e j(4). Solve 2*k**3 - v*k - 2 - 2*k + 2*k**2 + k + 2*k = 0 for k.
-1, 1
Let b(i) be the first derivative of 9*i**6/20 - 9*i**5/10 + 3*i**4/4 - i**3/3 + 3*i**2/2 + 5. Let c(o) be the second derivative of b(o). Factor c(m).
2*(3*m - 1)**3
Let l(k) = -k**2 - 1. Let a = -18 - -27. Let v(p) = 36*p**2 + 33*p + 15. Let m(t) = a*l(t) + v(t). Let m(h) = 0. Calculate h.
-1, -2/9
Let x be 1*-1 - (-10 - -9). Solve x - 6/5*q**4 + 3/5*q - 3/5*q**5 + 0*q**3 + 6/5*q**2 = 0.
-1, 0, 1
Let d(z) be the second derivative of -1/15*z**4 + 0*z**2 + 0 + 0*z**3 + 9*z. Let d(b) = 0. Calculate b.
0
Let y(f) be the first derivative of -3/8*f**2 - 1/4*f**3 + 3/4*f + 6 + 3/16*f**4. Let y(k) = 0. What is k?
-1, 1
Let x be (-46)/(-12) - 1/(-6). Let -19 + 21*n**2 - 9*n**4 + 0*n**x + 3*n**5 + 7 - 3*n**3 = 0. What is n?
-1, 1, 2
Let t be 34/9 + 10/45. Factor -7*f**3 - 2*f**t + f**3 + 0*f**2 + f**2 - 5*f**2.
-2*f**2*(f + 1)*(f + 2)
Let k(l) be the first derivative of l**6/10 + 3*l**5/16 + l**4/16 + 5*l - 6. Let r(p) be the first derivative of k(p). Factor r(m).
3*m**2*(m + 1)*(4*m + 1)/4
Let i = -16 - -24. Factor n**2 + 2*n - 3*n + i + 1 - 5*n.
(n - 3)**2
Let k(x) be the third derivative of -x**6/40 + x**5/10 + x**4/2 - 4*x**3 - 2*x**2. Suppose k(f) = 0. Calculate f.
-2, 2
Let a(r) be the third derivative of r**5/180 - r**4/18 + 2*r**3/9 + 9*r**2. Determine x so that a(x) = 0.
2
Let j = 115 + -113. What is k in -1/2*k**j + 2*k - 2 = 0?
2
Let p(r) be the first derivative of -r**8/1680 - r**7/525 - r**6/600 - r**2 - 3. Let f(w) be the second derivative of p(w). Solve f(o) = 0.
-1, 0
Solve 2/19*p**3 + 0 + 8/19*p**2 + 8/19*p = 0.
-2, 0
Suppose -2/9*g**3 + 2/9 - 2/3*g + 2/3*g**2 = 0. Calculate g.
1
Let u(p) be the third derivative of 0*p**3 + 0*p - 1/300*p**6 + 0 + 5*p**2 - 1/30*p**4 - 1/50*p**5. Let u(y) = 0. What is y?
-2, -1, 0
Factor -16/21 - 8/7*a - 2/21*a**3 - 4/7*a**2.
-2*(a + 2)**3/21
Let x(t) be the second derivative of -2*t**6/3 + 5*t**4/4 + 5*t**3/6 + 9*t. Factor x(w).
-5*w*(w - 1)*(2*w + 1)**2
Let a(g) be the second derivative of g**6/60 - g**4/4 - 2*g**3/3 + g**2 + 2*g. Let p(w) be the first derivative of a(w). Find h such that p(h) = 0.
-1, 2
Let n(u) be the second derivative of 1/20*u**5 + 0*u**4 + 0 - 1/90*u**6 - 2/9*u**3 + 5*u + 0*u**2. Solve n(m) = 0 for m.
-1, 0, 2
Let g(j) = 7*j**3 - 2*j**2 - 3*j + 2. Let x(m) = 48*m**3 - 15*m**2 - 21*m + 15. Let i(z) = 27*g(z) - 4*x(z). Solve i(y) = 0 for y.
-1, 1, 2
Let u(y) = 2*y**3 - 3*y**2 - 5*y - 2. Let c be u(4). Let o = 233/4 - c. Factor 0*t - o + 1/4*t**2.
(t - 1)*(t + 1)/4
Let l = 51 - 1376/27. Let s(k) be the third derivative of -1/540*k**6 + 1/90*k**5 + l*k**3 + 2*k**2 + 0*k + 0 - 1/36*k**4. Factor s(h).
-2*(h - 1)**3/9
Suppose 0*z - 20 = 5*z. Let c(h) = h**5 + h**3 - h + 1. Let w(t) = -5*t + 8*t**3 - t + t**5 + 4 + t**5. Let a(o) = z*c(o) + w(o). Determine x so that a(x) = 0.
-1, 0, 1
Let b(h) be the second derivative of h**4/54 + h**3/9 + 16*h. What is k in b(k) = 0?
-3, 0
Let o(q) = -2*q**5 - 8*q**3 - 2*q. Let t(f) = -f**5 - 7*f**3 - f. Let a(w) = 3*o(w) - 4*t(w). Determine y, given that a(y) = 0.
-1, 0, 1
Let g(z) be the second derivative of z**4/20 + z**3/2 - 9*z**2/5 + 33*z. Let g(l) = 0. What is l?
-6, 1
Let b be (-10)/75 + 3/18. Let c(d) be the second derivative of -1/50*d**5 - 2*d + 0*d**3 + 0*d**2 - b*d**4 + 0. Determine q, given that c(q) = 0.
-1, 0
Suppose -23*n + 24 = -15*n. Factor -2/11*h**4 + 0 + 0*h**n + 0*h + 0*h**2.
-2*h**4/11
Suppose 5*x + 32 = 2*m, -x = -2*m - 6*x + 32. Determine w, given that -4*w**3 - m*w + 24*w - 6*w + 2*w**5 = 0.
-1, 0, 1
Suppose -l - r = 21 - 19, 4*r = 3*l - 22. Let f be -1 + 0 - -2 - 1. Factor f - 2/3*t**l + 2/3*t.
-2*t*(t - 1)/3
Let u(o) be the second derivative of o**7/42 - o**6/60 - 3*o**5/40 + o**4/24 + o**3/12 - 9*o. Determine w so that u(w) = 0.
-1, -1/2, 0, 1
Let l(h) = -h**5 + h**3 - h**2 + 1. Let t(v) = -2*v**5 - 5*v**4 + 11*v**3 + v**2 - 5. Let s(r) = -5*l(r) - t(r). Solve s(u) = 0.
-2, 0, 2/7, 1
Suppose 5*s - 3 = 3*k + 4*s, 0 = -5*k + s - 3. Factor 0 + 0*j**3 + 2/9*j**4 + 0*j + k*j**2.
2*j**4/9
Let w = 4 + 1. Suppose -w*k - 5 = 0, -3*g = -2*k - k - 12. Solve g*n**5 + n**5 - 3*n**5 = 0 for n.
0
Let f(s) be the third derivative of -s**8/1008 - s**7/210 - s**6/180 + s**5/90 + s**4/24 + s**3/18 + 13*s**2. Factor f(c).
-(c - 1)*(c + 1)**4/3
Solve 18/5*o**2 - 24/5*o + 8/5 = 0.
2/3
Let t be 166/15 - (1 + (-3)/5). Factor -16/3*j - 2/3*j**2 - t.
-2*(j + 4)**2/3
Let h(r) be the second derivative of 1/60*r**5 + r + 0 - 1/6*r**3 + 0*r**4 - 1/3*r**2. Let h(m) = 0. Calculate m.
-1, 2
Let r(g) be the second derivative of -8*g**7/147 + g**5/5 + g**4/21 - 2*g**3/7 - 2*g**2/7 - 8*g. Solve r(p) = 0 for p.
-1, -1/2, 1
Factor -2 - 6 + 2*t + 3*t + 3 + 5*t**2 - 5*t**3.
-5*(t - 1)**2*(t + 1)
Let i(q) be the first derivative of -2/9*q**3 + 0*q**2 + 0*q**4 - 3 + 2/15*q**5 + 0*q. Suppose i(r) = 0. What is r?
-1, 0, 1
What is g in -16/15*g - 2/15*g**2 - 14/15 = 0?
-7, -1
Let u(z) be the first derivative of z**6/21 - 4*z**5/35 + 4*z**3/21 - z**2/7 - 7. Factor u(c).
2*c*(c - 1)**3*(c + 1)/7
What is k in 1/2*k**2 - 3/2 - k = 0?
-1, 3
Let d(g) be the first derivative of 4 - 4/3*g**3 + 4/5*g**2 + 5/6*g**4 + 4*g. Let f(i) be the first derivative of d(i). Suppose f(r) = 0. Calculate r.
2/5
Let a(h) be the second derivative of -3*h**7/35 - h**6/60 + h**5/45 + 3*h**2/2 - 7*h. Let f(y) be the first derivative of a(y). Determine w so that f(w) = 0.
-1/3, 0, 2/9
Let l be (0 - 1)/((-6)/30). Suppose 5*b = l*w - 35, 2*b + 18 = 4*w - 0*b. Find o, given that 0*o - 4*o - 3*o**3 + o**3 + 6*o**w = 0.
0, 1, 2
Let x = -145 - -145. Factor 0 - 6/5*y**4 - 4/5*y**3 + 0*y**2 + x*y - 2/5*y**5.
-2*y**3*(y + 1)*(y + 2)/5
Let i(y) = 4*y**2 - 6*y + 5. Let t(c) = 5*c**2 - 7*c + 6. Let h(o) = -4*i(o) + 3*t(o). What is x in h(x) = 0?
1, 2
Let d(h) = 6*h**2. Let t be d(1). Let f = t - 3. Determine c so that 4*c**2 + c - f*c**2 - c = 0.
0
Suppose -3*c - 5*k + 16 = -15, -k = -5. What is r in -c*r - 10*r**4 - 2 - 4*r - 2*r**5 - 4*r - 20*r**3 - 20*r**2 = 0?
-1
Determine k, given that 0*k + 0*k**2 + 4/3*k**3 + 0 = 0.
0
Let d(y) be the first derivative of y**5/5 + 3*y**4/4 - 3*y**3 + 5*y**2/2 - 35. Let d(w) = 0. What is w?
-5, 0, 1
Let j(d) be the third derivative of 7*d**6/1800 + d**5/120 - d**4/60 - 5*d**3/6 - 3*d**2. Let w(n) be the first derivative of j(n). Find k such that w(k) = 0.
-1, 2/7
Suppose -p - 3*x + x = 2, 4*x = 2*p - 12. Determine n so that 3/2*n**4 + n**3 - n - p*n**2 + 1/2 = 0.
-1, 1/3, 1
Let r(u) be the second derivative of -3*u**4 + 0 - 7*u + 0*u**2 - 4/3*u**3. Find o such that r(o) = 0.
-2/9, 0
Factor 2/9 + 2/9*r**3 - 2/9*r - 2/9*r**2.
2*(r - 1)**2*(r + 1)/9
Let v be 12/9*(-6)/(-4). Suppose j - v = -0*j. Determine t, given that -7*t**2 - 4*t + t**2 - 2 - 2*t - j*t**3 = 0.
-1
Let r(z) be the first derivative of z**5/30 - z**4/12 - 3*z**2/2 + 1. Let w(d) be the second derivative of r(d). Factor w(u).
2*u*(u - 1)
Factor 1/7*q**5 - 1/7*q**3 - 1/7*q**2 + 0 + 1/7*q**4 + 0*q.
q**2*(q - 1)*(q + 1)**2/7
Let o(r) be the second derivative of -r**6/210 + r**4/84 + 15*r. Factor o(a).
-a**2*(a - 1)*(a + 1)/7
Let t = 430 + -1711/4. Solve t*n + 9/4*n**2 + 3/4 + 3/4*n**3 = 0.
-1
Let g be (84/105)/((-18)/(-15)). Find o such that 2/3*o - g*o**3 + 0*o**2 + 0 = 0.
-1, 0, 1
Let 5*m**2 + 0 - 2*m - 1/4*m**5 - 9/2*m**3 + 7/4*m**4 = 0. What is m?
0, 1, 2
Let w be ((-2)/10)/((-48)/60). Let a(l) be the second derivative of -1/6*l**3 + w*l**2 + 1/24*l**4 - l + 0. Suppose a(s) = 0. What is s?
1
Let y(r) = -9*r**3 + 5*r**2 - 5*r + 2. Let i(g) = 8*g**3 - 4*g**2 + 4*g - 2. Let q(h) = -7*i(h) - 6*y(h). Let q(f) = 0. Calculate f.
-1, 1
Let r be 68/(-18) + 6/(-27). Let q be -4 - 18/r - 0. Factor -1/2*k**2 + 0*k + q.
-(k - 1)*(k + 1)/2
Suppose -10*y = -5*y - 15. Factor -y + 14*u**2 - 12*u**2 + 1.
2*(u - 1)*(u + 1)
Let w(j) be the second derivative of -2/33*j**3 + 1/11*j**2 + 0 - 1/66*j**4 + 1/55*j**5 + 2*j. Factor w(i).
2*(i - 1)*(i + 1)*(2*i - 1)/11
Let l(t) be the second derivative of t**5/20 + t**4/6 - 2*t**3/3 - t**2/2 - t. Let a be l(-3). Factor 4/5 - 6/5*r + 2/5*r**a.
2*(r - 2)*(r - 1)/5
Let v be 8 - (74/10 - 1). Determine u, given that -2/5*u**3 + 12/5*u**2 - 18/5*u + v = 0.
1, 4
Let u be (-12)/(-60) + -1 + 64/30. Factor -2/3*p**5 + 4/3*p