3)
Let r(o) be the first derivative of o**6/6 - o**4/2 + o**2/2 - 5. Let r(c) = 0. Calculate c.
-1, 0, 1
Let k(p) = 2*p**2 + 4*p + 3. Let z be k(-2). Let s = -7 + 9. Factor -2 + z*d - d**2 - d**s - 3*d**3 + 4*d**2.
-(d - 1)*(d + 1)*(3*d - 2)
What is m in -1/3 + 1/6*m**5 - 1/3*m**4 + 2/3*m**2 - 1/3*m**3 + 1/6*m = 0?
-1, 1, 2
Let s(z) be the second derivative of -z**7/14 + 3*z**6/10 - 3*z**5/10 - z**4/2 + 3*z**3/2 - 3*z**2/2 + 5*z. Factor s(j).
-3*(j - 1)**4*(j + 1)
Let h(z) be the first derivative of z**7/189 - z**5/45 + z**3/27 - z + 4. Let s(v) be the first derivative of h(v). Let s(j) = 0. Calculate j.
-1, 0, 1
Let -6*f + 3*f**2 + 30 + 33*f - 6*f**2 = 0. What is f?
-1, 10
Let s(l) be the first derivative of 2*l**3/21 - 8*l/7 + 10. Factor s(g).
2*(g - 2)*(g + 2)/7
Let o(u) = -u**3 + u**2 - u + 5. Suppose x - 3*x = 0. Let z be o(x). Factor -6 - 2*g - 4*g**3 + z*g**3 - g + 4.
(g - 2)*(g + 1)**2
Let k be (1 - (-8)/(-6))*-12. Let t be (1 - -1) + k/2. Let t*l**3 - l**3 + l - 4*l**3 = 0. Calculate l.
-1, 0, 1
Let m be (-2)/4*(0 + 0). Let c = m + 2. Solve 0*a**c - 3*a**2 + 4*a**2 - a**4 = 0 for a.
-1, 0, 1
Let w(r) = 14*r**4 + 8*r**3 + 4*r**2 + 10*r - 10. Let x(k) = -k**4 - k + 1. Let p(c) = w(c) + 10*x(c). Find f such that p(f) = 0.
-1, 0
Suppose 1344 = 8*q - 2*q. Find x, given that 234*x**3 + 188*x**2 - 315*x**5 - 25*x + x + 141*x**4 - q*x**2 = 0.
-2/3, -2/7, 0, 2/5, 1
Let z be 4/(-18) - (-2)/9. Suppose 0*a - 4*a = -4*c + 16, z = 5*a. Factor 1/3*y**3 - 1/3*y**5 + 0 + 0*y**c + 0*y**2 + 0*y.
-y**3*(y - 1)*(y + 1)/3
Let x(t) be the first derivative of t**6/40 - t**5/20 + 3*t**2/2 + 3. Let c(u) be the second derivative of x(u). Factor c(g).
3*g**2*(g - 1)
Find i such that 2/5*i**3 + 0*i - 1/5*i**4 - 1/5*i**2 + 0 = 0.
0, 1
Let o = 0 + 6. Suppose -o*z + 10 = -z. Factor -3 - 2*k**2 + 5 + 0*k**z.
-2*(k - 1)*(k + 1)
Let z be (-72)/63*14/(-4). Suppose z*p + 2 = 10. Suppose 0*a**p + 0*a**4 - 2/5*a**5 + 0*a + 0 + 2/5*a**3 = 0. Calculate a.
-1, 0, 1
Let o be (5/(-7))/1 - (-1 + 0). Suppose 0 = 2*m + m. Solve 0 + o*l**2 + m*l + 4/7*l**3 = 0.
-1/2, 0
Let h(a) be the second derivative of -a**5/5 + 2*a**3/3 + 7*a. Let h(n) = 0. Calculate n.
-1, 0, 1
Suppose -4/17*h**2 + 2/17*h + 0 + 2/17*h**3 = 0. What is h?
0, 1
Suppose -7 = -5*c + 2*d, 5*c - 5*d = -2*d + 8. Let f be c*3*(-6)/(-9). Factor 2*m**f - 4*m**3 - m - m**2 + 5*m**3 - m**4.
-m*(m - 1)**2*(m + 1)
Let n(y) be the third derivative of y**6/120 - y**5/5 + y**3/3 + 4*y**2. Let g be n(12). Factor -4/5*w**3 - 2/5*w**4 + 2/5 + 0*w**g + 4/5*w.
-2*(w - 1)*(w + 1)**3/5
Suppose 6*l - 15 = l, -2 = d - 2*l. Suppose 0*b = -2*b + d. Find y such that 5*y**b + 3 + 0 - 1 + 7*y = 0.
-1, -2/5
Let j(k) be the third derivative of -k**8/448 + 3*k**7/280 + k**6/40 - 20*k**2. Factor j(p).
-3*p**3*(p - 4)*(p + 1)/4
Let l(s) be the second derivative of 3*s**5/20 - s**4 + 2*s**3 + 9*s. Factor l(a).
3*a*(a - 2)**2
Suppose -3*l = 0, -l + 15 = -4*n - 33. Let q be n/78 - 28/(-13). Suppose 2/5*a**4 + 2/5*a + 6/5*a**q + 0 + 6/5*a**3 = 0. What is a?
-1, 0
Let d(z) be the second derivative of z**6/105 - z**5/14 - 3*z**4/14 + 27*z**3/7 - 108*z**2/7 - 15*z + 2. What is o in d(o) = 0?
-4, 3
Let q(z) = 4*z - 28. Let j be q(8). Let x(p) be the second derivative of -1/6*p**3 - p + 1/4*p**j + 0 + 0*p**2. What is w in x(w) = 0?
0, 1/3
Suppose -8*x - 41*x = 0. Suppose -4/7*w**2 - 1/7*w**4 + x + 0*w - 4/7*w**3 = 0. What is w?
-2, 0
Let t(u) be the third derivative of 0 + 0*u**6 + 0*u**4 + 0*u**3 + 1/270*u**5 + 0*u - 1/945*u**7 - u**2. Factor t(h).
-2*h**2*(h - 1)*(h + 1)/9
Determine o, given that 2 - 75*o**2 + 35*o**2 - 1 - 3*o + 3*o**3 + 39*o**2 = 0.
-1, 1/3, 1
Let m be ((-4)/(-10))/((-2)/20). Let f be (-48)/54*6/m. Factor 2/3*z**3 - f*z**2 + 0 + 2/3*z.
2*z*(z - 1)**2/3
Let w(t) = t**5 - t**2 + t - 1. Let y(z) = 5 + 41*z**3 + 37*z**2 + 2 + 2 + 20*z**3 + 42*z**4 - 5*z. Let f(i) = 18*w(i) + 2*y(i). Suppose f(c) = 0. Calculate c.
-2, -1/3, 0
Let q(b) be the first derivative of b**5/330 - b**2/2 + 2. Let r(m) be the second derivative of q(m). Factor r(u).
2*u**2/11
Let a(i) be the first derivative of -i**3/18 + i**2/6 - i/6 + 1. Factor a(v).
-(v - 1)**2/6
Let t(u) be the third derivative of 0 + 4/735*u**7 + 0*u + 0*u**4 - 1/84*u**6 + 0*u**3 + 2*u**2 + 1/105*u**5 - 1/1176*u**8. Factor t(l).
-2*l**2*(l - 2)*(l - 1)**2/7
Suppose 31 = -n + 38. Let s(y) be the first derivative of 8*y**4 - 2*y - 16/3*y**3 - 2 - n*y**2. Find g, given that s(g) = 0.
-1/4, 1
Let t(k) be the second derivative of 0 + 3*k - 1/39*k**3 + 1/78*k**4 - 2/13*k**2. Factor t(y).
2*(y - 2)*(y + 1)/13
Let x(y) be the second derivative of y**6/105 - y**5/14 + 3*y**4/14 - y**3/3 + 2*y**2/7 + 8*y. Let x(i) = 0. What is i?
1, 2
Let s(o) be the second derivative of -o**7/2 - 9*o**6/10 + 9*o**5/5 + o**4 + 41*o. Suppose s(y) = 0. Calculate y.
-2, -2/7, 0, 1
Let c(v) = -v**3 + v. Let m(l) = -10*l**3 + 10*l. Let q(f) = 35*c(f) - 4*m(f). Factor q(u).
5*u*(u - 1)*(u + 1)
Suppose 2/3*n**4 + 0*n**2 - 2/3 - 4/3*n + 4/3*n**3 = 0. Calculate n.
-1, 1
Suppose -y - 4*f = 4, -3*y - 5*f = -4*y + 32. Suppose -4*k = -y, -5*n + 0*n + 5*k - 15 = 0. Factor -3/4*m**4 - 1/4*m**2 + n - 3/4*m**3 - 1/4*m**5 + 0*m.
-m**2*(m + 1)**3/4
Let p(c) be the second derivative of 0 - 27/40*c**5 - 27/4*c**3 + 0*c**2 + 1/20*c**6 + 27/8*c**4 - 8*c. Factor p(q).
3*q*(q - 3)**3/2
Find n, given that 19/6*n**2 - 53/6*n**3 - 1/3*n + 6*n**4 + 0 = 0.
0, 2/9, 1/4, 1
Let i be 5 + 2 + (2 - 4). Let b(q) be the first derivative of 2/7*q + 2/35*q**i - 1 - 1/21*q**6 - 4/21*q**3 + 1/7*q**4 - 1/7*q**2. Factor b(v).
-2*(v - 1)**3*(v + 1)**2/7
Let b(l) be the second derivative of l**6/15 - l**5/2 + l**4 + 4*l**3/3 - 8*l**2 - 3*l. Factor b(p).
2*(p - 2)**3*(p + 1)
Suppose -51 = 5*w + h + 38, -3*w + 4*h - 58 = 0. Let y be (-25)/(-9) + (-4)/w. Determine f, given that -2 - 2*f**y + 2 + f**5 + f = 0.
-1, 0, 1
Factor 5 - 20/3*b + 5/3*b**2.
5*(b - 3)*(b - 1)/3
Let w(b) = 3*b - 9. Let s be w(4). Let o(t) be the first derivative of -25/3*t**s - 1 + 5*t**2 - t. Let o(v) = 0. What is v?
1/5
Let o(p) be the second derivative of p**5/15 - p**4/3 + 4*p**3/9 - 8*p. Factor o(y).
4*y*(y - 2)*(y - 1)/3
Let r(u) be the third derivative of u**8/10080 - u**7/2520 + u**5/30 - 3*u**2. Let d(c) be the third derivative of r(c). Find m, given that d(m) = 0.
0, 1
Let q(l) be the third derivative of 0*l**5 + 0*l - 1/36*l**4 - 5*l**2 + 0 + 0*l**3 + 1/180*l**6. Find u, given that q(u) = 0.
-1, 0, 1
Let b(s) = 11*s**4 - s**3 - 17*s**2 - 5*s - 5. Let p(v) = -6*v**4 + 9*v**2 + 3*v + 3. Let t(g) = -3*b(g) - 5*p(g). Solve t(a) = 0.
-1, 0, 2
Suppose w = -x + 4, -3*x - 2*w = -4*w - 7. Let d = 21 - 15. Solve -2/3*z + 0 + d*z**2 + 32/3*z**4 - 16*z**x = 0 for z.
0, 1/4, 1
Let i(r) = -13*r**3 - 5*r**2 + 8*r. Let f(m) = -72*m**3 - 28*m**2 + 44*m. Let w(t) = 5*f(t) - 28*i(t). Suppose w(d) = 0. What is d?
-1, 0, 1
Let o(p) be the third derivative of -p**8/84 - 4*p**7/105 + 2*p**5/15 + p**4/6 - 2*p**2. Let o(w) = 0. What is w?
-1, 0, 1
Let t be 7 + -10 + 20/6. Let q(c) be the second derivative of 2/9*c**4 + 4/3*c**5 - 11/18*c**3 - t*c**2 + 2*c + 0. Solve q(a) = 0 for a.
-1/4, 2/5
Let v be -2*-3*6/12. Determine j so that 1/4*j**v + 1/2 + 5/4*j + j**2 = 0.
-2, -1
Suppose -c + 4*u = 0, -4*c - 5*u = -6*c + 3. Suppose -2*h = -q - 3, -2*h - 2 = -c*q + 4. Suppose 1/3*v**2 + 0 - 2/3*v + 1/3*v**h = 0. What is v?
-2, 0, 1
Suppose 0 = 5*p + 4*m + 4, -3*m - 2 - 2 = 4*p. Let n be ((-3)/(-2))/((-3)/p). Factor b - 2*b + 2*b**2 - b + 7*b + n.
(b + 2)*(2*b + 1)
Let m be (16/20)/(-4) + 1. Factor 0 - m*c - 2/5*c**2.
-2*c*(c + 2)/5
What is y in 6/7*y**4 + 24/7*y**3 + 0 + 30/7*y**2 + 12/7*y = 0?
-2, -1, 0
Let m(u) be the first derivative of -u**6/2 + 3*u**5/5 + 3*u**4/4 - u**3 - 10. Factor m(r).
-3*r**2*(r - 1)**2*(r + 1)
Factor 0 + 9/4*d + 3/2*d**2 + 1/4*d**3.
d*(d + 3)**2/4
Let a(s) = 64*s**2 - 98*s + 38. Let r(j) = 64*j**2 - 99*j + 39. Let p(y) = -3*a(y) + 2*r(y). Determine u so that p(u) = 0.
3/4
Factor 1/3*d**3 + 7/3*d - 5/3*d**2 - 1.
(d - 3)*(d - 1)**2/3
Suppose 4*u - 6 = u. Factor -1 + b**2 - 5*b + 2*b**4 - 4*b**2 + 5*b**3 + u*b**4.
(b - 1)*(b + 1)**2*(4*b + 1)
Determine d so that 4/7*d**5 - 32/7*d**4 + 0 - 96/7*d**2 + 36/7*d + 88/7*d**3 = 0.
0, 1, 3
Let z = 1085 + -9757/9. Find o such that z*o**4 - 10/9*o + 