be the second derivative of 1/48*c**4 + 4*c + 0 + 0*c**2 + 0*c**3 - 1/80*c**5. Determine n, given that q(n) = 0.
0, 1
Factor 0 + 0*t + 2/5*t**4 + 4/5*t**3 + 2/5*t**2.
2*t**2*(t + 1)**2/5
Suppose 5*r - 6 - 19 = 0. Suppose r*m + 5 = 5*g, -4*g + 11 = m - g. Factor -4*w**3 + 1 + 5*w**m - 5*w**2 + 9*w**2 - 6*w.
-(w - 1)**2*(4*w - 1)
Let h = -32 + 58. Suppose -3*g - y + h = 2*g, -y - 28 = -4*g. Factor -5*k**3 + g*k**2 - 3*k + 2*k**3 - 6 + 2*k**3 + 4*k**3.
3*(k - 1)*(k + 1)*(k + 2)
Let x(m) = 2*m**2 - 4*m + 2. Suppose w - 20 = 5*w. Let u(q) = q**2 - 2*q + 1. Let r(a) = w*u(a) + 3*x(a). Suppose r(d) = 0. Calculate d.
1
Suppose 2*a + 4*a = 24. Let 2/5*t**a + 0 + 0*t - 1/5*t**3 + 0*t**2 - 1/5*t**5 = 0. Calculate t.
0, 1
Let b = -17 - -20. Suppose h**2 + 0 + 1/2*h + 1/2*h**b = 0. Calculate h.
-1, 0
Let u = -20131/11739 + 1/1677. Let a = u - -50/21. Find c such that 0 - a*c + 2/3*c**3 - 8/3*c**2 + 8/3*c**4 = 0.
-1, -1/4, 0, 1
Let m be 180/(-594) - 2/(-3). Factor 2/11*p**4 + 0*p + 2/11*p**2 + m*p**3 + 0.
2*p**2*(p + 1)**2/11
Find v such that -1/6 + 0*v + 1/6*v**2 = 0.
-1, 1
Let k(g) be the third derivative of -g**5/15 + 8*g**3/3 - 5*g**2. Let k(z) = 0. Calculate z.
-2, 2
Solve 4*g + 24*g + 8 - 56*g - 16*g**2 = 0.
-2, 1/4
Let l(g) be the third derivative of 0*g - 1/108*g**6 + 2/27*g**3 + g**2 - 1/12*g**4 + 0 + 2/45*g**5. Factor l(t).
-2*(t - 1)**2*(5*t - 2)/9
Let n(j) = j - 2. Let q be n(8). Let 2*t - 22*t**3 + 1 - 19*t**4 - 6*t**5 - q*t**2 + 0 + 2*t**3 = 0. Calculate t.
-1, -1/2, 1/3
Let c(z) = -2*z**3 - z**2 + 2*z + 1. Let x be c(-2). Let f be (-3)/(-2)*12/x. Solve -m**2 - 2*m - m**2 + 4*m**f = 0.
0, 1
Let j(r) = r**2 + r + 3. Suppose 2*m + m = 0. Let c be j(m). Factor -10*f**3 - 12*f**5 - 4*f**2 - 1 + 0*f + c*f**5 + 3*f + 10*f**2 - 21*f**4.
-(f + 1)**3*(3*f - 1)**2
Let w(a) be the first derivative of -a**6/11 + 2*a**5/11 + 5*a**4/22 - 10*a**3/33 - 2*a**2/11 + 45. Suppose w(g) = 0. What is g?
-1, -1/3, 0, 1, 2
Let j(u) = 3*u**4 - 6*u**3 - 3*u**2 + 6*u + 4. Let k(i) = -4*i**4 + 7*i**3 + 4*i**2 - 7*i - 5. Let w(v) = -5*j(v) - 4*k(v). Factor w(r).
r*(r - 1)*(r + 1)*(r + 2)
What is l in 2 - 2*l - 3*l**2 + 5*l**2 - 2 = 0?
0, 1
Let j(z) = -z**2 + 11*z + 12. Let s(f) = -4*f**2 + 56*f + 60. Let t(w) = 16*j(w) - 3*s(w). Find a such that t(a) = 0.
-1, 3
What is f in 2/3 - 4/3*f**3 + 0*f - 2*f**2 = 0?
-1, 1/2
Let o(f) be the first derivative of 45*f**4/4 + 20*f**3 + 10*f**2 + 16. Factor o(j).
5*j*(3*j + 2)**2
Suppose 0*x - x = -2. Determine o so that 4*o**x - 3*o + 6*o - o**2 = 0.
-1, 0
Let a(u) be the first derivative of 5*u**4 + 25*u**3/3 + 5*u**2/2 + 37. Factor a(f).
5*f*(f + 1)*(4*f + 1)
Suppose 3*y - 23 + 5 = 0. Let x(z) be the third derivative of 2*z**2 - 1/27*z**3 - 1/36*z**4 - 1/540*z**y + 0*z + 0 - 1/90*z**5. Determine b so that x(b) = 0.
-1
Suppose 0 = -20*y + 57 - 17. Factor 3/2*o**3 - 3/2*o + 3*o**y - 3.
3*(o - 1)*(o + 1)*(o + 2)/2
Factor 4/9*i**2 + 16/9*i - 20/9.
4*(i - 1)*(i + 5)/9
Solve -5*j**2 - 61*j - 245 + 39*j - 48*j = 0 for j.
-7
What is d in -23*d**3 + 8*d**2 - 4*d**4 + 51*d**3 - 24*d**3 = 0?
-1, 0, 2
Suppose -8 = 3*n - 17. Factor 2/7*x + 2/7*x**5 + 0*x**2 - 4/7*x**n + 0 + 0*x**4.
2*x*(x - 1)**2*(x + 1)**2/7
Let g(a) = a**5 + 3*a**4 - a**3 - a**2 - 4*a. Let l(k) = k**3 - k**2 + k. Let t(n) = -g(n) - 2*l(n). Suppose t(z) = 0. What is z?
-2, -1, 0, 1
Solve -7*z**3 + 1 - 16*z**2 - 4 - 10*z - z**3 + 1 = 0.
-1, -1/2
Suppose -58 = 4*s + 4*i - 2*i, s - 4*i + 10 = 0. Let h = s + 16. Factor -2*w**3 + 1/2 + h*w - 1/2*w**2.
-(w - 1)*(w + 1)*(4*w + 1)/2
Let h(u) = u + 1. Let g be h(1). Suppose 0 + 1/3*x**3 - 1/3*x**g - 1/3*x + 1/3*x**4 = 0. Calculate x.
-1, 0, 1
Let u = 623/4 + -621/4. Let x(r) = r**2 - 5*r - 6. Let t be x(6). Factor z + u*z**2 + t.
z*(z + 2)/2
Let w = 7 + -3. Suppose 2*m = -w*l + 6, 3*l = m + m - 6. Determine b so that -4/3*b**2 - 14/3*b**5 + 8*b**4 + 0 - 2*b**m + 0*b = 0.
-2/7, 0, 1
Let b(k) be the first derivative of -3*k**5/10 - 3*k**4/8 + k**3 + 12. Factor b(p).
-3*p**2*(p - 1)*(p + 2)/2
What is n in -2/5*n + 3/10 + 1/10*n**2 = 0?
1, 3
Let v(r) be the first derivative of -1/35*r**5 + 0*r - 1/21*r**3 + 0*r**2 - 4 - 1/14*r**4. Solve v(s) = 0 for s.
-1, 0
Let b be 12/(-100) + (-2)/(-10). Let u = 56/75 - b. Factor 0 + f**2 - 1/3*f**3 - u*f.
-f*(f - 2)*(f - 1)/3
Solve -4/5*y**3 + 2/5*y**4 + 0 + 2/5*y**2 + 0*y = 0.
0, 1
Let s be ((-18)/60*1)/(6/(-5)). Factor 1/4*n**3 + 0 + 0*n + s*n**2.
n**2*(n + 1)/4
Let p(f) be the first derivative of f**5/10 - f**4/4 + f**2/2 - f/2 - 8. Factor p(h).
(h - 1)**3*(h + 1)/2
Let h = 83 + -78. Let z(f) be the third derivative of 3*f**2 + 1/84*f**4 + 0*f - 1/210*f**h + 0 + 2/21*f**3. Find d such that z(d) = 0.
-1, 2
Let j(a) = -2*a**5 - 15*a**4 + 2*a**3 - 2*a**2 - 2*a. Let d(u) = u**5 - u**3 - u**2 - u. Let t(m) = -2*d(m) + j(m). Factor t(i).
-i**3*(i + 4)*(4*i - 1)
Suppose 7*v + 110 = 8*v. Let i = v - 548/5. Factor 4/5*j**2 - 2/5 - 2/5*j**5 + 4/5*j**3 - 2/5*j - i*j**4.
-2*(j - 1)**2*(j + 1)**3/5
Let z(y) = 6*y**2 - 12. Let w(h) = h**3 - h**2. Let n(f) = -3*w(f) + z(f). Factor n(s).
-3*(s - 2)**2*(s + 1)
Let x(a) be the first derivative of -8/3*a**3 - 1/3*a**6 - 4*a**4 + 0*a + 0*a**2 + 1 - 2*a**5. Factor x(t).
-2*t**2*(t + 1)*(t + 2)**2
Let g(a) = -10*a**5 + 11*a**4 - 13*a**3 - 10*a. Let s(j) = j**5 - j**4 + j**3 + j. Let y(i) = -2*g(i) - 22*s(i). Let y(p) = 0. Calculate p.
-1, 0, 1
Suppose 10 = -2*r, y + 5*r - 3*r + 5 = 0. Let u(s) be the third derivative of 0*s**3 + 1/60*s**6 + 2*s**2 + 1/12*s**4 + 0*s + 0 - 1/15*s**y. Solve u(h) = 0.
0, 1
Let s(m) = -2*m**2 - 43*m + 27. Let g be s(-22). Determine c so that -1/2*c + 0 - 7/2*c**3 + 9/4*c**4 + 9/4*c**2 - 1/2*c**g = 0.
0, 1/2, 1, 2
Suppose u - 1 - 1 = 0. Let n be 4*(3 + 2)/10. Factor i**u - i**n + i**2 + i**2.
2*i**2
Find n such that 2*n**3 - 3*n**3 - 2*n + 2*n**3 - n**2 + 0*n**3 = 0.
-1, 0, 2
Let x(g) be the first derivative of g**7/21 - g**6/15 - g - 3. Let j(i) be the first derivative of x(i). Factor j(m).
2*m**4*(m - 1)
Let q(k) be the third derivative of 14*k**7/15 - 14*k**6/15 + 4*k**5/15 + 7*k**2. Factor q(p).
4*p**2*(7*p - 2)**2
Let y(s) = -s**2 + 20*s - 49. Let b be y(3). Factor -2/13*w**b + 2/13 + 0*w.
-2*(w - 1)*(w + 1)/13
Suppose -k + 1 = 3*p - 12, 0 = 3*p + 5*k - 29. Factor 0 + 3/4*d**p - 3/4*d**2 - 3/2*d.
3*d*(d - 2)*(d + 1)/4
Let m = 3 + -1. Let k = 7 - -7. Suppose 4*r + k*r**3 + 3*r**2 + 0*r + 15*r**m = 0. What is r?
-1, -2/7, 0
Let x be 1*14*2/4. Let s = x - 5. Factor 0*g - 2*g**3 + 1/2*g**s + 0.
-g**2*(4*g - 1)/2
Let z(q) be the third derivative of -q**9/2520 + q**8/480 - q**7/252 + q**6/360 - q**4/6 + 2*q**2. Let a(v) be the second derivative of z(v). Factor a(d).
-2*d*(d - 1)**2*(3*d - 1)
Let p(z) be the second derivative of -z**4/7 + 2*z**3/3 + 20*z**2/7 + 29*z. Solve p(q) = 0.
-1, 10/3
Let d = -4 + 6. Let z(l) = 10*l**3 + 5*l**2 + l + 2. Let b(f) = 19*f**3 + 9*f**2 + 2*f + 5. Let s(j) = d*b(j) - 5*z(j). Let s(i) = 0. Calculate i.
-1/3, -1/4, 0
Let j be (-101)/582 + 1/6. Let u = 200/873 + j. Factor 2/9*q + 2/9*q**4 - u*q**2 + 0 - 2/9*q**3.
2*q*(q - 1)**2*(q + 1)/9
Let a(i) = -2*i**2 + 15*i - 3. Let w(m) = m**2 - m - 1. Let n(g) = a(g) + 5*w(g). Factor n(x).
(x + 4)*(3*x - 2)
Suppose -2/5*s**3 - 4/5 + 6/5*s + 0*s**2 = 0. What is s?
-2, 1
Let j(m) = 5*m**4 - 2*m**3 - 3*m**2 + 2. Let p(z) = -z**3 + z**2 + 1. Let q(h) = j(h) - 2*p(h). Factor q(o).
5*o**2*(o - 1)*(o + 1)
Let t(r) be the third derivative of -r**5/120 + r**4/24 - r**3/12 + 6*r**2. Let t(f) = 0. What is f?
1
Let z(w) = w**2 + 6*w - 2. Let b be z(-5). Let u be (-19)/b + (-6)/(-21). Factor -5/2*x**4 + 0*x - 7/2*x**u + 0 - x**2.
-x**2*(x + 1)*(5*x + 2)/2
Let y be 148/(-480) - 1/(-3). Let l(w) be the second derivative of 1/12*w**3 + 2*w + 1/12*w**4 + y*w**5 + 0 + 0*w**2. Factor l(f).
f*(f + 1)**2/2
Suppose 0 = j + 1, -5*j = 3*z - 3*j - 1. Let r(y) = -y**2. Let u(v) = -5*v**2 - 1. Let f(i) = z*u(i) - 6*r(i). Factor f(h).
(h - 1)*(h + 1)
Let f(m) be the first derivative of m**6/195 - 3*m**5/130 + m**4/26 - m**3/39 + m - 1. Let i(x) be the first derivative of f(x). Find c, given that i(c) = 0.
0, 1
Factor -12/7 + 12/7*g**3 + 9/7*g**2 + 3/7*g**4 - 12/7*g.
3*(g - 1)*(g + 1)*(g + 2)**2/7
Let v(n) be the third derivative of 5*n**2 + 0*n + 0*n**5 - 1/540*n**6 - 2/27*n**3 + 0 + 1/36*n**4. Su