- 7. Let z be k(-6). Let c be ((-12)/(-10))/((-10)/z). Determine y, given that y**2 - y + y**3 + c*y**2 + 0*y**2 - 7*y**4 + 3*y**4 = 0.
-1, 0, 1/4, 1
Let y(r) be the second derivative of 7*r**5/20 + 4*r**4 + 71*r**3/6 + 15*r**2 - 500*r. Find v such that y(v) = 0.
-5, -1, -6/7
Let x(h) = -h**3 - 1. Let a(s) = -4*s**3 + s**2 - 3. Let w(o) = -4*a(o) + 12*x(o). Factor w(p).
4*p**2*(p - 1)
Let g(d) be the first derivative of -d**4/14 - 32*d**3/21 - 11*d**2 - 28*d + 208. Let g(u) = 0. Calculate u.
-7, -2
Let i be (16/5 - 2) + 3300/(-3375). Factor -4/9 + 2/9*o + i*o**2.
2*(o - 1)*(o + 2)/9
Let s(u) = -8 - 4*u**2 + 3*u**2 - 6*u + 17. Let l be s(-7). Factor 4/11 - 2/11*m - 2/11*m**l.
-2*(m - 1)*(m + 2)/11
Let r(t) = 70*t**4 - 200*t**3 + 165*t**2 - 50*t - 5. Let s(f) = -f**4 - 1. Let y(x) = -r(x) + 10*s(x). Find l, given that y(l) = 0.
1/4, 1
Let v(x) = 9*x**4 - 9*x**3 - 15*x**2 - 32*x. Let i(l) = -8*l**4 + 8*l**3 + 16*l**2 + 28*l. Let a(j) = -5*i(j) - 4*v(j). Let a(o) = 0. What is o?
-1, 0, 3
Let x(h) be the first derivative of -4*h**3/3 + 248*h**2 - 15376*h + 76. Factor x(d).
-4*(d - 62)**2
Let v(w) be the second derivative of -w**6/270 - 13*w**5/180 - 11*w**4/108 + 13*w**3/54 + 2*w**2/3 - w + 20. Let v(b) = 0. Calculate b.
-12, -1, 1
Suppose -5*u + 323 = -172. What is v in 2*v**4 - 100*v**3 + 0*v**4 + u*v**3 - v**5 = 0?
0, 1
Let p = 1384 - 1379. Let d(u) be the first derivative of -3 + 1/2*u**4 + 2/5*u**p - 2/3*u**3 + 0*u - 1/3*u**6 + 0*u**2. Factor d(o).
-2*o**2*(o - 1)**2*(o + 1)
Let 174/5*h**2 + 54/5 - 9/5*h**3 - 219/5*h = 0. What is h?
1/3, 1, 18
Let g(c) = c**3 + 2*c**2 + 1. Let k(z) = z**3 - 55*z**2 + 48*z - 2. Let w(v) = 2*g(v) + k(v). Factor w(f).
3*f*(f - 16)*(f - 1)
Let c(v) be the second derivative of -v**7/2520 + v**6/720 + v**4/4 - 18*v. Let r(i) be the third derivative of c(i). Find z such that r(z) = 0.
0, 1
Let q(d) be the second derivative of -d**10/15120 - d**9/18900 - 11*d**4/12 - 7*d. Let j(b) be the third derivative of q(b). Factor j(a).
-2*a**4*(5*a + 2)/5
Suppose 9*p + 17 = 71. Let g(q) = -3*q**2 + 18*q - 15. Let b(l) = -9*l**2 + 54*l - 45. Let i(t) = p*b(t) - 17*g(t). Find u, given that i(u) = 0.
1, 5
Let k(w) be the first derivative of -2*w**5/5 + 5*w**4 + 2*w**3/3 - 10*w**2 - 180. Factor k(x).
-2*x*(x - 10)*(x - 1)*(x + 1)
Factor 7*h**5 + 17*h - 6*h**4 + 15*h - 29*h - 12*h**5 + 2*h**5 + 6*h**2.
-3*h*(h - 1)*(h + 1)**3
Let p(w) = 160*w**2 + 14*w - 13. Let n be p(1). Let o = 1289/8 - n. Factor 1/8*i**3 + 1/4*i**2 - 1/4 - o*i.
(i - 1)*(i + 1)*(i + 2)/8
Suppose -25*v = 12*v - 222. Suppose -5*x + 5*r - 5 = 0, 7*r = 4*x + 4*r + 3. Factor x*p + v - 3/2*p**2.
-3*(p - 2)*(p + 2)/2
Let y(w) be the second derivative of w**5/4 - 25*w**4/12 + 35*w**3/6 - 15*w**2/2 + 171*w. What is a in y(a) = 0?
1, 3
Let h = -2150 + 15065/7. Let -3/7 - 3/7*n + h*n**2 - 9/7*n**3 = 0. What is n?
-1/3, 1
Let d(i) = 9*i**4 + 11*i**3 + 9*i**2 - 3*i + 2. Let p(k) = -8*k**4 - 12*k**3 - 11*k**2 + 2*k - 1. Let o(q) = -5*d(q) - 6*p(q). Factor o(j).
(j + 1)**2*(j + 4)*(3*j - 1)
Let w(b) be the third derivative of 0*b**3 + 1/300*b**6 - 1/75*b**5 + 1/60*b**4 - b**2 + 0*b + 0. Let w(l) = 0. What is l?
0, 1
Factor 971*d - 1343*d + 2*d**2 - 252 + 622*d.
2*(d - 1)*(d + 126)
Solve 71 + 256 - 127 - 2*s**2 - 198*s = 0.
-100, 1
Let p be ((-4)/120*-5)/((-2)/(-942)). Let z = -76 + p. Factor 5/4*c**5 - 1/2 - z*c**2 + 3*c**4 - 9/4*c + c**3.
(c - 1)*(c + 1)**3*(5*c + 2)/4
Factor 8/5*d + 0 + 4/5*d**3 + 12/5*d**2.
4*d*(d + 1)*(d + 2)/5
Let f(u) be the third derivative of -u**8/112 + u**7/35 + 3*u**6/20 - u**5 + 19*u**4/8 - 3*u**3 - 5*u**2 + 5. Let f(w) = 0. What is w?
-3, 1, 2
Factor 6*j**3 - 3*j**4 + 28*j**2 - 3456*j + 6920*j - j**5 - 3440*j.
-j*(j - 3)*(j + 2)**3
Let d(u) be the second derivative of -u**7/210 + u**6/6 - 19*u**5/10 + 9*u**4/2 + 81*u**3/2 + 729*u**2/10 - 5*u + 9. Factor d(t).
-(t - 9)**3*(t + 1)**2/5
Let w be (-4 + (-6)/(-1))/(-1). Let n be (-1)/w*(-7 + 7). Factor -1/5*h + n - 1/5*h**2.
-h*(h + 1)/5
Let b(s) = -s**3 - 5*s**2 - 18*s - 142. Let n be b(-6). Solve 0*u**3 - 1/4*u + 1/4*u**5 + 0 + 1/2*u**4 - 1/2*u**n = 0.
-1, 0, 1
Let x(u) be the second derivative of -u**8/26880 - u**7/1260 - 13*u**4/12 + 39*u. Let s(k) be the third derivative of x(k). Factor s(r).
-r**2*(r + 8)/4
Let u = -816 - -821. Let s(y) be the third derivative of 0*y**3 + 0*y + 0 + 1/30*y**u + 1/12*y**4 - 6*y**2. What is o in s(o) = 0?
-1, 0
Let x(o) be the second derivative of o**4/12 + 3*o**3/2 + 8*o**2 - 12*o. Let v be x(-7). Let 1/2*n - 1/2*n**v + 0 = 0. What is n?
0, 1
Factor -2*z**3 + 17*z + z**2 - 9 - 8*z + z**3.
-(z - 3)*(z - 1)*(z + 3)
Solve 1/2*z**4 - 2166*z + 0 + 73/2*z**3 + 608*z**2 = 0 for z.
-38, 0, 3
Let g(t) = t**3 + 8*t**2 + 3*t - 13. Let c be g(-5). Factor c*m**2 + 27*m**4 + 15*m**3 - 36*m**4 - 60*m + 25*m + 6.
-(m - 3)*(m + 2)*(3*m - 1)**2
Suppose -2 = 5*b + 4*f - 6, -4*f = -5*b + 36. Suppose 8*c = b*c. Let c*g**3 - 4*g**2 + 2 + 4*g - 2*g**3 + 2*g**4 + 4*g**5 - 6*g**3 = 0. What is g?
-1, -1/2, 1
Suppose -5*o - 5*k + 25 = 0, -4*o + 15 = 5*k - 7. Let b(p) = -76*p - 150. Let g be b(-2). Let -2/3*m**g + 2/9*m**o + 4/9*m + 0 = 0. Calculate m.
0, 1, 2
Suppose 6 = 6*v + 6. Let y(t) be the third derivative of v*t**6 + 0*t**3 + t**2 - 1/1344*t**8 + 0 + 1/96*t**4 + 0*t + 1/120*t**5 - 1/420*t**7. Factor y(a).
-a*(a - 1)*(a + 1)**3/4
Let q be 0*(9/(-6) - -2). Let x(s) be the third derivative of -1/60*s**6 + q*s + 1/12*s**4 + 0 + 1/105*s**7 + 0*s**3 + 2*s**2 - 1/30*s**5. Factor x(g).
2*g*(g - 1)**2*(g + 1)
Let h(u) be the third derivative of 1/300*u**6 - 9*u**2 - 1/30*u**4 + 0 - 1/150*u**5 + 0*u + 0*u**3. Find y such that h(y) = 0.
-1, 0, 2
Factor -14*w - 8*w - 5*w + w + w**2 + 3*w.
w*(w - 23)
Solve -12 - 21/2*s + 3/2*s**2 = 0 for s.
-1, 8
Suppose -4/7*q + 0 - 2/7*q**2 + 2/7*q**4 + 4/7*q**3 = 0. Calculate q.
-2, -1, 0, 1
Factor 11/4*x**2 + 1 + 15/4*x.
(x + 1)*(11*x + 4)/4
Factor -15/2*u + 9 + 3/2*u**2.
3*(u - 3)*(u - 2)/2
Suppose 26*s - 77*s + 30 = -36*s. What is g in -2/5*g + 0 + 1/5*g**s = 0?
0, 2
Let y(t) = t**4 + 17*t**3 - 23*t**2 + 3*t. Let p(x) = -2*x**4 - 50*x**3 + 68*x**2 - 8*x. Let a(i) = 3*p(i) + 8*y(i). What is r in a(r) = 0?
0, 2, 5
Let k be 6 + 6 + 69/(-6). Let u(s) be the first derivative of -k*s**4 + 2/3*s**3 + s**2 - 2*s + 1. Determine t, given that u(t) = 0.
-1, 1
Let m be 8 + 0 - (-3 - -6). Let z(d) be the second derivative of 0 + 2*d + 0*d**2 + 0*d**3 + 1/4*d**m + 1/18*d**6 - 5/36*d**4 - 5/42*d**7. Solve z(u) = 0 for u.
-1, 0, 1/3, 1
Let m(r) = -r + 11. Let w be m(9). Factor -c + c + 7*c**w - 5*c**2.
2*c**2
Let j(l) = -10*l**3 - 5*l**2 + 10*l + 5. Let k(n) = 60*n**3 + n**2 - 1 - 30*n**3 - 29*n**3 - n. Let w(y) = -2*j(y) - 22*k(y). Determine x, given that w(x) = 0.
-6, -1, 1
Let y = -200 - -214. Suppose y*k = 1 - 1. Factor 2*f**3 - 1/2*f + 0 + k*f**2.
f*(2*f - 1)*(2*f + 1)/2
Let i(r) be the first derivative of 4*r**5/5 - 56*r**4 + 436*r**3/3 - 108*r**2 + 110. Let i(q) = 0. What is q?
0, 1, 54
Let i(p) = -6*p**2 - 3*p - 3. Suppose n + 1 = -l - 0*l, 3*l - 5*n - 37 = 0. Let g(r) = r**3 - 5*r**2 - 4*r - 4. Let v(w) = l*i(w) - 3*g(w). Factor v(a).
-3*a**2*(a + 3)
Let x(h) be the third derivative of h**8/168 + 8*h**7/105 - 7*h**6/10 + 34*h**5/15 - 47*h**4/12 + 4*h**3 + 105*h**2. Factor x(v).
2*(v - 1)**4*(v + 12)
Let o(b) = -38*b**3 + b**2 - 2*b. Let q be o(1). Let j = q + 79/2. Suppose j*v + 1/4*v**2 + 0 = 0. What is v?
-2, 0
Let k(u) be the first derivative of 0*u**3 - 2/5*u**2 + 3/20*u**4 + 0*u + 1/25*u**5 - 24. Determine d, given that k(d) = 0.
-2, 0, 1
Let q(d) be the second derivative of 0*d**2 + 4/3*d**3 - 3/5*d**5 + 0 - 1/3*d**4 - 5*d. Factor q(i).
-4*i*(i + 1)*(3*i - 2)
Let h(w) = -6*w**4 + 4*w**3 + 2*w**2 - 9*w - 1. Let b = 25 - 24. Let s(d) = d**4 - d**2 + d + 1. Let m(z) = b*h(z) + 5*s(z). Find v, given that m(v) = 0.
-1, 1, 2
Let i(l) be the third derivative of l**7/210 - l**6/135 - l**5/30 + l**4/9 + 4*l**3/3 - 7*l**2. Let h(v) be the first derivative of i(v). Factor h(g).
4*(g - 1)*(g + 1)*(3*g - 2)/3
Let v(g) = -g**3 - 6*g**2 + 7*g + 5. Let r be v(-7). Suppose 8 - 109*y**3 + 242*y**3 + 33*y**4 + 7*y**r - 18*y + 9*y**2 - 122*y**3 - 50*y**2 = 0. What is y?
-4, -1, 2/7, 1
Let p = 1 + -7. Let o be (28/(-21))/(4/p). Factor -2 - 76*z + 2*z**o + 76*z.
2*(z - 1)*(z +