q**6/540 - q**5/135 + q**4/108 + 9*q**2. Factor i(y).
2*y*(y - 1)**2/9
Let u(r) be the second derivative of -r**4/48 - r**3/6 - r**2/2 - 4*r. What is h in u(h) = 0?
-2
Let y be ((-4)/7)/((-8)/28). Determine u, given that 2/9*u**y + 0*u + 0 - 4/9*u**3 + 2/9*u**4 = 0.
0, 1
Let u(f) be the third derivative of -f**6/840 + f**5/140 - f**4/84 - f**2. Factor u(m).
-m*(m - 2)*(m - 1)/7
Let i(x) be the third derivative of 0 + 0*x**5 + 0*x + 0*x**3 + 1/60*x**6 + 4*x**2 - 1/12*x**4. Factor i(b).
2*b*(b - 1)*(b + 1)
Let h be (-3 - 84/(-16))*(0 - -81). Factor 2 + h*r**3 + 243/2*r**2 + 27*r.
(9*r + 2)**3/4
Let m(a) be the first derivative of -5 - 3/16*a**4 + 3/8*a**2 + 3/2*a - 1/2*a**3. Let m(q) = 0. What is q?
-2, -1, 1
Let z(b) be the second derivative of -b**7/168 - b**6/120 + b**5/80 + b**4/48 - 4*b. Determine a, given that z(a) = 0.
-1, 0, 1
Let l(r) = -2*r + 1. Let t be l(-4). Let v(j) = -j**3 + 4*j**2 + j + 3. Let i be v(4). What is q in 3 - 10*q**4 + 6*q + i*q**4 - t*q**3 + 3*q**3 = 0?
-1, 1
Let w(u) be the third derivative of 3*u**5/20 - u**4/8 - u**3 + 28*u**2. Let w(n) = 0. Calculate n.
-2/3, 1
Suppose 3*d - 4*d**3 + 6*d**4 - 4*d**2 - 17*d**5 - 2 + 3*d + 15*d**5 = 0. What is d?
-1, 1
Let x(j) = j + 7. Let u be x(-7). Let z(i) be the first derivative of 2 - 1/4*i**4 + u*i + 1/3*i**3 + 0*i**2. Find d, given that z(d) = 0.
0, 1
Let x(g) be the first derivative of -6*g**5/5 - g**4/2 + 16*g**3/3 - 4*g**2 - 2. Suppose x(u) = 0. What is u?
-2, 0, 2/3, 1
Let c be 2/12 + (6 - 185/30). Let l(u) be the third derivative of 1/180*u**5 + 2/9*u**3 - 1/18*u**4 + 0 + c*u - 2*u**2. Factor l(q).
(q - 2)**2/3
Let f(p) = p + 7. Let w be f(-5). Let u(m) = -2*m**3 + m**2 - m - 1. Let q be u(-1). Determine b so that q*b - 2 + b**2 + 4*b**2 + w*b**2 - 2*b**2 = 0.
-1, 2/5
Factor 1/2*o**5 - 1/2*o**3 + 0*o**2 + 0*o**4 + 0*o + 0.
o**3*(o - 1)*(o + 1)/2
Let n(x) = -x**3 - 9*x**2 - 2*x - 10. Let c be n(-9). Find o, given that -4*o**5 + 4*o**3 + 7*o**5 + 2*o**2 + 3*o**3 + c*o**4 = 0.
-1, -2/3, 0
Let o(y) be the first derivative of 3*y**4/8 + y**3 - 3*y**2/4 - 3*y + 1. Determine s, given that o(s) = 0.
-2, -1, 1
Suppose -9 = d - 3*j, -2*j - j - 27 = 3*d. Let s be d/(-2) + 12/(-8). Factor 0*l**3 - l**2 - 3*l**s + 3*l**2 + l**3.
-2*l**2*(l - 1)
Factor -4*a**3 - 11*a**3 + 9*a**4 + 11*a**2 - 8*a**2 + 3*a.
3*a*(a - 1)**2*(3*a + 1)
Let u(n) be the second derivative of n**5/70 - n**4/7 + 3*n**3/7 - 4*n**2/7 - 31*n. Let u(f) = 0. Calculate f.
1, 4
Let t(f) = 1. Let z(c) = -2*c**2 + 2*c + 5. Let d(p) = -5*t(p) + z(p). Factor d(i).
-2*i*(i - 1)
Let r be (-2)/13*(-728)/168. Solve 0*b**2 + 2/3*b**4 + 4/3*b - r - 4/3*b**3 = 0.
-1, 1
Let t be (-4)/24 - 44/(-120). Let 1/5 + 2/5*y + t*y**2 = 0. What is y?
-1
Suppose 3*m - 2*f - 7 = 0, 2*m - 3*f = -0*f + 3. Let 1 - 6*a**2 + 3*a - m*a**2 + 5 = 0. What is a?
-2/3, 1
Let y(g) be the first derivative of -g**4/28 + 5*g**3/21 - 4*g**2/7 + 4*g/7 - 5. Factor y(b).
-(b - 2)**2*(b - 1)/7
Suppose 0 = 5*s - 5*a - 25, 2*s - 5*a + 9*a + 2 = 0. Factor 0 + 0*u - 2/7*u**s - 4/7*u**2 + 2/7*u**4.
2*u**2*(u - 2)*(u + 1)/7
Let f(m) = 14*m**4 - 25*m**3 + 41*m**2 + 45*m - 19. Let w(y) = -5*y**4 + 8*y**3 - 14*y**2 - 15*y + 6. Let i(g) = 3*f(g) + 8*w(g). Factor i(k).
(k - 3)**2*(k + 1)*(2*k - 1)
Let -1 + 5/4*q - 1/4*q**2 = 0. What is q?
1, 4
Determine b so that 4*b**2 - 6*b**2 + 0*b - 3*b + 5*b**2 = 0.
0, 1
Let g = -27 - -47. Suppose 5*w + 5*c + 12 + 13 = 0, 0 = 5*w - 4*c - g. Factor 7*t**3 - 2*t + 0*t**2 + 2*t**2 + 3*t**2 + w*t.
t*(t + 1)*(7*t - 2)
Let v = -5/119 + 25/17. Suppose -b = 3 - 7. Let 2/7*r**5 + 20/7*r**3 - 20/7*r**2 + 10/7*r - v*r**b - 2/7 = 0. What is r?
1
Let l be ((-24)/20)/((-2)/5). Factor 6 - 2*k - 3*k**2 - k**3 - 2*k**2 - k + l.
-(k - 1)*(k + 3)**2
Let b = -98/5 + 20. Let q(o) be the first derivative of -b*o**5 + 0*o**2 + 0*o**3 + 0*o - 2 + 0*o**4. Factor q(m).
-2*m**4
Let w(y) be the second derivative of y**5/30 - y**4/6 + y**3/3 + 3*y**2/2 + 2*y. Let a(q) be the first derivative of w(q). Determine p, given that a(p) = 0.
1
Let x = 10 - 6. Suppose 0 = -2*c - 0*c. Find n such that 1 + c*n**5 - 2*n**5 - 5*n + 10*n**2 - 10*n**3 + n**5 + 5*n**x = 0.
1
Let p(i) = -i**3 - 8*i**2 - 8*i + 8. Let v be p(-7). Let k be 8/v + 3/(-15). Find s such that k*s**2 + 2/3 - s = 0.
1, 2
Let n be (-5 - -4)*(0 + 0). Let w be 1/(n + 4 - 1). Suppose 1/6*r + w - 1/6*r**2 = 0. What is r?
-1, 2
Suppose 7*x = -44 + 128. Let c be 20/(-16) - (-15)/x. Solve c*l**2 + 0 + 1/4*l**3 + 0*l = 0 for l.
0
Suppose -20/3*a**4 - 2/3 + 4/3*a**2 + 3*a - 9*a**3 = 0. Calculate a.
-1, 1/4, 2/5
Let 2/9*q - 8/9*q**5 + 0 + 2/3*q**3 + 10/9*q**4 - 10/9*q**2 = 0. Calculate q.
-1, 0, 1/4, 1
Let p(c) be the first derivative of 17/2*c**4 - 32/3*c**3 - 2*c**5 + 0*c + 4*c**2 - 5. Factor p(g).
-2*g*(g - 2)*(g - 1)*(5*g - 2)
Let m be ((-1)/(-2))/1*0. Factor -4*q**3 + m*q**3 + 2*q**3.
-2*q**3
Let y be (3*(-6)/9)/(-2 - -1). Solve 14/3*q**y - 4/3*q - 2/3 - 8/3*q**3 = 0.
-1/4, 1
Let j(w) be the third derivative of -w**5/70 + w**4/28 - 12*w**2. Determine n, given that j(n) = 0.
0, 1
Let d(b) = -b + 10. Let c be d(10). Solve 0 + 0*i**3 + c*i + 0*i**2 - 2/5*i**5 - 2/5*i**4 = 0 for i.
-1, 0
Let b(w) be the third derivative of -w**6/60 - w**5/15 + w**4/12 + 2*w**3/3 + 3*w**2. Factor b(g).
-2*(g - 1)*(g + 1)*(g + 2)
Let t(g) = 10*g**4 + 10*g**3 - 20*g**2 - 10*g + 10. Let c(r) = -11*r**4 - 11*r**3 + 21*r**2 + 11*r - 10. Let i(o) = 5*c(o) + 6*t(o). What is y in i(y) = 0?
-2, -1, 1
Let j(m) = m + 3. Let w be j(-3). Suppose 2*p + 0*p = w. Let -1/4*q**2 + p + 1/4*q = 0. What is q?
0, 1
Let q(s) be the third derivative of 7*s**8/48 - 2*s**7/15 - 3*s**6/8 + 7*s**5/15 - s**4/6 + s**2. Let q(l) = 0. Calculate l.
-1, 0, 2/7, 1
Let i = 373/7 - 53. Suppose 4*x - 9 = -p, -4*p + 14 = 4*x + 2. Factor 0 + 0*a**x + 2/7*a - i*a**3.
-2*a*(a - 1)*(a + 1)/7
Let o be (1/4*12)/1. Let 2/9*u**4 + 2/3*u**o - 2/9*u**5 - 4/9*u - 2/9*u**2 + 0 = 0. Calculate u.
-1, 0, 1, 2
Let s(z) = z + 10. Let g be s(-6). Let v = g + -2. Solve 4*o + 0*o**v - 3*o**2 - 4 + 2*o**2 = 0.
2
Let -27/8 - 5/4*i**3 - 7/8*i**4 + 27/8*i + 9/4*i**2 - 1/8*i**5 = 0. Calculate i.
-3, 1
Solve -4/3*a + 1/3*a**2 + 1 = 0.
1, 3
Let q(y) be the third derivative of y**7/1155 - y**6/330 + y**5/330 + 5*y**2. Factor q(h).
2*h**2*(h - 1)**2/11
Solve 226/19*k**2 + 82/19*k**3 - 234/19*k**4 + 8/19 + 80/19*k - 162/19*k**5 = 0 for k.
-1, -2/9, 1
Let u(b) = 48*b**4 + 69*b**3 - 252*b**2 + 321*b - 105. Let t(p) = 7*p**4 + 10*p**3 - 36*p**2 + 46*p - 15. Let i(v) = 27*t(v) - 4*u(v). Factor i(h).
-3*(h - 1)**3*(h + 5)
Let y(t) be the second derivative of 5*t**7/42 - t**6/2 + t**5/4 + 5*t**4/4 - 5*t**3/3 + 21*t. Suppose y(x) = 0. Calculate x.
-1, 0, 1, 2
Factor -1 + 0 + 3*g**2 + 9*g + 7.
3*(g + 1)*(g + 2)
Let m(j) be the second derivative of 0*j**3 - 1/24*j**4 + 0*j**2 - 1/20*j**5 + 3*j - 1/60*j**6 + 0. Factor m(y).
-y**2*(y + 1)**2/2
Let c(s) be the first derivative of 3*s**4/16 - s**3/4 - 6. What is h in c(h) = 0?
0, 1
Let r(l) be the first derivative of l**9/3024 + l**8/420 + l**7/280 - l**6/90 - l**5/30 - l**3 - 2. Let x(t) be the third derivative of r(t). Factor x(z).
z*(z - 1)*(z + 1)*(z + 2)**2
Let u(v) be the first derivative of v**6/2 - 9*v**5/5 + 9*v**4/4 - v**3 + 2. Factor u(q).
3*q**2*(q - 1)**3
Let n be 4/(-96) - 3/(-18). Let w(h) be the first derivative of 2 - n*h**2 + 1/16*h**4 - 1/12*h**3 + 1/4*h. Factor w(p).
(p - 1)**2*(p + 1)/4
Let p(b) be the second derivative of 0*b**2 + 1/40*b**5 + 1/12*b**4 - b + 0 + 1/12*b**3. Find u such that p(u) = 0.
-1, 0
Let b(p) be the first derivative of -9/2*p**2 + 4 + 27/4*p**3 + p. Factor b(u).
(9*u - 2)**2/4
Let m be (-708)/(-472) - ((-73)/14 - 1). Factor 4/7 - 22/7*i**4 + 10/7*i - m*i**2 + 62/7*i**3.
-2*(i - 1)**3*(11*i + 2)/7
Let y be 0 - ((-2)/(-4) + 52/(-72)). Solve y*c**4 - 4/9*c**3 + 0 + 0*c + 0*c**2 = 0 for c.
0, 2
Let o(a) = 2*a + 1. Let t be o(1). Let 3*z - 2*z + 5*z + 3*z**2 + t = 0. Calculate z.
-1
Suppose 3 = -213*b + 214*b. Solve 0 + 14/5*n**b + 2/5*n - 11/5*n**2 = 0.
0, 2/7, 1/2
Let d(q) be the first derivative of -q**6/90 + q**5/60 + q**4/36 - q**3/18 + 4*q + 1. Let g(p) be the first derivative of d(p). Factor g(a).
-a*(a - 1)**2*(a + 1)/3
Let d(w) = w**3 - 6*w**2 - 7*w. Let r(c) = -c**3 + 5*c**2 + 6*c. Let z(h) = -5*d(h) - 6*r(h).