6 - 3*o**3 - 3*o. Factor r(n).
3*(n - 1)*(n + 1)
Let -26426*j**2 + 162*j - 288 + 26390*j**2 + 2*j**3 + 72 = 0. What is j?
3, 12
Let n(g) be the second derivative of g**7/280 - 11*g**6/240 + 3*g**5/20 - g**4/3 + 8*g. Let w(a) be the third derivative of n(a). Find k such that w(k) = 0.
2/3, 3
Let b(u) be the second derivative of -5*u**7/14 + u**6/6 + 29*u**5/4 + 85*u**4/4 + 85*u**3/3 + 20*u**2 + 2*u + 58. Suppose b(n) = 0. What is n?
-1, -2/3, 4
Let p(v) be the third derivative of 0*v - 9*v**2 + 3/14*v**4 - 4/7*v**3 + 0 - 3/70*v**5 + 1/280*v**6. Find w, given that p(w) = 0.
2
Suppose 0 = -5*h + 49*h + 10*h. Factor h - 2/3*f - 13/3*f**2 - 7*f**3.
-f*(3*f + 1)*(7*f + 2)/3
Determine z, given that 52*z**3 - 52*z + 164/3*z**2 - 160/3 - 4/3*z**4 = 0.
-1, 1, 40
Let g(p) be the second derivative of 0*p**2 + 4/57*p**3 + 0 + 9/190*p**5 + 11*p + 10/57*p**4. Fa