**5. Determine v so that k(v) = 0.
-1
Let r be ((-4)/(-10))/((-6)/302). Let f = 64/3 + r. Find w, given that -f*w - 2/5 + 4/5*w**3 + 2/5*w**5 - 4/5*w**2 + 6/5*w**4 = 0.
-1, 1
Suppose -3/2*a**2 - 3/4*a**4 - 9/2*a**3 + 9/4 + 15/4*a + 3/4*a**5 = 0. What is a?
-1, 1, 3
Let z be ((7 + -1)/(-24))/(-2 + 1). Let u(v) be the first derivative of 1/20*v**5 - 8 - 1/4*v**4 - 1/2*v**2 + 1/2*v**3 + z*v. Factor u(y).
(y - 1)**4/4
Let v(x) be the first derivative of -5*x**5 - 10*x**4 + 220*x**3/3 - 40*x**2 - 149. Solve v(n) = 0.
-4, 0, 2/5, 2
Suppose -v + 4*v = 3*a + 12, 20 = -2*v - 5*a. Let y(d) be the first derivative of 3 + 1/8*d**4 + d**2 + v*d + 2/3*d**3. Factor y(m).
m*(m + 2)**2/2
Determine u, given that 5/3*u**2 + 1/3*u**3 + 12 - 32/3*u = 0.
-9, 2
Let u(n) be the third derivative of -n**7/525 + n**6/100 - n**5/50 + n**4/60 - 483*n**2. Factor u(f).
-2*f*(f - 1)**3/5
Let h(i) = -3*i**3 + i**2 + 2*i + 2. Let f be h(0). Solve -34*w**2 - w**5 + w + 66*w**2 + 2*w**4 - 34*w**f = 0.
-1, 0, 1
Let x = -145 + 178. Let n = x - 33. What is r in 2/3*r**3 + n*r**2 - 2/3*r - 1/3*r**4 + 1/3 = 0?
-1, 1
Let g = 2084 + -2082. What is y in 2/9*y**g - 2/9*y - 4/9 = 0?
-1, 2
Let l(z) be the third derivative of -2*z**7/147 + 4*z**6/105 + 4*z**5/105 + z**2 + 12. Suppose l(w) = 0. Calculate w.
-2/5, 0, 2
Let l(u) be the third derivative of 3*u**5/40 + 5*u**4/24 - 10*u**2 - u. What is z in l(z) = 0?
-10/9, 0
Factor 0*t + 16*t**2 + 0 - 4/3*t**3.
-4*t**2*(t - 12)/3
Let w(u) be the second derivative of u**7/210 + 2*u**6/75 + 3*u**5/50 + u**4/15 + u**3/30 + 2*u + 1. What is g in w(g) = 0?
-1, 0
Let g(x) be the first derivative of 5*x**3/3 - 475*x**2/2 + 476. Factor g(c).
5*c*(c - 95)
Let d(x) be the first derivative of -18 + 0*x**2 + 0*x - 2/39*x**3. Find v, given that d(v) = 0.
0
Determine t so that 2/15*t**3 + 34*t - 578/15 + 22/5*t**2 = 0.
-17, 1
Determine w, given that 12*w**2 - 1212 + 1212 + 4*w**4 + 20*w**3 - 36*w = 0.
-3, 0, 1
Let l(w) be the first derivative of -w**4/24 - 319*w**3/18 - 8533*w**2/4 - 8427*w/2 + 629. Factor l(y).
-(y + 1)*(y + 159)**2/6
Let b(h) be the first derivative of 2*h**5/45 - 11*h**4/18 - 2*h**3/27 + 11*h**2/9 - 235. Find c, given that b(c) = 0.
-1, 0, 1, 11
Let u(p) = 4*p**3 - 4*p**2. Suppose -5*h + h = -288. Suppose -9*l + 12*l = -h. Let f(b) = b**3 - b**2. Let n(j) = l*f(j) + 5*u(j). Factor n(t).
-4*t**2*(t - 1)
Let w = -27 - -32. Suppose 0 = w*f - 0*f - 10. Factor -26*i**5 + 0*i**4 + 28*i**5 - 2*i**3 + f*i**4 - 2*i**2.
2*i**2*(i - 1)*(i + 1)**2
Let t(j) be the third derivative of 3*j**6/40 + j**5/5 - j**4/8 - j**3 - 47*j**2 + 2. Factor t(x).
3*(x + 1)**2*(3*x - 2)
Let g(h) be the second derivative of 4/15*h**3 + 4/15*h**2 + 13/90*h**4 + 1/225*h**6 + 12*h + 1/25*h**5 + 0. Let g(u) = 0. Calculate u.
-2, -1
Let j(l) be the first derivative of l**9/2016 - 3*l**8/1120 + l**6/60 - 4*l**3/3 + 11. Let c(w) be the third derivative of j(w). Factor c(h).
3*h**2*(h - 2)**2*(h + 1)/2
Suppose 15 = -w + 5*n, 4*w - 4*n = 5*w - 3. Let p be (3 + 7)/w - (-28)/5. Let -54/5*l + p*l**2 + 54/5 - 2/5*l**3 = 0. What is l?
3
Let y(d) be the first derivative of -2*d**3/3 + 12*d**2 + 26*d - 135. Factor y(b).
-2*(b - 13)*(b + 1)
Let o(t) = 3*t**2 + 129*t - 133. Let m(l) = l**2 - l + 1. Let c(y) = m(y) + o(y). Let c(z) = 0. What is z?
-33, 1
Factor 6*n**4 + 2014*n**3 - 2020*n**3 - 2*n**4 - 8 - 30*n - 32*n**2.
2*(n - 4)*(n + 1)**2*(2*n + 1)
Let m(v) be the second derivative of -1/3*v**3 - 25*v - 6/5*v**2 + 1/30*v**4 + 0. Find c, given that m(c) = 0.
-1, 6
Suppose -4 = -3*v + j, 4 - 7 = -2*v + j. Let u(x) = -x**3 - x**2 + x. Let n(f) = -152*f**3 + 52*f**2 + 16*f - 4. Let w(b) = v*n(b) - 8*u(b). Factor w(p).
-4*(3*p - 1)**2*(4*p + 1)
Suppose 9/2*m - 3/2*m**2 - 3 = 0. What is m?
1, 2
Let k(i) be the third derivative of i**8/1512 + i**7/945 - 7*i**6/540 - i**5/270 + i**4/18 + 6*i**2 - 20. Find g such that k(g) = 0.
-3, -1, 0, 1, 2
Let c(i) be the second derivative of i**5/110 - 5*i**4/22 + 21*i**3/11 - 49*i**2/11 + 256*i. Solve c(y) = 0 for y.
1, 7
Solve 144/5*x + 6/5*x**4 - 104/5*x**2 - 64/5 - 2/5*x**5 + 4*x**3 = 0.
-4, 1, 2
Let j(m) be the third derivative of -m**5/30 - 7*m**4/12 - 7*m**3/6 + 18*m**2. Let o(r) = 9*r**2 + 69*r + 36. Let p(a) = -24*j(a) - 5*o(a). Factor p(b).
3*(b - 4)*(b + 1)
Let z(n) be the third derivative of n**10/90720 - n**9/22680 - 7*n**4/8 - 12*n**2. Let l(s) be the second derivative of z(s). Find v such that l(v) = 0.
0, 2
Let -2/5*l**3 - 5936/3*l - 842/15*l**2 - 1960/3 = 0. What is l?
-70, -1/3
Let a(g) = g**2 - 8*g + 10. Let f be a(7). Suppose 5*v**3 + 6*v - 3*v**f - 6*v**2 - 2 + 0 + 0*v = 0. What is v?
1
Let p(s) be the third derivative of -s**6/24 - s**5/4 + 5*s**4/24 + 5*s**3/2 + 52*s**2. Suppose p(w) = 0. Calculate w.
-3, -1, 1
Let y(w) be the first derivative of 28*w**5/25 - 236*w**4/5 + 6784*w**3/15 + 2016*w**2 + 5184*w/5 - 784. Suppose y(n) = 0. What is n?
-2, -2/7, 18
Let t(o) be the first derivative of -o**4/2 + 20*o**3/7 - 29*o**2/7 + 12*o/7 - 49. Let t(r) = 0. What is r?
2/7, 1, 3
Let u(c) = 2*c + 2. Let r be u(6). Let f be 6*(r/(-4))/(-7). Let 2/5*q**5 + 0 + 0*q**2 + 4/5*q**4 + 0*q**f + 0*q = 0. What is q?
-2, 0
Suppose -56 = -k + 5*k. Let z be (k/(-21))/(1/3). Factor -2*p**z - 4*p**2 + 5*p**2 - p + 0*p.
-p*(p + 1)
Let f(r) be the first derivative of r**5/8 + 247*r**4/32 + 1609*r**3/12 + 258*r**2 + 144*r - 443. Solve f(q) = 0 for q.
-24, -1, -2/5
Let f = -7936 - -15877/2. Let 2*t**2 + 1/2*t + t**4 + f*t**3 + 0 = 0. Calculate t.
-1, -1/2, 0
Let y(g) be the third derivative of g**6/1080 - g**5/540 - g**4/216 + g**3/54 - g**2 + 11. Factor y(j).
(j - 1)**2*(j + 1)/9
Let q be (27/12 - 3)*-4. Suppose 0 = -i + q. Find s, given that 3*s**2 - s**4 - 3*s**4 + 2*s**i - 4*s**4 + 5*s**2 - 2*s = 0.
-1, 0, 1/4, 1
Let j(w) be the third derivative of 0 + 0*w**3 - 1/30*w**4 - 1/1680*w**8 - 13/600*w**6 - 1/175*w**7 - 1/25*w**5 - 7*w**2 - 3*w. Suppose j(a) = 0. Calculate a.
-2, -1, 0
Factor -72*j**3 - 1889568*j + 1/9*j**4 + 76527504 + 17496*j**2.
(j - 162)**4/9
Suppose -2*b - 2*b = 0. Let p = 2 - b. Find c, given that 13*c**p + c**3 + c**3 + 5*c - 6*c**2 + 1 + c**3 = 0.
-1, -1/3
Let s(c) be the third derivative of -c**5/30 + 5*c**4/12 + 2*c**3 - 116*c**2. Factor s(o).
-2*(o - 6)*(o + 1)
Let a be -26 - -24 - 10/(-4). What is i in 1 + a*i - 1/2*i**2 = 0?
-1, 2
Let f(s) be the third derivative of s**7/28 + 3*s**6/80 - 47*s**5/40 - 27*s**4/16 + 9*s**3/2 - s**2 + 4*s. Determine i so that f(i) = 0.
-3, -1, 2/5, 3
Let s = -90/113 - 93091/452. Let q = s - -209. What is a in 0 + 3/2*a - 3/4*a**2 + 3/4*a**5 - q*a**3 + 3/4*a**4 = 0?
-2, -1, 0, 1
Suppose 5*c - 14 = 2*i, 0 = -54*i + 58*i - 3*c. Let k(q) be the second derivative of -1/10*q**5 + 8*q - 1/3*q**i + 0 - 1/3*q**4 + 0*q**2. Solve k(u) = 0.
-1, 0
Let z(f) be the first derivative of 4*f**5/5 - 2*f**4 + 4*f**3/3 + 49. Find v, given that z(v) = 0.
0, 1
Let n(p) be the second derivative of -p**6/840 + p**4/56 - p**3/21 + 39*p**2/2 - 27*p. Let r(y) be the first derivative of n(y). Solve r(g) = 0 for g.
-2, 1
Let n be 1 - (-4 - (-3 - -1)). Let z(a) = -a**2 - 7*a + 13. Let k(r) = -3*r + 6. Let p(l) = n*z(l) - 5*k(l). Determine d so that p(d) = 0.
-3, 1
Factor -86*o**2 - 173*o**4 + 114*o**2 - 8*o - 8*o**3 + 161*o**4.
-4*o*(o - 1)*(o + 2)*(3*o - 1)
Let b(y) = 74*y + 603. Let s be b(-8). Let o(f) be the first derivative of 1/21*f**3 + s + 1/14*f**2 + 0*f - 1/28*f**4 - 1/35*f**5. Solve o(r) = 0 for r.
-1, 0, 1
Let b(l) be the second derivative of -1/10*l**6 + 5*l + 3/4*l**4 + 0 + 0*l**2 + 0*l**5 + l**3. Solve b(z) = 0.
-1, 0, 2
Let t(f) be the first derivative of -f**4/24 + f**3/18 + f**2/12 - f/6 + 64. Solve t(c) = 0.
-1, 1
Let a(y) be the second derivative of 1/12*y**4 + 1/40*y**5 - 7/12*y**3 + y**2 + 0 + 28*y. Factor a(q).
(q - 1)**2*(q + 4)/2
Suppose -17*l + 445 = -12*l. Factor l*m**3 - 3*m**2 + 2*m**4 - 87*m**3 - m**2.
2*m**2*(m - 1)*(m + 2)
Let a(i) be the second derivative of i**6/120 + 9*i**5/160 + 11*i**4/96 - i**2/4 - 9*i - 4. Solve a(d) = 0.
-2, -1, 1/2
Determine m so that -312*m**2 + 39*m + m**4 + 139*m**2 + 144*m**2 - 2*m**4 - 13 - 5 + 9*m**3 = 0.
1, 2, 3
Let b be 6/7*7/2. Factor -3*t**3 + b*t**3 + 0*t**3 + 3*t**2 - 3*t**3.
-3*t**2*(t - 1)
Suppose -3*c + 5*n + 373 - 1130 = 0, -c - 269 = -5*n. Let q = c + 247. L