he second derivative of l**4/144 + l**3/72 - l**2/12 - l. Determine b, given that i(b) = 0.
-2, 1
Let -5/3*t**2 - 3*t**3 - 2/3 + 3*t + 7/3*t**4 = 0. What is t?
-1, 2/7, 1
Suppose 9 = 2*h - 1. Let b = 184/595 + -2/85. Suppose 2/7*x**h + 0 - b*x**3 + 0*x - 2/7*x**4 + 2/7*x**2 = 0. What is x?
-1, 0, 1
Suppose 3*b = 30 - 6. Factor 6*d**3 - b*d - 8*d**2 - 2*d**5 + 0*d**3 + 4*d**5 + 8*d**4.
2*d*(d - 1)*(d + 1)*(d + 2)**2
Let b(m) be the second derivative of -m - m**3 + 3/5*m**5 + 3/10*m**6 - 1/4*m**4 + 0*m**2 + 0. Determine a, given that b(a) = 0.
-1, 0, 2/3
Let u(z) be the second derivative of -z**7/3780 - z**6/810 - z**3/6 + 3*z. Let c(x) be the second derivative of u(x). Factor c(w).
-2*w**2*(w + 2)/9
Let h(s) be the first derivative of s**6/360 - s**4/24 - s**3/9 + 3*s**2 + 4. Let j(q) be the second derivative of h(q). Factor j(c).
(c - 2)*(c + 1)**2/3
Let s(w) = -7*w**3 + 4*w**2 + 5*w + 6. Let j(i) = -6*i**3 + 3*i**2 + 4*i + 5. Let m(v) = -6*j(v) + 5*s(v). Determine x so that m(x) = 0.
-1, 0
Let c = 517/7305 + -2/487. Let m(f) be the second derivative of 1/6*f**3 + 0*f**5 - c*f**6 - 1/42*f**7 + 0 + 0*f**2 + 1/6*f**4 - 2*f. Factor m(b).
-b*(b - 1)*(b + 1)**3
Suppose -4 = -4*f - 8. Let n(y) = y**5 + y**4 - y**3 - y**2. Let m(o) = 8*o**5 - 2*o**4 - 3*o**3 + o**2 - 5*o + 1. Let k(h) = f*m(h) + 5*n(h). Solve k(d) = 0.
-1, 1/3, 1
Let s(g) = -5*g. Suppose 3*h = -0*h - 3. Let o be s(h). Let 0 - o*n**2 + 2*n + 0 = 0. Calculate n.
0, 2/5
Let u = 1 - -1. Determine m so that -10*m**2 + 21*m**u - 2*m**2 + 6*m + 3*m**3 = 0.
-2, -1, 0
Let x(u) be the first derivative of -u**4/4 + 2*u**3/3 + u**2/2 - 2*u - 3. Let m(o) = -2*o**3 + 2*o**2 + o - 3. Let h(j) = -2*m(j) + 3*x(j). Factor h(p).
p*(p + 1)**2
Let s(w) = -2*w. Let o be s(-3). Find q, given that 3*q**3 - q**2 - o*q**3 + 5*q + 4*q**2 + q = 0.
-1, 0, 2
Suppose 2*m + 1 = 21. Suppose 5*n = 10 + m. Factor 0*i**3 + 2/3*i**5 + 2/3*i**n + 0*i + 0 + 0*i**2.
2*i**4*(i + 1)/3
Let -2/11*n**4 + 2/11*n**3 - 16/11 - 8/11*n + 12/11*n**2 = 0. What is n?
-2, -1, 2
Let c(f) be the third derivative of -4*f**2 + 1/504*f**8 - 1/315*f**7 + 0*f**3 - 1/180*f**6 + 0*f + 0*f**4 + 0 + 1/90*f**5. Suppose c(v) = 0. What is v?
-1, 0, 1
Let u(k) = k - 2. Let t be u(9). Factor 3*l - t*l**2 - 2 + 17*l**2 - 11*l**2.
-(l - 2)*(l - 1)
Let j be 4/8 + (-18)/(-4). Suppose -2*t - j*m + 1 = 0, 2*m + 0*m + 11 = 3*t. Let 0*k**t + 0*k**2 + 2/3*k**4 + 0 + k**5 + 0*k = 0. What is k?
-2/3, 0
Suppose 7*b**4 - 7*b**4 + 160*b**2 + 64 - 160*b - 80*b**3 - 2*b**5 + 20*b**4 = 0. What is b?
2
Let i(t) be the second derivative of -1/100*t**5 - 9/10*t**3 + 27/10*t**2 + t + 3/20*t**4 + 0. Let i(c) = 0. Calculate c.
3
Let w(o) be the first derivative of o - 1/70*o**5 + 0*o**2 - 1 - 1/42*o**4 + 0*o**3. Let p(u) be the first derivative of w(u). Factor p(d).
-2*d**2*(d + 1)/7
Let c = -2 - -18. Factor 18*x**2 - c*x**2 - x - x.
2*x*(x - 1)
Suppose 8*q - 4*q - 132 = 0. Let g = -33 + q. What is d in 0 + g*d - 1/4*d**2 = 0?
0
Let p(h) = h**5 - h**2 - h + 1. Let w(q) = -8*q**5 - 6*q**4 - 2*q**3 + 12*q**2 + 10*q - 6. Let j(t) = -6*p(t) - w(t). Let j(s) = 0. What is s?
-2, -1, 0, 1
Determine g so that 8/5*g + 2/5 + 12/5*g**2 + 8/5*g**3 + 2/5*g**4 = 0.
-1
Let t = 1586 - 333059/210. Let r(h) be the third derivative of 0*h**4 + 0*h + 0*h**6 - 2*h**2 - t*h**7 + 1/336*h**8 + 0 + 0*h**5 + 0*h**3. Factor r(k).
k**4*(k - 1)
Let f(m) = -m**3 - 3*m**2 + 7*m - 7. Let u be f(-7). Let a = u - 98. Factor -a*d**3 - 48*d**2 - 8*d + 98*d**4 - 8 + 8.
2*d*(d - 1)*(7*d + 2)**2
Factor 4/7 + 2*b + 10/7*b**3 + 2/7*b**4 + 18/7*b**2.
2*(b + 1)**3*(b + 2)/7
Suppose -2*r = 13 - 21. Let b(p) be the second derivative of -1/126*p**7 + 0*p**2 + 1/45*p**6 + 0*p**r + 2*p + 0 + 0*p**3 - 1/60*p**5. Factor b(d).
-d**3*(d - 1)**2/3
Let n(f) = f + 8. Let i be n(-7). Let q = i + 1. Determine l, given that 2/11*l**q + 0*l - 2/11 = 0.
-1, 1
Let o(d) be the second derivative of 0*d**2 - 2/15*d**3 + 3/100*d**5 - 1/15*d**4 + 2/75*d**6 - 3*d + 1/210*d**7 + 0. Suppose o(p) = 0. Calculate p.
-2, -1, 0, 1
Let u = -2 + 8. Let t = 20/3 - u. Factor 0 + t*l - 3*l**2.
-l*(9*l - 2)/3
Let i = -16 - -49/3. Let d(u) be the first derivative of -1/4*u**4 - 2 - i*u**3 + 0*u + 0*u**2. Factor d(y).
-y**2*(y + 1)
Let n be (1 + 2)/((-6)/(-8)). Solve 24*m**3 - m**n + m**2 - 24*m**3 = 0 for m.
-1, 0, 1
Let n be (-3 - -3) + 1 + 7/(-9). Let w(p) be the first derivative of 1/3*p**2 + 0*p + n*p**3 + 3. Determine v, given that w(v) = 0.
-1, 0
Let s(v) = -v**3 + v**2. Let z(x) = 9*x**3 - 12*x**2 + 3*x. Let b(o) = 6*s(o) + z(o). Solve b(r) = 0.
0, 1
Let t(i) be the third derivative of i**9/120960 + i**8/40320 + i**5/20 - 2*i**2. Let y(g) be the third derivative of t(g). Find d, given that y(d) = 0.
-1, 0
Suppose 4/5*t**2 + 0 - 4/5*t**4 + 0*t**3 + 0*t = 0. Calculate t.
-1, 0, 1
Solve -l + 7/2*l**2 + l**3 + 0 - 7/2*l**4 = 0.
-1, 0, 2/7, 1
Let m be 7/28 + (-10)/(-24). Factor 1/3 + 1/3*z**2 + m*z.
(z + 1)**2/3
Let g(y) be the second derivative of y**9/6048 - y**8/840 + y**7/280 - y**6/180 + y**5/240 + y**3/2 - y. Let l(a) be the second derivative of g(a). Factor l(r).
r*(r - 1)**4/2
Let o(c) be the second derivative of 0 + 1/3*c**3 + 1/12*c**4 - 6*c + 0*c**2. Determine s, given that o(s) = 0.
-2, 0
Let h(w) be the second derivative of 0*w**2 - 37/10*w**5 + 0 - 4/3*w**6 + 4/3*w**4 + 4/3*w**3 + 2*w. Find n, given that h(n) = 0.
-2, -1/4, 0, 2/5
Let m(t) be the second derivative of t**9/52920 + t**4/3 + 3*t. Let x(p) be the third derivative of m(p). Find f, given that x(f) = 0.
0
Let i be 201/39 - 16/104. Factor 1/2*k**4 - 1/2*k**i + 0 + 1/2*k**3 - 1/2*k**2 + 0*k.
-k**2*(k - 1)**2*(k + 1)/2
Let d(i) be the second derivative of -i**7/280 - i**6/120 + i**5/40 + i**4/8 + i**3/3 - 5*i. Let u(a) be the second derivative of d(a). Factor u(t).
-3*(t - 1)*(t + 1)**2
Let j = 15/31 + 1/62. Factor -1/4*o**2 - j - 3/4*o.
-(o + 1)*(o + 2)/4
What is l in 2*l**2 - 36*l + 4*l**2 + 14*l**3 + 17 - 5*l**3 + 7 - 3*l**4 = 0?
-2, 1, 2
Let m be 3 + 0 + 0/1. Suppose 0*w = -2*w + 4. Factor 0*v**2 + w*v**2 + 5 - 5 + v**m + v.
v*(v + 1)**2
Let d(y) be the second derivative of -9*y**5/80 + 3*y**4/16 + y**3/24 - y**2/8 - 3*y. Factor d(g).
-(g - 1)*(3*g - 1)*(3*g + 1)/4
Let b(x) be the third derivative of -3*x**8/112 + x**7/14 + x**6/40 - x**5/4 + x**4/4 + x**2. Suppose b(z) = 0. Calculate z.
-1, 0, 2/3, 1
Let b(p) be the third derivative of -p**7/3360 + p**5/480 + p**3/3 + 2*p**2. Let d(c) be the first derivative of b(c). Determine i, given that d(i) = 0.
-1, 0, 1
Let z(q) be the first derivative of -4 - 1/8*q**4 + 0*q**2 + 0*q - 2/5*q**5 - 1/4*q**6 + 0*q**3. Factor z(r).
-r**3*(r + 1)*(3*r + 1)/2
Let y be (-4)/(-210)*6/12. Let z = 29/105 + y. Solve 0*g**2 - z*g**3 + 0*g + 0 - 2/7*g**4 = 0 for g.
-1, 0
Let q(d) = 9*d - 77. Let i be q(9). Let c(y) be the first derivative of 1/9*y**3 + 0*y + i + 1/2*y**2. Factor c(u).
u*(u + 3)/3
Let v(b) = -35*b + 143. Let i be v(4). Factor -2/11*a**4 + 0 + 2/11*a**2 + 0*a**i + 0*a.
-2*a**2*(a - 1)*(a + 1)/11
Suppose -3*x - 2*m - 225 + 39 = 0, -5*x + 2*m = 294. Let j be 9/12 + 21/x. Let 2/5 + j*z**4 + 8/5*z**3 + 12/5*z**2 + 8/5*z = 0. Calculate z.
-1
Let w(a) be the third derivative of 2*a**7/21 - 2*a**6/5 - 31*a**5/15 - a**4 + 16*a**3/3 + 2*a**2. Let w(z) = 0. What is z?
-1, 2/5, 4
Let d(j) = -j**2 - 6*j - 1. Suppose -p = 3*p - 3*v + 20, -v = 0. Let f(y) = y**2 + 7*y + 1. Let w(o) = p*d(o) - 4*f(o). Let w(r) = 0. What is r?
-1
Let m be 1447/(-9) - 8/2. Let w = m - -165. Find r such that w*r**2 + 0*r - 2/9*r**3 + 0 = 0.
0, 1
Let a(i) = -9*i**4 + 13*i**3 - 5*i**2 - 5*i - 6. Let w(n) = -19*n**4 + 27*n**3 - 10*n**2 - 11*n - 13. Let y(p) = -13*a(p) + 6*w(p). Suppose y(b) = 0. What is b?
0, 1/3, 1
Let j(k) = 2*k - 1 - 4*k**2 + 6*k**2 - 4*k - k**2. Let p(c) = 3*c**2 - 4*c - 2. Let q(d) = 5*j(d) - 2*p(d). Factor q(h).
-(h + 1)**2
Let b(w) = -3*w**2 + 9*w - 6. Let v(u) = u**2 - u + 1. Let c be 21/3 + 1/(-1). Let n(k) = c*v(k) + b(k). Solve n(p) = 0 for p.
-1, 0
Find x, given that 18/5*x**2 + 6/5*x**3 - 6/5*x - 18/5 = 0.
-3, -1, 1
Let z be (4/5)/((-90)/(-175)). Suppose 66*b**4 - z*b + 10*b**2 - 4/9 + 54*b**3 = 0. What is b?
-1/3, 2/11
Let c = 2 - -1. Let v(l) = 1 + 0*l**4 + l**4 + c*l - 2*l. Let f(k) = 8*k**4 + 6*k + 6. Let u(i) = -f(i) + 6*v(i). Factor