9*n. Find v, given that g(v) = 0.
-1, 1
Let w(i) = -35*i + 0*i**3 + i**3 + 37*i + 4*i**2 + 2. Let c(z) = 6*z**3 + 23*z**2 + 11*z + 11. Let r(j) = -6*c(j) + 34*w(j). Determine h so that r(h) = 0.
-1, 1
Let t(a) = -5*a**4 + 48*a**3 + 134*a**2 + 112*a + 31. Let h(x) = 2*x**4 - 16*x**3 - 45*x**2 - 37*x - 10. Let m(z) = -8*h(z) - 3*t(z). Solve m(d) = 0 for d.
-13, -1
Let m(v) be the second derivative of 1/9*v**6 + 6*v + 0 - 25/42*v**7 + 2/9*v**3 + 53/60*v**5 - 7/9*v**4 + 0*v**2. Determine a, given that m(a) = 0.
-1, 0, 1/3, 2/5
Factor 0 - 2/9*m**2 + 0*m**3 + 2/9*m**4 + 0*m.
2*m**2*(m - 1)*(m + 1)/9
Factor -48/7*c**4 + 0 + 0*c + 27/7*c**5 + 15/7*c**3 + 6/7*c**2.
3*c**2*(c - 1)**2*(9*c + 2)/7
Let a(y) be the second derivative of -y**6/160 + y**5/24 - y**4/24 - y**3/2 - y. Let i(o) be the second derivative of a(o). Determine g, given that i(g) = 0.
2/9, 2
Let n(g) = 79*g**2 - 56*g + 16. Let o(r) be the second derivative of 13*r**4/2 - 19*r**3/2 + 15*r**2/2 + 2*r. Let k(u) = 3*n(u) - 4*o(u). Factor k(i).
-3*(5*i - 2)**2
Determine h, given that -5*h**3 + 3*h**3 + h**3 - 8 - 24*h - 3*h**3 - 18*h**2 = 0.
-2, -1/2
Let a = 293 + -291. Determine d so that 2*d - 4/3 + 2/3*d**a - 2*d**3 + 2/3*d**4 = 0.
-1, 1, 2
Let i(j) be the third derivative of j**5/450 - j**4/180 - 2*j**3/45 + 2*j**2. What is h in i(h) = 0?
-1, 2
Suppose 7*i + 3*i - 30 = 0. Let z(g) be the first derivative of 5/24*g**6 + 7/20*g**5 + 0*g**i + 0*g - 3 + 0*g**2 + 1/8*g**4. Let z(k) = 0. What is k?
-1, -2/5, 0
Let x(j) be the third derivative of 2*j**7/735 - j**6/105 + j**5/105 - 3*j**2. Let x(y) = 0. Calculate y.
0, 1
Let t(g) = -6*g - 13 + 4*g + 7*g. Let d be t(3). Determine q, given that -5/3*q**d + 0 - 1/3*q = 0.
-1/5, 0
Let v(f) be the first derivative of -3*f**4/16 - 5. Factor v(a).
-3*a**3/4
Let o(a) be the third derivative of -a**6/720 + a**5/72 - 7*a**4/144 + a**3/12 + 21*a**2. Suppose o(k) = 0. Calculate k.
1, 3
Let x(u) = -u**3 + 3*u**2 - u - 3. Let d be x(3). Let i = d - -9. What is v in 10/7*v**2 - 10/7*v**4 - 4/7*v**i + 0 + 4/7*v = 0?
-1, -2/5, 0, 1
Let l be (-29)/(-9) - (-4)/(-18). Factor l*o**2 - 7*o + 0*o + 3*o**3 + o.
3*o*(o - 1)*(o + 2)
Let i(a) = 4*a**2 - 3*a + 5. Let l(x) = -2*x**2 + 2*x - 2. Let z(r) = -2*i(r) - 5*l(r). Factor z(s).
2*s*(s - 2)
Let r(v) = v**2 - v - 9. Let b be r(7). Suppose 4*l - 5*o = b, -2*o - 7 - 7 = -2*l. Let 0 + 1/2*x**3 - 1/2*x + 0*x**l = 0. What is x?
-1, 0, 1
Let q(f) = -f**3 - 4*f**2 - 5*f - 3. Let s be q(-3). Let l = 17 - 15. Factor 2*h**l - 4*h**3 + h + h**5 + 8 + 2*h**s - h**4 - 9.
(h - 1)**3*(h + 1)**2
Let y(v) = -4. Suppose -4 = 3*u + 4*i + 6, 5*i = -2*u - 2. Let c be 9/6*20/u. Let n(f) = f**2 + 9. Let w(p) = c*y(p) - 2*n(p). Factor w(m).
-2*(m - 1)*(m + 1)
Let a(v) be the third derivative of -v**7/3150 + v**6/600 - v**5/300 - 11*v**4/24 + 8*v**2. Let b(q) be the second derivative of a(q). Factor b(l).
-2*(l - 1)*(2*l - 1)/5
Let o(d) = 7*d**3 - 7*d**2 - 15*d + 23. Let g(h) = 2*h**3 - 2*h**2 - 5*h + 8. Let x(i) = -8*g(i) + 3*o(i). Suppose x(w) = 0. What is w?
-1, 1
Let i(o) be the second derivative of o**8/20160 - o**7/2520 + o**6/1080 + o**4/12 - 5*o. Let b(w) be the third derivative of i(w). What is s in b(s) = 0?
0, 1, 2
Let k(m) be the third derivative of -m**9/1008 + m**8/560 + m**7/280 - m**6/120 + m**3/3 + 10*m**2. Let v(c) be the first derivative of k(c). Factor v(o).
-3*o**2*(o - 1)**2*(o + 1)
Let j = -12 - -6. Let g = j - -9. Factor -3*t**4 - 7*t**3 - t + 3*t**2 - 4*t**g + 5*t**3 + 7*t.
-3*t*(t - 1)*(t + 1)*(t + 2)
Let a(b) = -3*b**5 - 9*b**4 + 6*b**3 - 14*b**2 + 9*b + 3. Let q(z) = 2*z**5 + 8*z**4 - 7*z**3 + 13*z**2 - 8*z - 2. Let n(r) = -3*a(r) - 4*q(r). Factor n(s).
(s - 1)**5
Let f(o) be the second derivative of 1/24*o**4 + 0*o**3 - 1/20*o**5 + 1/60*o**6 + 0 + 0*o**2 + o. Factor f(v).
v**2*(v - 1)**2/2
Let w be 716/(-712) + (-3 - -4). Let y = 269/356 + w. Find v, given that y*v + 3/4*v**2 + 1/4*v**3 + 1/4 = 0.
-1
Let l(y) be the third derivative of y**7/2100 + y**6/1800 - y**4/12 + 3*y**2. Let u(c) be the second derivative of l(c). Factor u(z).
2*z*(3*z + 1)/5
Let u be (30/(-54))/((-13)/6 + 2). Solve -2*x**3 + 2*x + 2/3 - u*x**2 + 8/3*x**4 = 0.
-1, -1/4, 1
Let v(i) be the third derivative of 3/20*i**5 + 0*i + 3*i**2 + 1/12*i**4 + 0 + 1/8*i**6 + 11/210*i**7 + 1/112*i**8 + 0*i**3. Find l such that v(l) = 0.
-1, -2/3, 0
Let v(s) be the second derivative of s**5/300 + s**4/40 + s**3/15 + 3*s**2/2 + 2*s. Let p(w) be the first derivative of v(w). Find d such that p(d) = 0.
-2, -1
Factor 3*o**3 + 3/2*o**5 - 9/2*o + 9/2*o**4 - 3*o**2 - 3/2.
3*(o - 1)*(o + 1)**4/2
Let l be 3/(-6)*(5 + (-7 - 2)). Determine z so that 0 + 0*z + 2/11*z**3 - 2/11*z**l = 0.
0, 1
Let k(n) = -3*n. Let f(d) = -d**2 - 5*d + 1. Let x(l) = -3*f(l) + 5*k(l). Factor x(v).
3*(v - 1)*(v + 1)
Let w = 26 - -72. Determine p so that -w*p**3 + 48*p + 10 + 61*p**2 - 19*p**2 - 2 = 0.
-2/7, 1
Factor 1 + 1/3*i**2 - 4/3*i.
(i - 3)*(i - 1)/3
Suppose 0*m + 3*m = 0. Factor 1/4*k**3 - 1/4*k + m + 1/4*k**2 - 1/4*k**4.
-k*(k - 1)**2*(k + 1)/4
Factor -61/3*q**2 - 4/3 + 49/6*q**4 + 10*q + 7/2*q**3.
(q - 1)*(q + 2)*(7*q - 2)**2/6
Let s = 4/15 + -1/15. Factor 1/5*w**2 + 1/5*w**3 - s*w**4 + 0 + 0*w - 1/5*w**5.
-w**2*(w - 1)*(w + 1)**2/5
Let g be 3/((-27)/24) + 12/4. What is p in -g*p**3 - 1/3*p + 0 - 2/3*p**2 = 0?
-1, 0
Let z = 111/71 - 9/142. Factor 1/8*c**3 + z*c**2 + 8 + 6*c.
(c + 4)**3/8
Suppose -2*d**5 + 6*d**2 - 6*d**4 - 4*d**5 - 9*d**3 + 15*d**5 = 0. Calculate d.
-1, 0, 2/3, 1
Let v(x) = -21*x**4 - 25*x**3 + 17*x**2 + 8*x - 7. Let w(o) = 11*o**4 + 13*o**3 - 8*o**2 - 4*o + 4. Let u(b) = -4*v(b) - 7*w(b). Let u(r) = 0. What is r?
-2, -2/7, 0, 1
Suppose -3*q - 2*t + 18 = -28, 4*t - 20 = 0. Suppose 4*w = -0*w + q. Let 2 - w*l + l - l - 4*l**2 + 2*l**2 = 0. What is l?
-2, 1/2
Let z(m) be the third derivative of m**8/112 - m**7/10 + 9*m**6/20 - m**5 + m**4 + 9*m**2. Let z(p) = 0. Calculate p.
0, 1, 2
Let d(x) be the second derivative of 9*x**7/280 + x**6/10 - 11*x**5/40 + x**4/4 - 5*x**3/6 - 3*x. Let j(b) be the second derivative of d(b). Factor j(q).
3*(q + 2)*(3*q - 1)**2
Let a(m) be the second derivative of m**7/21 - 2*m**5/5 + 31*m. Determine b so that a(b) = 0.
-2, 0, 2
Let a(b) be the third derivative of -b**5/60 + 5*b**4/12 + 5*b**3/2 + 2*b**2. Let k be a(11). Factor -6*z**2 - 12 + 3*z**4 + 9*z**3 - 8 - 36*z - k.
3*(z - 2)*(z + 1)*(z + 2)**2
Solve 0 - 6/13*m**4 + 0*m + 0*m**2 + 4/13*m**3 = 0.
0, 2/3
Let o(c) = -3*c - 3. Let f(p) be the first derivative of -p**3/3 + p**2 + 2*p - 2. Let i(h) = -3*f(h) - 2*o(h). Factor i(d).
3*d**2
Let h(b) be the third derivative of -b**3 - 5/8*b**4 + 0 + b**2 + 33/20*b**5 + 0*b. Let h(u) = 0. What is u?
-2/11, 1/3
Let p(j) = 4*j**3 + 22*j**4 + 28 + 5*j + 35*j - 34*j**2 - 4. Let u(i) = i**3 + 15*i + i - 11*i**2 + 7*i**4 + 8 - 3*i. Let m(c) = 5*p(c) - 16*u(c). Factor m(d).
-2*(d - 2)**2*(d + 1)**2
Let t(f) be the third derivative of f**5/30 - f**4/12 - 2*f**3/3 - 17*f**2. Factor t(p).
2*(p - 2)*(p + 1)
Suppose -5*g - 4 = -14. Let b = g + 0. Suppose -2*q**2 + 0*q**3 - q + q**b + q**4 + q**3 = 0. What is q?
-1, 0, 1
Let b be ((-4)/6)/(1 - (-70)/(-54)). Find n, given that -b + 3/2*n - 1/4*n**2 = 0.
3
Suppose -16*z + 2 + 14 = 0. Let -1/2*j**3 - z - 5/2*j - 2*j**2 = 0. Calculate j.
-2, -1
Let o = -1 + -1. Let g = -5/3 - o. Factor w - 2/3 - g*w**2.
-(w - 2)*(w - 1)/3
Let s(p) be the second derivative of -p**7/490 - p**6/280 + p**5/140 + p**4/56 - 3*p**2/2 - 3*p. Let j(u) be the first derivative of s(u). Factor j(z).
-3*z*(z - 1)*(z + 1)**2/7
Let j be (-160)/28 - (-4)/(-14). Let a be 2/(-21)*18/j. Solve a*v - 2/7*v**2 + 0 = 0 for v.
0, 1
Suppose 3*y = -4*n + 16, 55*y - 50*y = -3*n + 12. Suppose -2/3*j + 2/3*j**3 + 0 - 1/3*j**n + 1/3*j**2 = 0. What is j?
-1, 0, 1, 2
Suppose -w = -5*d + 21, d = 2*w + 5*d - 28. Factor -6*g**2 - 4 + w*g + 4*g**2 + g**2.
-(g - 2)**2
Let z be (-160)/(-222) - (-72)/(-1332). Factor 2/3*r**4 - z*r - 2*r**3 + 2*r**2 + 0.
2*r*(r - 1)**3/3
Let x(p) be the third derivative of -p**6/60 + p**5/30 + p**4/12 - p**3/3 + 4*p**2. Let x(k) = 0. What is k?
-1, 1
Let g(f) be the second derivative of -f**6/6 - f**5/2 + 5*f**4/3 + 5*f**3/3 - 15*f**2/2 - 11*f. Factor g(z).
-5*(z - 1)**2*(z + 1)*(z + 3)
Let y(p) = p + 3. Let z be y(-3). Factor z -