= 0.
0, 1
Let a be (2/(-16))/((-78)/104). Let r(o) be the first derivative of -a*o**2 - 2 - 2/3*o + 2/9*o**3 + 1/12*o**4. Factor r(h).
(h - 1)*(h + 1)*(h + 2)/3
Let y(z) be the second derivative of 0 - 3/20*z**5 + 1/10*z**6 - 1/4*z**4 + z + 0*z**2 + 1/2*z**3. Determine r, given that y(r) = 0.
-1, 0, 1
Let v(y) be the first derivative of y**3/3 - y**2/2 + y/4 - 4. Find p, given that v(p) = 0.
1/2
Let n(o) = -o**3 + o**2 + o - 1. Let t(w) = -2*w**4 - 18*w**3 + 10*w**2 + 18*w - 8. Let l(i) = 12*n(i) - t(i). Suppose l(s) = 0. Calculate s.
-2, -1, 1
Let a = -6 + 6. Determine b so that -2*b**2 + 0 - 4 + a*b**3 + 8*b + b**3 - 3*b**2 = 0.
1, 2
Let w(c) be the first derivative of -c**7/84 - 2*c**6/45 - c**5/60 + c**4/6 + c**3/3 - 2. Let r(a) be the third derivative of w(a). Factor r(p).
-2*(p + 1)**2*(5*p - 2)
Let y be 18/(-4)*8/(-12). Let n be (-2)/y - 16/(-6). Factor -f + 1 + 6*f**n + 7*f**5 - 1 - 5*f**4 - 4*f**5 - 1 - 2*f**3.
(f - 1)**3*(f + 1)*(3*f + 1)
Let j(y) = -2*y**2 - 83*y - 320. Let b(h) = 3*h**2 + 82*h + 320. Let m(x) = -3*b(x) - 2*j(x). Suppose m(c) = 0. Calculate c.
-8
Let q be 28/4 - (1 - -2). Let y = q + -2. Determine b, given that -b**3 - 16 + y*b**4 - b**5 + 16 = 0.
0, 1
Let u be 4 + (6/(-1))/(-3). Let f(a) = -3*a**2 + 8*a + 7. Let j(m) = -6*m**2 + 15*m + 13. Let q(w) = u*j(w) - 11*f(w). Let q(i) = 0. Calculate i.
-1/3, 1
Let b be (-3)/(-2) - (-88)/(-64). Let p(s) be the first derivative of b*s**4 + 3 + 1/3*s**3 - 1/4*s**2 - s. Factor p(n).
(n - 1)*(n + 1)*(n + 2)/2
Let o(v) be the third derivative of -v**9/4536 - v**8/840 - v**7/630 - v**3/6 + v**2. Let h(f) be the first derivative of o(f). Factor h(c).
-2*c**3*(c + 1)*(c + 2)/3
Factor 38 - 4*a**2 - 20 - 18 + 28*a.
-4*a*(a - 7)
Let f(m) be the second derivative of m**4/48 - m**3/24 - m**2/4 - 9*m. Factor f(a).
(a - 2)*(a + 1)/4
Let y(a) be the third derivative of a**5/240 - a**4/96 + 3*a**2. Let y(g) = 0. What is g?
0, 1
Factor -6*m**2 + 2*m**3 - 1/4*m**4 - 4 + 8*m.
-(m - 2)**4/4
Let t(q) be the first derivative of 1 - 1/15*q**3 - 2/5*q + 3/10*q**2. Let t(p) = 0. What is p?
1, 2
Let h = 209/7170 + 1/239. Let p(r) be the third derivative of 0*r**3 + 0*r + 1/105*r**7 + h*r**5 + 0 - 1/30*r**6 + 0*r**4 - 3*r**2. Let p(n) = 0. Calculate n.
0, 1
Let r be 180/(-28) - -5 - -1*2. What is d in -6/7*d**2 + 2/7 + 0*d + r*d**3 = 0?
-1/2, 1
Suppose 5*k - 10 - 15 = 0, -4*k = o - 20. Suppose 1/3*c**2 + 0*c + o = 0. What is c?
0
Let m = 4 + 9. Suppose -4*k + m - 1 = 0. Factor k*h**2 - 3*h**3 - h**4 + 0*h + 2*h**4 + 0*h - h.
h*(h - 1)**3
Let t(h) be the second derivative of h**7/126 + h**6/30 + h**5/30 + 2*h. Factor t(s).
s**3*(s + 1)*(s + 2)/3
Let b(d) be the third derivative of -d**6/210 - 2*d**5/105 + d**4/42 + 4*d**3/21 + 28*d**2. Factor b(l).
-4*(l - 1)*(l + 1)*(l + 2)/7
Let q(f) be the third derivative of -f**7/70 + f**6/40 + f**5/4 + 3*f**4/8 - 10*f**2. Suppose q(x) = 0. What is x?
-1, 0, 3
Let w(p) be the third derivative of -p**6/300 + p**5/150 + p**4/60 - p**3/15 + 12*p**2. Factor w(b).
-2*(b - 1)**2*(b + 1)/5
Let l(v) be the first derivative of 0*v**2 + 0*v + 0*v**4 + 1/24*v**6 + 4 - 1/20*v**5 + 0*v**3. Solve l(f) = 0.
0, 1
Let p = -21 + 26. Factor -5*r**3 + 23*r**3 + 2*r + 4*r**p - r**2 - 9*r**2 - 14*r**4.
2*r*(r - 1)**3*(2*r - 1)
Let w = -10/7 - -145/28. Factor w*i + 3*i**2 - 3/2 - 9/4*i**3.
-3*(i - 2)*(i + 1)*(3*i - 1)/4
Let w(b) be the second derivative of -b**6/6 - b**5/2 + 5*b**3/3 + 5*b**2/2 - 37*b. Factor w(z).
-5*(z - 1)*(z + 1)**3
Let x(y) be the second derivative of -3*y**7/49 + 8*y**6/35 - 9*y**5/35 + y**3/7 - 19*y - 1. Factor x(j).
-6*j*(j - 1)**3*(3*j + 1)/7
Let r(a) be the third derivative of a**6/200 + a**5/100 - 24*a**2. Factor r(s).
3*s**2*(s + 1)/5
Let m(t) be the third derivative of 7*t**6/40 - 9*t**5/20 + t**4/4 - 2*t**2. Factor m(d).
3*d*(d - 1)*(7*d - 2)
Let w(x) = 7*x**2 + 3*x - 3. Let q(f) be the first derivative of -13*f**3/3 - 5*f**2/2 + 5*f + 8. Let s(j) = -3*q(j) - 5*w(j). Factor s(i).
4*i**2
Factor -2/13*k**3 - 2/13*k + 0 - 4/13*k**2.
-2*k*(k + 1)**2/13
Let z(g) be the second derivative of -2*g**7/147 + 2*g**6/105 + g**5/5 - 13*g**4/21 + 4*g**3/7 - 25*g. Let z(h) = 0. What is h?
-3, 0, 1, 2
Let p(y) be the third derivative of -y**5/60 - 5*y**4/24 - y**3 + 15*y**2. Factor p(g).
-(g + 2)*(g + 3)
Factor -2/7 - 4/7*l + 0*l**2 + 2/7*l**4 + 4/7*l**3.
2*(l - 1)*(l + 1)**3/7
Let b(c) be the third derivative of -1/60*c**6 + 0 + 0*c**5 + 0*c**4 - 2*c**2 + 0*c + 1/210*c**7 + 0*c**3. Suppose b(o) = 0. Calculate o.
0, 2
What is w in -5/3*w**2 - w**3 - 1/3*w + 1/3 = 0?
-1, 1/3
Let k(p) be the third derivative of p**7/840 - p**6/120 + p**5/48 - p**4/48 - 18*p**2. Factor k(m).
m*(m - 2)*(m - 1)**2/4
Suppose -y = -3*k + 7, -5 + 13 = 4*y. Solve -4*s**k + 3*s**3 - 1 + 8*s**2 - 5*s**2 + 2 - 3*s = 0 for s.
1
Suppose 0 = -2*j + 6, -2*x + j = 4*j - 13. Determine m, given that -16 + 5 + 24*m - 7*m**x + 2*m**3 - 5 - 5*m**2 = 0.
2
Let i(r) = r**3 + 6*r**2 - 5*r. Let v(o) = o**3 + 5*o**2 - 4*o. Let q(f) = -4*i(f) + 5*v(f). Factor q(g).
g**2*(g + 1)
Let g(h) be the second derivative of h**9/1512 - h**8/420 + h**7/420 - 2*h**3/3 - 3*h. Let a(q) be the second derivative of g(q). Solve a(i) = 0.
0, 1
Let z be (-76)/(-20) - (-1)/5. Factor -2*t - t**4 - 3*t**2 + t**2 - 2*t**3 + 4*t + 3*t**z.
2*t*(t - 1)**2*(t + 1)
Let g = 37 + -443/12. Let k(w) be the third derivative of -1/60*w**6 + 0*w - 1/30*w**5 - 4*w**2 + 0 + 1/3*w**3 + g*w**4. What is z in k(z) = 0?
-1, 1
Let b(q) be the second derivative of -q**4/27 + q**3/9 + 2*q**2/9 - q. Find h, given that b(h) = 0.
-1/2, 2
Let d(j) be the first derivative of j**6/12 - j**5/6 + j**4/24 + j**3/18 - 26. Factor d(x).
x**2*(x - 1)**2*(3*x + 1)/6
Let j(b) be the second derivative of 2*b**7/7 + 11*b**6/10 + 9*b**5/10 - 2*b**4 - 5*b**3 - 9*b**2/2 + 6*b. Solve j(n) = 0.
-1, -3/4, 1
Let x(h) = h**2 + 2*h + 3. Let r be x(-3). Suppose -y = y - r. Factor -4*i**4 - 3*i**5 - i**y + 3*i**3 + 5*i**5.
2*i**3*(i - 1)**2
Let g(d) be the second derivative of -d**7/273 - d**6/195 + d**5/130 + d**4/78 - 32*d. Determine i, given that g(i) = 0.
-1, 0, 1
Let g(s) be the second derivative of -s**6/225 + s**4/30 - 2*s**3/45 + 15*s. Factor g(t).
-2*t*(t - 1)**2*(t + 2)/15
Let g = -1/2 + 3/4. Factor 1/4*h**3 - g*h - 1/4*h**2 + 1/4.
(h - 1)**2*(h + 1)/4
Let u(q) = 3*q**2 + 5*q + 2. Let k(o) = -2*o - o**2 - 5 - 1 + 6 - 1. Let y(a) = -5*k(a) - 2*u(a). Suppose y(l) = 0. What is l?
-1, 1
Let d be (-2)/(-6) + (-10)/48*-8. Factor -18/5*h + 27/5 + 3/5*h**d.
3*(h - 3)**2/5
Let i(f) = 2 - 2 - 3*f**2 + f**4 + 3*f + 0*f**3 - 3 - 5*f**3. Let o(k) = -k**4 + k**3 + k**2 - k + 1. Let d(j) = i(j) + 3*o(j). Factor d(x).
-2*x**3*(x + 1)
Let u(v) be the third derivative of -v**10/30240 + v**9/15120 - v**4/12 + 3*v**2. Let b(f) be the second derivative of u(f). Factor b(o).
-o**4*(o - 1)
Let g = -354 - -356. Suppose -8/15*m**3 + 0 + 2/15*m + 2/5*m**g = 0. Calculate m.
-1/4, 0, 1
Let l = 190/9 - 1033/63. Let f = l - 125/28. Factor -f*g**3 - 1/4*g**2 + 1/4 + 1/4*g.
-(g - 1)*(g + 1)**2/4
Let y(m) be the second derivative of -m**7/210 + m**6/60 - m**5/60 - m**2 + m. Let p(q) be the first derivative of y(q). Factor p(t).
-t**2*(t - 1)**2
Let n(g) be the second derivative of g**6/480 + g**5/240 - g**4/96 - g**3/24 - 3*g**2/2 - g. Let b(a) be the first derivative of n(a). Factor b(w).
(w - 1)*(w + 1)**2/4
Let c(g) be the first derivative of 1/24*g**6 + 1/8*g**2 + 0*g**5 - 1/8*g**4 - 2 + 0*g**3 + 0*g. Factor c(y).
y*(y - 1)**2*(y + 1)**2/4
Suppose 5*n - 15 = 4*y, y + n = 6*n - 15. Let i(w) be the first derivative of 1/2*w**2 + y*w + 1 - 1/3*w**3. Factor i(b).
-b*(b - 1)
Let a(n) be the second derivative of n**4/3 - n**3/2 - 26*n. Suppose a(m) = 0. What is m?
0, 3/4
Let c(s) = -5*s**5 + 17*s**4 + 106*s**3 + 296*s**2 + 319*s + 131. Let m(k) = -k**5 + k**2 - k + 1. Let a(f) = -c(f) + 6*m(f). Factor a(r).
-(r + 1)**2*(r + 5)**3
Let x(q) be the second derivative of 0*q**4 + 0*q**2 - q + 1/120*q**6 + 0 - 1/2*q**3 + 1/20*q**5. Let m(j) be the second derivative of x(j). Factor m(p).
3*p*(p + 2)
Let z(y) be the third derivative of -y**8/1008 + y**7/630 + y**6/360 - y**5/180 + 8*y**2. Factor z(t).
-t**2*(t - 1)**2*(t + 1)/3
Let b be ((-3)/(15/8))/(13 + -14). Factor b*w - 2/5*w**2 - 8/5.
-2*(w - 2)**2/5
Let t(f) 