given that g(o) = 0.
-3, -1, 1
Determine d so that 11/6*d**2 - 1/6*d**3 - 5/3*d + 0 = 0.
0, 1, 10
Let x = -142 + 143. Let a = 1/3 + x. Factor -a*d**2 + 1/3*d**5 + 2*d**3 + 0 + 1/3*d - 4/3*d**4.
d*(d - 1)**4/3
Let w(m) be the first derivative of -2*m**7/21 - 2*m**6 - 84*m**5/5 - 208*m**4/3 - 128*m**3 - 49*m + 48. Let k(x) be the first derivative of w(x). Factor k(f).
-4*f*(f + 3)*(f + 4)**3
Let l(a) be the second derivative of -a**5/4 - 35*a**4/12 - 5*a**3 - 70*a. Let l(f) = 0. Calculate f.
-6, -1, 0
Suppose -l - 55 = -5*n, 23 = 3*n - 5*l - 32. Suppose n = 5*w + 2*u, 2*w - u - 8 = -2*w. Factor 2 + q**w + 3 + q + 3*q - 1.
(q + 2)**2
Suppose 0 = -5*h + 5*j - 3*j - 6, -3 = -h - j. Suppose a + 2*a = h, 2*a + 15 = 5*t. Factor -w**2 + 0*w**4 + w**4 - t*w**3 + 2*w**3 + 5*w - 4*w.
w*(w - 1)**2*(w + 1)
Let d(a) be the first derivative of -a**3/12 - 3*a**2/8 + 35*a/2 - 561. Determine l so that d(l) = 0.
-10, 7
Suppose -4*q = -6*q + 32. Let c be q/5 + (-5)/25. Factor 2*a**3 + 9*a**2 - 6*a**c - 2*a - 4*a**3 + a**3.
-a*(a - 1)*(7*a - 2)
Let p(j) = j**2 - 20*j + 6. Let c be p(20). Let f(d) = -d**2 - d. Let b(u) = 4*u**2 + u - 3. Let a(k) = c*f(k) + 2*b(k). Determine y so that a(y) = 0.
-1, 3
Let u(y) be the second derivative of -8/15*y**4 + 14*y + 6/5*y**3 + 0 - 4/5*y**2 - 2/35*y**7 + 4/15*y**6 - 6/25*y**5. Find m, given that u(m) = 0.
-1, 1/3, 1, 2
Let w(k) = -k**5 - 5*k**4 + 55*k**3 - 3*k**2 - 62*k + 24. Let a(y) = -y**4 + 18*y**3 - y**2 - 21*y + 8. Let g(c) = 8*a(c) - 3*w(c). Suppose g(m) = 0. What is m?
-4, -1, 2/3, 1
Let k(c) be the second derivative of 2*c**6/15 + 31*c**5/5 + 113*c**4/3 + 274*c**3/3 + 108*c**2 - 2*c - 11. Determine a, given that k(a) = 0.
-27, -2, -1
Factor 1/3*f**3 + 1/3*f**4 - 1/3*f**2 - 1/3*f + 0.
f*(f - 1)*(f + 1)**2/3
Let d(f) be the second derivative of f**4/18 - 10*f**3/9 - 11*f**2/3 - 137*f. Factor d(k).
2*(k - 11)*(k + 1)/3
Let d(c) be the second derivative of 13*c + 0*c**2 + 1/3*c**4 + 0*c**5 + 0*c**3 - 1/10*c**6 - 1/42*c**7 + 0. Suppose d(h) = 0. What is h?
-2, 0, 1
Let j(l) be the third derivative of -l**5/270 + l**4/4 + 199*l**2. Solve j(d) = 0 for d.
0, 27
Let r(c) be the first derivative of 28/9*c**3 - 1/2*c**2 - 1/3*c + 17. Factor r(v).
(4*v - 1)*(7*v + 1)/3
Suppose 78*m - 98*m + 241*m - 442 = 0. Find h such that 2/3 + 2/9*h**m - 8/9*h = 0.
1, 3
Let t = -82 + 126. Find v such that t*v**2 + 96*v**3 - 118 - 144*v**4 + 118 + 4*v = 0.
-1/6, 0, 1
Let b = 12 + -10. Suppose f - b*f = 0. Find t, given that f*t**2 + t**2 - 4*t + 11*t**3 + 5*t**3 + 11*t**2 = 0.
-1, 0, 1/4
Determine b, given that 33*b**2 - 4*b**3 + 3*b**4 + 2525*b - 2507*b - 24*b**3 + 3*b**4 - b**4 = 0.
-2/5, 0, 3
Suppose 0 = -33*p + b + 45 + 47, -2*p + 4*b = 22. Determine h, given that -5/3*h + 2/3*h**2 - 2 + 1/3*h**p = 0.
-3, -1, 2
Let p(u) be the third derivative of -u**8/28 + 5*u**7/14 - 13*u**6/20 + u**5/4 + 60*u**2. Let p(z) = 0. Calculate z.
0, 1/4, 1, 5
Let w be ((-27)/(-9090))/((-2)/(-1576)*3). Let c = w + 2/101. Determine d so that -2/5*d**4 + 4/5*d**2 - c*d**3 + 2/5*d**5 - 2/5 + 2/5*d = 0.
-1, 1
Let w be ((-6)/54)/((-1)/3). Let v(l) be the first derivative of 0*l - 1/3*l**2 - 1/12*l**4 + 5 + w*l**3. Find i, given that v(i) = 0.
0, 1, 2
Let q(h) = -12*h - 2*h**2 + 2*h**3 + 2 + 16*h + 8*h**2 + 0*h**2. Let i(b) = b**3 + 5*b**2 + 4*b + 3. Let m(d) = -2*i(d) + 3*q(d). Solve m(f) = 0.
-1, 0
Suppose 546*v - 523*v - 92 = 0. Let 12 - 525/2*a**3 + 147/2*a**v + 279*a**2 - 102*a = 0. What is a?
2/7, 1, 2
Let l(f) be the second derivative of 0*f**4 - 1/120*f**6 + 1/60*f**5 + 1/2*f**2 + 4*f + 0*f**3 + 0. Let x(v) be the first derivative of l(v). Factor x(j).
-j**2*(j - 1)
Let u(s) = 2*s**5 - s**4 + 2*s**3. Let h(t) = -13*t**5 - 55*t**4 - 166*t**3 + 1440*t**2 - 1728*t. Let z(a) = -h(a) - 5*u(a). What is q in z(q) = 0?
-12, 0, 2
Let q = 38 - 31. Suppose 20 = q*k + 3*k. Factor 18*t - 6 - 15/2*t**k.
-3*(t - 2)*(5*t - 2)/2
Let p be (-4)/(-6) + 55/(-15). Let i = 5 + p. Suppose n**i - 8 + 18 + n**2 + 8 - 12*n = 0. What is n?
3
Let v(p) be the second derivative of 0*p**3 + 0*p**2 - 1/30*p**5 + 0 - 1/90*p**4 + 5*p - 4/225*p**6. Factor v(m).
-2*m**2*(m + 1)*(4*m + 1)/15
Suppose -4*t - 10*t + 42 = 0. Factor 3*m**4 - 507*m**2 - t*m**3 + 507*m**2 - 2*m**4 + 4*m.
m*(m - 2)**2*(m + 1)
Solve 15/4*x - 9/4*x**4 - 7/2*x**3 + 17/2*x**2 - 25/4 - 1/4*x**5 = 0 for x.
-5, -1, 1
Let b(r) be the second derivative of 95*r**4/12 + 65*r**3 + 20*r**2 + 358*r. Factor b(t).
5*(t + 4)*(19*t + 2)
Let w(c) be the first derivative of 7*c**6/6 - 3*c**5 + c**4/2 - 61. Factor w(i).
i**3*(i - 2)*(7*i - 1)
Let g(p) = p**3 + 2*p**2 + p - 2. Let h(k) = 8*k**3 - 8*k**2 + 8*k + 16. Let x(f) = -4*g(f) + h(f). Factor x(t).
4*(t - 3)*(t - 2)*(t + 1)
Let t(p) be the third derivative of -p**6/420 - 4*p**5/35 - 15*p**4/28 - 22*p**3/21 + 29*p**2 - 2. Factor t(k).
-2*(k + 1)**2*(k + 22)/7
Let v(s) = -9*s**3 + 28*s**2 - 440*s + 1704. Let t(a) = -a**3 - a**2 - a - 3. Let f(h) = 24*t(h) - 3*v(h). Find m, given that f(m) = 0.
12
Let q(m) = -3*m**2 + m - 5. Let j be q(3). Let l = 34 + j. Factor 0*k**2 + 2/9*k**l + 0*k**4 + 0*k + 0*k**3 + 0.
2*k**5/9
Let 0*s**2 - 12*s + 2*s**2 - 110 + 65 + 55 = 0. What is s?
1, 5
Let x(z) be the second derivative of 6*z**2 + 0 - 10*z**3 - 21*z + 9/4*z**4. Determine i, given that x(i) = 0.
2/9, 2
Let p(q) = 1. Suppose -3 = 4*a - a. Let k(f) = 3*f**3 + 3*f**2 - 15*f + 24. Let i(h) = a*k(h) + 15*p(h). Factor i(j).
-3*(j - 1)**2*(j + 3)
Factor -9*r**3 + 47*r - 71/2*r**2 - 5/2.
-(r - 1)*(r + 5)*(18*r - 1)/2
Let y(k) = -3*k + 33. Let b be y(10). Suppose 2*z**b - z**3 - z**4 + 4*z**2 - 17*z + 13*z + 0*z**4 = 0. Calculate z.
-2, 0, 1, 2
Let z(w) be the third derivative of -w**6/480 - w**5/60 - w**4/96 + w**3/4 - 12*w**2 + 2*w. Solve z(n) = 0.
-3, -2, 1
Let p = 47844/167503 - -2/23929. Factor 2/7*d**3 + 2/7 - 2/7*d**2 - p*d.
2*(d - 1)**2*(d + 1)/7
Suppose 16*n - 3 + 3 = 0. Let s(q) be the third derivative of 0 + n*q - 5*q**2 + 0*q**3 + 1/210*q**5 + 0*q**4. Let s(b) = 0. Calculate b.
0
Let w = 33 - 21. Suppose l - w = 2*l. Let n(k) = 5*k**2 - 4*k - 8. Let c(h) = h**2 - h - 1. Let b(p) = l*c(p) + 3*n(p). Find a such that b(a) = 0.
-2, 2
Let x be 0/(2/(-4)*2). Let a(h) be the third derivative of 3/40*h**6 + 0*h**3 + 0 + 3/70*h**7 + 1/20*h**5 + 1/112*h**8 + 0*h**4 + x*h - 5*h**2. Factor a(y).
3*y**2*(y + 1)**3
Suppose -2*u + 23*i + 19 = 20*i, i = u - 9. Let z(h) be the first derivative of 2/3*h**3 + 0*h**2 - u*h - 4. Suppose z(b) = 0. What is b?
-2, 2
Suppose -24/11*l**2 + 26/11*l**3 - 2/11*l**4 + 0 + 0*l = 0. Calculate l.
0, 1, 12
Let j(h) be the first derivative of 2*h**3/15 - 11*h**2/5 + 159. Find x, given that j(x) = 0.
0, 11
Suppose -6*t = 3*j - 4*t - 97, -5*j = 4*t - 161. Suppose -n + j = 10*n. Factor 8/3*u + 1/3*u**4 + 4*u**2 + 0 + 2*u**n.
u*(u + 2)**3/3
Let o = -2 - -1. Let v(r) be the third derivative of -r**4/3 - 4*r**3/3 + 4*r**2 - 15*r. Let x(z) = -z**2 + 1. Let q(f) = o*v(f) - 4*x(f). Factor q(i).
4*(i + 1)**2
Let f(o) be the first derivative of -o**9/12096 - o**8/2240 - o**7/1120 - o**6/1440 - 4*o**3/3 - 4. Let k(t) be the third derivative of f(t). Factor k(a).
-a**2*(a + 1)**3/4
What is c in 2*c**4 - 22479*c + 22479*c - 44*c**2 - 18*c**3 = 0?
-2, 0, 11
Let s(l) = -3*l**4 - l**3 - l**2 + l. Let h(u) = -5*u**4 - 44*u**3 + 61*u**2 - 16*u - 12. Let w(k) = -h(k) + 4*s(k). Solve w(t) = 0.
-2/7, 1, 2, 3
Suppose 18*n - 15*n - 10 = -2*l, 5*n - 10 = 0. Determine q so that 0 - 1/4*q**l + 1/4*q = 0.
0, 1
Let q(c) be the third derivative of 1/6*c**4 + 0 + 11/30*c**5 - 12*c**2 + 17/105*c**7 + 0*c + 7/20*c**6 + 5/168*c**8 + 0*c**3. Factor q(v).
2*v*(v + 1)**3*(5*v + 2)
Let x(g) = 2*g**2 + g + 1. Let y(p) = 5*p**2 - 8*p - 37. Let a(j) = -2*x(j) + y(j). Find h such that a(h) = 0.
-3, 13
Let q(b) = 3 - 28*b - 60*b**2 + 56*b**2 - 1. Let v(f) = 1. Let t(r) = -q(r) + 2*v(r). Determine u so that t(u) = 0.
-7, 0
Let g(p) = 120*p**2 - 220*p - 88. Let n(w) = -24*w**2 + 44*w + 18. Let d(l) = -5*g(l) - 24*n(l). Suppose d(u) = 0. Calculate u.
-1/6, 2
Factor -22*k**2 + 104*k - 25*k**2 + 224 - 22*k**2 + 97*k**2 - 32*k**2.
-4*(k - 28)*(k + 2)
Let k(p) = -9*p - 15. Let v be k(-2). Let i(z) be the third derivative of 11/8*z**4 - 7/10*z**5 + 0*z - z**3 + 0 + v*z**2. Factor i(l).
-3*(2*l - 1)*(7*l - 2)
Let h(n) be the 