c(w) + 5*f(w). Find g such that s(g) = 0.
1
Let f(b) be the third derivative of b**7/21 - b**6/24 - b**5/6 + 5*b**4/24 - 10*b**2. Factor f(p).
5*p*(p - 1)*(p + 1)*(2*p - 1)
Solve 48/7*v - 48/7 - 24/7*v**3 + 24/7*v**2 - 3/7*v**4 + 3/7*v**5 = 0 for v.
-2, 1, 2
Let s(u) be the second derivative of u**4/12 + 7*u**3/6 + 4*u**2 + 7*u. Let j be s(-6). Solve 0*l**j - 1/4*l**4 + 1/2*l**3 - 1/2*l + 1/4 = 0 for l.
-1, 1
Let h(t) be the first derivative of -5/9*t**2 + 8/27*t**3 - 1/18*t**4 - 10 + 4/9*t. Factor h(q).
-2*(q - 2)*(q - 1)**2/9
Suppose d = 6*d. Let p be (2 - 2)/(-3 - d). Factor 0*h - 2*h**4 - 1/4*h**2 + h**5 + p + 5/4*h**3.
h**2*(h - 1)*(2*h - 1)**2/4
Suppose g + 3*t = t + 12, 0 = -5*g - t + 15. Let j be (3/g)/(2 - 1). Factor -1/2 - j*k**2 + 1/2*k**3 + 3/2*k.
(k - 1)**3/2
Let c(u) = 2*u**2 + u + 9. Let f(m) = -m**3 + 11*m**2 + m - 15. Let r be f(11). Let z(w) = 2*w**2 + 2*w + 8. Let d(g) = r*c(g) + 5*z(g). Solve d(l) = 0 for l.
-2, -1
Let k(a) be the second derivative of a**6/195 + a**5/130 - a**4/78 - a**3/39 - 76*a. What is w in k(w) = 0?
-1, 0, 1
Let b(h) be the second derivative of h**5/30 + h**4/6 - h**3/9 - h**2 - 13*h. Factor b(v).
2*(v - 1)*(v + 1)*(v + 3)/3
Let s(x) be the third derivative of 0 + 3*x**2 - 1/60*x**5 + 0*x**3 + 0*x + 1/12*x**4. Factor s(p).
-p*(p - 2)
Let i be 303*(-4)/(-180) + (-2)/6. Factor -22/5*a - i*a**2 - 14/5*a**3 - 4/5.
-2*(a + 1)**2*(7*a + 2)/5
Factor 0 + 2/21*u**2 + 2/21*u.
2*u*(u + 1)/21
Let h be (-7 - -3) + 1 + 10. Solve 2*i**2 + 4*i**2 - 8*i**4 + 9*i**3 - h*i**4 = 0 for i.
-2/5, 0, 1
Let z(u) be the first derivative of u**6/360 - u**5/120 - 4*u**3/3 + 2. Let r(w) be the third derivative of z(w). Determine m so that r(m) = 0.
0, 1
Suppose 5*u - 8 = n, 3*n - 10 = -u - u. Find f, given that -2*f**u + 4*f**2 - 6*f**2 + f**2 = 0.
0
Let k(o) be the third derivative of o**7/1050 - o**6/200 - o**5/300 + o**4/40 + 20*o**2. Suppose k(v) = 0. What is v?
-1, 0, 1, 3
Suppose 0 - 2/3*c**3 + 2/3*c**4 + 2/3*c - 2/3*c**2 = 0. What is c?
-1, 0, 1
Let p = -10288/597 + -20/199. Let i = -17 - p. Determine l, given that 2/3*l + 0 + i*l**2 = 0.
-2, 0
Suppose i - 6 = -3*a - 2*i, 6 = 2*a + i. Suppose a = 4*o - 2*c, -4*c = 3*o + c - 16. Factor 3 - 8*u + 4 + 2*u**o + 1.
2*(u - 2)**2
Let y(a) = a**2 + 7*a + 6. Let w be y(-6). Suppose r + w = 3. Factor 0 - l**3 - 2 - 6*l - l**r - 6*l**2.
-2*(l + 1)**3
Let b be -8*6/(-280) + (-2)/(-5). Factor 0 + 4/7*w**4 + 12/7*w**2 - b*w - 12/7*w**3.
4*w*(w - 1)**3/7
Let w(m) be the third derivative of -m**6/120 + m**5/24 - m**4/24 - 37*m**2. Suppose w(c) = 0. What is c?
0, 1/2, 2
Determine z so that 19*z + 716*z**2 + 29*z - 16 - 712*z**2 - 12*z**3 = 0.
-2, 1/3, 2
Let o(g) be the third derivative of -g**6/360 - g**5/180 + g**4/72 + g**3/18 - 3*g**2. Let o(j) = 0. Calculate j.
-1, 1
Let q(o) = -4*o**2 - 13*o - 3. Let n(v) = 8*v**2 + 27*v + 5. Let y(c) = 3*n(c) + 5*q(c). Solve y(g) = 0 for g.
-4, 0
Let s = -430 - -434. What is q in -160/3*q**s + 98/3*q**3 + 50/3*q**5 - 16/3 - 40/3*q + 68/3*q**2 = 0?
-2/5, 1, 2
Let g be (-28639)/19110 - 3/(-2). Let u(f) be the third derivative of 1/420*f**6 - g*f**7 + 1/70*f**5 + 0*f - 5/84*f**4 + 2/21*f**3 + f**2 + 0. Factor u(p).
-2*(p - 1)**3*(p + 2)/7
Let r(t) = t**2 + t - 2. Let n(g) = -5*g**2 - g + 6. Let x(y) = -2*n(y) - 14*r(y). Find h, given that x(h) = 0.
-4, 1
Let n be 3 - ((-2)/(-4))/(3/18). Factor 3/2*m - 3*m**2 + 3/2*m**3 + n.
3*m*(m - 1)**2/2
Let h(f) be the third derivative of f**6/40 + f**5/20 - f**4/8 - f**3/2 - 5*f**2. Solve h(j) = 0.
-1, 1
Let f(j) be the third derivative of j**5/15 + j**4/3 - 4*j**2. Factor f(g).
4*g*(g + 2)
Let d be (0 - 1)*(3 - -4). Let y be -4 - ((-175)/(-6))/d. Factor -y*a + 7/6*a**3 + 2/3*a**4 + 0 + 1/3*a**2.
a*(a + 1)**2*(4*a - 1)/6
Let m = 82 - 77. Let z(g) be the second derivative of -1/6*g**4 + 0 + 4/15*g**6 + 0*g**2 - 1/20*g**m - 3*g + 0*g**3 - 5/42*g**7. Suppose z(u) = 0. Calculate u.
-2/5, 0, 1
Suppose -2*s + 4 = 4*i, 3*s = -2*i - i + 18. Suppose s - 6 = w. Factor 0 + 0*g - 1/3*g**2 + 1/3*g**w - 1/3*g**3 + 1/3*g**5.
g**2*(g - 1)*(g + 1)**2/3
Let r be ((-3)/(-5))/(3/15). Suppose -21*l - 3*l - 3*l**r - 5 + 15*l**2 + 7 + 10 = 0. Calculate l.
1, 2
Let s(r) = r + 9. Let b be s(-8). Let v = 1 + b. Factor v*t**2 + 2/5*t**4 - 4/5*t - 8/5*t**3 + 0.
2*t*(t - 2)*(t - 1)**2/5
Let y(b) be the second derivative of -b**6/150 + b**5/25 - b**4/20 - 2*b**3/15 + 2*b**2/5 + 7*b. Suppose y(q) = 0. What is q?
-1, 1, 2
Let -54*l + 54*l + 4*l**3 + 8*l**2 = 0. Calculate l.
-2, 0
Suppose -3*v = -15 + 6. Let r = -6 - -9. Factor -n**2 - 3*n**v - 2*n**3 + 5*n**r + n**3.
n**2*(n - 1)
Let k(r) be the second derivative of r**6/60 + r**5/60 - r**4/24 + r**2/2 - 2*r. Let h(t) be the first derivative of k(t). Factor h(b).
b*(b + 1)*(2*b - 1)
Let y(n) be the first derivative of 2*n**4/3 - 14*n**3/9 + 2*n**2/3 + 2*n/3 - 4. Factor y(u).
2*(u - 1)**2*(4*u + 1)/3
Let m(k) be the second derivative of k**4/60 + k**3/10 - 3*k. Suppose m(v) = 0. What is v?
-3, 0
Suppose 39*u - 24 = 31*u. Factor 0*c + u*c**2 - 3/2*c**3 + 9/2*c**5 - 6*c**4 + 0.
3*c**2*(c - 1)**2*(3*c + 2)/2
Let j(b) = -6*b**3 + 50*b**2 - 40*b. Let l(f) = 2*f**3 - 17*f**2 + 13*f. Let m(c) = 5*j(c) + 14*l(c). Factor m(x).
-2*x*(x - 3)**2
Let b = 87 - 173/2. Let y = 33/10 + -14/5. Factor -r**2 + b*r**3 + y*r + 0.
r*(r - 1)**2/2
Let c = 3 - 3. Factor c*p**3 - 6*p**2 + 2*p**2 + 2*p**2 + p**3.
p**2*(p - 2)
Let v(d) be the first derivative of -d**7/3360 + d**5/480 + d**3/3 - 4. Let u(o) be the third derivative of v(o). Factor u(y).
-y*(y - 1)*(y + 1)/4
Suppose -12*i**4 + 3*i**3 - 3*i + 14*i**4 + 3*i**2 - 5*i**4 = 0. What is i?
-1, 0, 1
Let l(f) = f + 1. Let g = 21 + -18. Let a be l(g). Factor -3/2*w**3 + 0 + 1/2*w**a + 3/2*w**2 - 1/2*w.
w*(w - 1)**3/2
Solve 29*z**5 + 5*z**2 - 2*z**3 - 27*z**5 + 2*z**2 - 3*z**2 - 4*z**4 = 0.
-1, 0, 1, 2
Let w(h) be the first derivative of h**5/150 - h**2/2 - 3. Let t(n) be the second derivative of w(n). What is l in t(l) = 0?
0
Let l(y) be the second derivative of 2*y**7/231 - 3*y**6/55 + 8*y**5/55 - 7*y**4/33 + 2*y**3/11 - y**2/11 - 30*y. Factor l(k).
2*(k - 1)**4*(2*k - 1)/11
Suppose 25*m - 3*m**2 - 20 - 5*m**2 + 2*m**2 + m**2 = 0. What is m?
1, 4
Let o(f) be the third derivative of 3*f**7/14 - 2*f**6 + 22*f**5/3 - 40*f**4/3 + 40*f**3/3 + 4*f**2. Find q, given that o(q) = 0.
2/3, 2
Let d(k) be the first derivative of k**4/2 - 4*k**3 + 12*k**2 - 16*k - 6. Factor d(v).
2*(v - 2)**3
Let l(c) be the second derivative of -c**7/21 - c**6/10 + c**5/10 - 2*c. Factor l(f).
-f**3*(f + 2)*(2*f - 1)
Suppose -2*g = -5*g - 18. Let f be ((-9)/g)/(6/8). Suppose 0 - 1/3*i**3 + 1/3*i**f + 1/3*i**5 + 0*i - 1/3*i**4 = 0. Calculate i.
-1, 0, 1
Suppose -9 = -5*q + 6. Let j(l) be the first derivative of 2/3*l**q - 2 + l**2 + 0*l. Factor j(z).
2*z*(z + 1)
Let b be (-164)/(-35) - 4 - (-2)/(-7). Let a(r) be the second derivative of -1/12*r**4 - b*r**2 + r + 4/15*r**3 + 1/100*r**5 + 0. Factor a(o).
(o - 2)**2*(o - 1)/5
Let v = -28 - -33. Let s(j) be the third derivative of 0 + 1/8*j**4 + 2*j**2 + 1/40*j**v + 1/480*j**6 + 0*j + 1/3*j**3. Factor s(u).
(u + 2)**3/4
Suppose 3*v = 3*f - 3, f = 2*f - 2*v. Let m(t) = t**3 - t**2 - t + 1. Let g(w) = 2*w**3 - 4*w**2 + 2*w. Let q(i) = f*m(i) - 2*g(i). Factor q(j).
-2*(j - 1)**3
Let d = -11 - -15. Factor -4*x**2 - 3*x**3 - 6*x**2 + d*x**2.
-3*x**2*(x + 2)
Let a(p) be the first derivative of -5 + 3*p - p**3 - 13*p + 10*p. Factor a(w).
-3*w**2
Let x(c) = -3*c - 2*c - 2*c**2 + 1 + 3*c. Let r(g) be the second derivative of g**4/4 + g**3/2 - g**2/2 - g. Let a(n) = -6*r(n) - 10*x(n). Factor a(t).
2*(t - 1)*(t + 2)
Let v(m) = m**2 + 5*m - 6. Let h be v(-6). Let d(f) = -f - 8. Let s be d(-8). Factor -1/5*l**4 + 1/5*l**2 + s*l**3 + 0 + h*l.
-l**2*(l - 1)*(l + 1)/5
Let x(y) = -y**5 - 5*y**4 + 4*y**3 - 4*y**2 + 4*y - 4. Let b(o) = o**5 + 6*o**4 - 5*o**3 + 5*o**2 - 5*o + 5. Let j(d) = 4*b(d) + 5*x(d). Factor j(v).
-v**4*(v + 1)
Let y(p) be the third derivative of p**6/540 + p**5/135 - p**4/108 - 2*p**3/27 - p**2. Factor y(g).
2*(g - 1)*(g + 1)*(g + 2)/9
Suppose -3*c + 24 + 0 = 0. Let s be (-2)/c + (-1)/(-4). Factor p + s*p**2 - 3*p**2 + 2*p**2.
-p*(p - 1)
Suppose 7 = 5*w + d - 21, -3*w + 5*d = -28. Let r be (w/14)/(2/4). Determine s so that -r*s**2 + 0 - 2/7*s = 0.
-