y**5.
-4*y**4*(y - 1)
What is h in 1/8*h**3 + h**2 + 9/4 + 21/8*h = 0?
-3, -2
Let r be (3/2)/((-29)/2 + 15). Suppose -14/3*q**4 - 86/3*q**2 + 16*q + 20*q**r - 8/3 = 0. What is q?
2/7, 1, 2
Let d(j) = 83*j - 163. Let q be d(2). Determine t so that 2/5*t**q - 6/5 - 2*t**2 + 14/5*t = 0.
1, 3
Let y(h) be the first derivative of h**6/6 - 7*h**5/5 + 3*h**4/2 + 64. Factor y(j).
j**3*(j - 6)*(j - 1)
Let u(d) be the first derivative of -d**5/2 + 45*d**4/8 + 25*d**3/3 + 781. Factor u(f).
-5*f**2*(f - 10)*(f + 1)/2
Let h(w) be the first derivative of 36/5*w**5 - 19 + 81/8*w**4 + 17/12*w**2 + 1/6*w + 11/2*w**3. Suppose h(z) = 0. What is z?
-1/3, -1/8
Let w(d) be the first derivative of d**4/6 + 2*d**3 + 9*d**2 - 9*d + 3. Let c(p) be the first derivative of w(p). Factor c(j).
2*(j + 3)**2
Let i be 2/(0 + (-4)/(-8)). Factor 4*g**4 + 24*g**2 + 2 + 16*g**3 + 0 - 2 + 16*g + i.
4*(g + 1)**4
Suppose 6*c - c - 4*t + 10 = 0, -3*t = 4*c - 23. Let u be (2*1/(-2))/(-2 - 0). Solve -1/2*l**c + 0 + 1/2*l**4 - u*l**3 + 1/2*l = 0 for l.
-1, 0, 1
Let v be (4 - 20)/(-4) + 2. Suppose 20*a - v = 17*a. Determine f, given that 11*f - 4*f + 5*f + 4*f**a = 0.
-3, 0
Suppose 0 = 2*q - 7*q + 20. Suppose -q*b = -3*c + c + 8, 4*c = b + 23. Suppose c*n**4 - 6 - 28*n**3 + 9*n**5 + 21*n - 3*n**3 + n**3 = 0. What is n?
-2, -1, 1/3, 1
Suppose -69 = -14*m - 9*m. Let w(b) be the second derivative of 0 - 2*b**2 - 1/6*b**4 + b**m + 2*b. Factor w(k).
-2*(k - 2)*(k - 1)
Let d(m) be the third derivative of -m**8/84 - 2*m**7/105 + m**6/30 + m**5/15 + 163*m**2. Factor d(i).
-4*i**2*(i - 1)*(i + 1)**2
Let 213444/5 - 1848/5*s + 4/5*s**2 = 0. Calculate s.
231
Let n(t) be the first derivative of 6*t**5/5 + 19*t**4/2 - 34*t**3 - 91*t**2 - 48*t + 35. Determine k so that n(k) = 0.
-8, -1, -1/3, 3
Let h(q) = 5*q**2 + 42*q + 34. Let u(x) = 4*x**2 + 40*x + 34. Let y(c) = -2*h(c) + 3*u(c). Let y(b) = 0. What is b?
-17, -1
Let c be -63*23/1035 + 23/5. Factor -2/5*h**3 - 4/5*h + c - 2*h**2.
-2*(h - 1)*(h + 2)*(h + 4)/5
Factor -3/4*s**2 - 1/4*s**3 + 3/4 + 1/4*s.
-(s - 1)*(s + 1)*(s + 3)/4
Let x(w) = 11*w**3 - 10*w**2 + 7*w + 10. Let u(g) = 246 - 251 - 5*g**3 - 2*g - g + 5*g**2. Let t(o) = -9*u(o) - 4*x(o). Factor t(k).
(k - 5)*(k - 1)*(k + 1)
Find k such that 75*k**3 - 44*k**3 - 693*k**3 - 1690*k + 6175*k**2 + 35*k**4 - 258*k**3 = 0.
0, 2/7, 13
Let b be -7 + (9 - (-14 - -10)). Factor 54/7 - 90/7*n + b*n**2 - 6/7*n**3.
-6*(n - 3)**2*(n - 1)/7
Let i(l) be the second derivative of l + 22/3*l**3 - 5*l**4 + 0 - 4*l**2. Suppose i(w) = 0. Calculate w.
1/3, 2/5
Let s(l) be the second derivative of -l**6/240 + l**5/40 - l**4/24 - 21*l**2/2 - 7*l. Let f(b) be the first derivative of s(b). Determine d so that f(d) = 0.
0, 1, 2
Suppose 60*r**2 + 30*r**4 + 141*r**5 - 44*r**5 - 65*r**3 - 47*r**5 - 20*r - 55*r**5 = 0. What is r?
0, 1, 2
Let h(z) be the second derivative of -z**7/168 - 2*z**6/15 + 7*z**5/16 - 3*z**4/8 - 71*z. Factor h(k).
-k**2*(k - 1)**2*(k + 18)/4
Let -2/5*a**3 + 4*a - 48/5 + 6/5*a**2 = 0. Calculate a.
-3, 2, 4
Let n(p) be the third derivative of 0*p - 1/70*p**7 + 7/360*p**6 + 45*p**2 + 0 + 0*p**4 + 1/90*p**5 + 0*p**3. Factor n(r).
-r**2*(r - 1)*(9*r + 2)/3
Let b(y) be the first derivative of -y**5/240 - y**4/48 - 3*y**2 + 19. Let a(x) be the second derivative of b(x). Suppose a(q) = 0. Calculate q.
-2, 0
Suppose -18*w - 1092 = -6*w. Let v = w - -93. Solve 4*g**3 - 16/5 - 68/5*g**v + 64/5*g = 0 for g.
2/5, 1, 2
Suppose -161*i + 151*i = -30. Let k(v) be the first derivative of -11 + 0*v - 3*v**i - 3/4*v**4 - 3*v**2. Find r such that k(r) = 0.
-2, -1, 0
Let m = 16006 - 16003. Let 6/5*g + 0 + 3*g**2 - 21/5*g**m = 0. Calculate g.
-2/7, 0, 1
What is y in 28*y - 88*y + 25 - y**3 + 46*y**2 - 11*y**3 + y**4 = 0?
1, 5
Let v = -95 - -97. Suppose 0 = v*n + 5*j - 28, 16 = 4*j - 0*j. Find p such that 0 + 0*p + 1/3*p**2 + 5/3*p**3 + p**5 + 7/3*p**n = 0.
-1, -1/3, 0
Let q(u) = 1 - 6*u**2 + 2*u**2 + 5*u**2 - 13*u. Let j(n) = 12*n. Let w(f) = -5*j(f) - 4*q(f). Determine y, given that w(y) = 0.
-1
Let f(w) be the second derivative of 0 + 0*w**2 - 7/72*w**4 + 1/6*w**3 - 6*w - 1/40*w**5. Factor f(b).
-b*(b + 3)*(3*b - 2)/6
Let q = 3 - -21. Suppose 2*k = -4*o + q, o + 3*k - 2*k = 8. Factor 2*w**5 - 3*w - o*w**4 - w**2 + w + 5*w**2.
2*w*(w - 1)**3*(w + 1)
Let t be (4/(-12))/(((-1)/15)/1). Factor -15*b**2 + 5*b**3 - 173 - t*b + 92 + 96.
5*(b - 3)*(b - 1)*(b + 1)
Let p(k) be the third derivative of k**7/420 - k**6/24 + 3*k**5/10 - 7*k**4/6 + 8*k**3/3 - 270*k**2. Determine f, given that p(f) = 0.
2, 4
Let a(m) be the second derivative of -m**7/1260 + m**6/270 + m**5/60 + 5*m**3/2 - 4*m. Let b(n) be the second derivative of a(n). Factor b(o).
-2*o*(o - 3)*(o + 1)/3
Suppose -325*y + 1252 = -12*y. Factor 0 + 36/5*w**3 + 4/5*w**2 + y*w**5 - 8/5*w - 52/5*w**4.
4*w*(w - 1)**3*(5*w + 2)/5
Suppose 2/3*y**2 - 10 - 4/3*y = 0. Calculate y.
-3, 5
Let d(f) = -f**2 + 13*f + 26. Let z(u) = 5*u**2 - 50*u - 105. Let q(w) = -15*d(w) - 4*z(w). Factor q(j).
-5*(j - 3)*(j + 2)
Let w(k) be the third derivative of 0 - 1/360*k**5 + 8*k**2 + 1/720*k**6 + 0*k + 1/36*k**3 - 1/144*k**4. Let w(d) = 0. What is d?
-1, 1
Let u be (-1)/(-3) - 120/(-18). Let i(k) be the first derivative of -6*k**2 + 4/3*k**3 + 8*k + u. What is h in i(h) = 0?
1, 2
Let s(w) be the first derivative of -28 - 3/5*w**5 + 18*w**2 - 12*w - 13*w**3 + 9/2*w**4. Find y such that s(y) = 0.
1, 2
Factor -6*h - 28 + 10 + 12*h**2 + 6*h**3 + 9 - 3*h**4.
-3*(h - 3)*(h - 1)*(h + 1)**2
Let r(d) be the first derivative of d**4/12 + 5*d**3/9 + 7*d**2/6 + d + 144. Factor r(b).
(b + 1)**2*(b + 3)/3
Factor 4*q**3 - 2*q**4 + 0 + q + 1/3*q**5 - 10/3*q**2.
q*(q - 3)*(q - 1)**3/3
Suppose -2*i = 8170 - 8174. Determine x so that 0*x**3 - 3/2*x**i + 3/4*x**4 + 3/4 + 0*x = 0.
-1, 1
Let n(p) be the first derivative of 0*p**3 - 6 + 0*p**4 + 0*p + 2*p**2 + 1/90*p**5. Let y(z) be the second derivative of n(z). Factor y(j).
2*j**2/3
Let h(f) be the first derivative of 5/4*f**4 + 10*f**2 - 15 - 20/3*f**3 + 0*f. Determine x so that h(x) = 0.
0, 2
Let v(g) be the first derivative of 2*g**3/27 + 5*g**2/9 + 5. Solve v(y) = 0 for y.
-5, 0
Solve 129/2*i**3 - 33/2*i**4 - 207/2*i**2 + 54*i + 3/2*i**5 + 0 = 0 for i.
0, 1, 3, 4
Let q(m) = m - 5. Let c be q(8). Factor -6*t**c + 7*t**3 + 30*t + 45*t**2 + 5 + 19*t**3.
5*(t + 1)**2*(4*t + 1)
Let s(c) be the first derivative of 1/24*c**6 + 1/20*c**5 - 1/12*c**3 - 1/16*c**4 + 0*c - 9 + 0*c**2. Factor s(f).
f**2*(f - 1)*(f + 1)**2/4
Solve 1715*i + 0*i**2 + i**2 - 1640*i = 0.
-75, 0
Let w = 198 - 85. Factor w*r + 21*r**3 + 9*r**2 - r**5 - 113*r + 15*r**4 + 4*r**5.
3*r**2*(r + 1)**2*(r + 3)
Let r(y) be the second derivative of -y**7/504 - y**6/8 - 27*y**5/8 - 10*y**4/3 - 33*y. Let d(v) be the third derivative of r(v). Determine a so that d(a) = 0.
-9
Let g(p) be the second derivative of p**8/336 - p**7/84 - p**6/72 + p**5/12 - p**3/6 + 11*p. Let b(a) be the second derivative of g(a). Factor b(h).
5*h*(h - 2)*(h - 1)*(h + 1)
Let a(l) be the first derivative of -1/10*l**6 - 6/25*l**5 - 8 + 6/5*l + 3/10*l**4 + 8/5*l**3 + 21/10*l**2. Factor a(u).
-3*(u - 2)*(u + 1)**4/5
Let p(m) = -m**3 - 17*m**2 - 67*m - 78. Let x be p(-12). Factor -9/4*g**2 + 9/4 - x*g.
-3*(g + 3)*(3*g - 1)/4
Let b be 148/72 + (8 - 10). Let n(t) be the second derivative of -4/3*t**2 + 0 + 8/9*t**3 + 3*t + 1/63*t**7 - b*t**4 + 1/45*t**6 - 1/6*t**5. Factor n(x).
2*(x - 1)**3*(x + 2)**2/3
Suppose -5*p + 45 = 15. Suppose -7*k - 4*a + 8 = -3*k, p = 3*k - 5*a. Factor 7 - 7 + 4*w**4 + 4*w - 4*w**3 - 6*w**4 + k*w**2.
-2*w*(w - 1)*(w + 1)*(w + 2)
Let c be 1 - ((10 - 6) + -1 + -10 - -6). Determine j so that -64/19*j - 22/19*j**c - 56/19 - 2/19*j**3 = 0.
-7, -2
Let r(w) be the third derivative of -w**5/30 + 7*w**4/12 + 8*w**3/3 + 34*w**2 - 1. Factor r(f).
-2*(f - 8)*(f + 1)
Let s(z) = 6*z - 7*z + 2*z - z**4 - z**3. Let b(l) = 16*l**4 + 18*l**3 - 2*l**2 - 18*l. Let d(t) = -2*b(t) - 28*s(t). Let d(w) = 0. What is w?
-2, -1, 0, 1
Let d(t) be the third derivative of 27*t**2 - 1/120*t**5 - 1/72*t**4 + 0 + 0*t + 0*t**3 - 1/720*t**6. Factor d(x).
-x*(x + 1)*(x + 2)/6
Let s(v) be the third derivative of 4/3*v**3 + 1/480*v**5 + 5*v**2 + 0*v**4 + 0 + 1/480*v**6 + 0*v. Let o(u) be the first derivative of s(u). Factor o(a).
a*(3*a + 1)/4
Let u