 - 1/6*o**2.
-o*(o - 3)/6
Let r(u) be the second derivative of -3*u + 0*u**2 + 1/45*u**5 + 0*u**3 - 1/54*u**4 + 0 - 1/135*u**6. Factor r(f).
-2*f**2*(f - 1)**2/9
Let y = -1 - -1. Suppose 3*n + y - 9 = 0. Find k such that k**4 + 1/3*k**2 - 1/3*k**5 + 0*k + 0 - k**n = 0.
0, 1
Let g(s) = s - 7. Let y be g(10). Let q(d) be the first derivative of -2/9*d**y - d**2 - 4/3*d + 2. Factor q(x).
-2*(x + 1)*(x + 2)/3
Let s(y) be the second derivative of -1/2*y**2 + 1/6*y**3 - 5/48*y**4 - 2*y + 1/40*y**5 + 0. Let u(h) be the first derivative of s(h). Factor u(d).
(d - 1)*(3*d - 2)/2
Let w(a) be the third derivative of -a**5/270 + 17*a**2. Suppose w(n) = 0. What is n?
0
Let n(d) be the second derivative of 3/20*d**5 + 1/4*d**4 + 0 - 1/2*d**3 - 3/2*d**2 + 3*d. Factor n(u).
3*(u - 1)*(u + 1)**2
Let p(u) = -u**3 - u. Let n(c) = -2*c**3 - 6*c**2 - 10*c. Let h(y) = n(y) - p(y). Factor h(a).
-a*(a + 3)**2
Let 12*z - 22*z**3 - 2*z**2 + 9 + 18*z**3 + z**4 + 0 = 0. Calculate z.
-1, 3
Suppose -x = 1 - 2. Let y(a) = 9*a**2 + 9*a + 6. Let w(h) = -h**2 - h + 1. Let f be (3/(-2))/((-2)/(-4)). Let o(d) = f*w(d) + x*y(d). Let o(q) = 0. Calculate q.
-1/2
Let r = 18 + -14. Suppose 4 + 8 = r*h. Find b, given that 0 + 0*b**2 + 2/11*b - 2/11*b**h = 0.
-1, 0, 1
Let v(i) be the first derivative of -i**9/1512 - i**8/1400 + i**7/1050 + i**3/3 - 1. Let z(b) be the third derivative of v(b). What is r in z(r) = 0?
-1, 0, 2/5
Let h be 2/(-15)*(-135)/81. Let o(t) be the first derivative of h*t**3 + 4 + 1/12*t**4 + 1/6*t**2 + 0*t. Factor o(q).
q*(q + 1)**2/3
Solve -42*h**2 - 118*h**2 + 61*h**4 + 370*h**4 + 53*h**4 - 16*h - 308*h**3 = 0.
-2/11, 0, 1
Let m be (-1)/(3/(-12)*2). Let i(j) be the first derivative of 0*j + 4/9*j**3 - 1/3*j**m + 1 - 1/6*j**4. Factor i(z).
-2*z*(z - 1)**2/3
Suppose -5*w = -w. Let m(k) be the third derivative of 0 + w*k + 2*k**2 - 1/96*k**4 + 1/480*k**6 - 1/24*k**3 + 1/240*k**5. Factor m(n).
(n - 1)*(n + 1)**2/4
Let z = 78 - 78. Determine f, given that 2/7*f**2 + 2/7*f**3 - 2/7*f**4 - 2/7*f + z = 0.
-1, 0, 1
Let n(i) be the first derivative of -3*i**4/2 - 4*i**3/3 + 3*i**2 + 4*i + 53. Factor n(p).
-2*(p - 1)*(p + 1)*(3*p + 2)
Let l(d) = 2*d - 3. Let a be l(3). Let p = 5 - 2. Factor -5*w - 6*w**2 - a*w - 2*w**p + 2*w - 2.
-2*(w + 1)**3
Suppose -k + 3*k + 5*c = -12, 32 = 5*k - 3*c. Suppose -6*n - 8*n**2 - 4*n**3 - 2*n - k*n**2 = 0. What is n?
-2, -1, 0
Let p be (24/30)/((-22)/(-110)). Factor 0 - 1/2*d**2 + 1/2*d**p + d - d**3.
d*(d - 2)*(d - 1)*(d + 1)/2
Let k be 23/6 - 5/(-30). Suppose 0 = 5*b + 1 - 6. Factor 3*p - 3*p**2 + 2*p**2 + p**3 - k*p + b.
(p - 1)**2*(p + 1)
Let d(l) be the first derivative of l**4/8 + l**3/3 + l**2/4 - 6. Factor d(g).
g*(g + 1)**2/2
Let p(g) be the second derivative of -g**4/36 + 4*g**3/9 - 8*g**2/3 - g. Solve p(u) = 0.
4
Let y be 0 + -9 + 0/1. Let f be -3*(4/y)/2. Factor 0 + 1/3*a + 1/3*a**3 + f*a**2.
a*(a + 1)**2/3
Let a = -78 - -80. Let z(w) be the second derivative of 0*w**4 + 1/12*w**3 + 0 + 1/8*w**a - 1/120*w**6 - 3*w - 1/40*w**5. Suppose z(u) = 0. Calculate u.
-1, 1
Let r be ((-4)/(-5))/((-20)/(-750)). Suppose 5*j = 5*h - r, 3*j - 4 + 1 = -4*h. Factor 1/2*b**2 + 1/4*b + 0 + 1/4*b**h.
b*(b + 1)**2/4
Suppose 3*h + 4*f = -41, 6*f + 31 = -3*h + 4*f. Let j(g) = g**2 + 8*g + 9. Let q be j(h). Factor -2*b**3 + 3*b**3 - 4*b**2 + b + 5*b**2 - 1 - q*b**3.
-(b - 1)**2*(b + 1)
Let k(r) be the third derivative of 1/24*r**3 + 1/80*r**5 - 1/480*r**6 + 0 - 2*r**2 - 1/32*r**4 + 0*r. Suppose k(p) = 0. Calculate p.
1
Let p = 1466/65 - 112/5. Factor 4/13*r**4 - 4/13*r**2 - p*r + 0*r**3 + 0 + 2/13*r**5.
2*r*(r - 1)*(r + 1)**3/13
Let s(u) be the second derivative of -u**6/540 - u**5/90 - u**4/36 - u**3/2 + u. Let z(q) be the second derivative of s(q). Find y such that z(y) = 0.
-1
Let y = 14 + -7. Let j(q) = q**3 - 3*q**2 + 2*q - 4. Let a be j(3). Factor a*f + 5*f**2 - y*f**3 + 4*f - 4*f.
-f*(f - 1)*(7*f + 2)
Let x(f) be the second derivative of -2/7*f**2 + 1/21*f**3 + 0 + 1/42*f**4 - f. Factor x(v).
2*(v - 1)*(v + 2)/7
Let z(r) be the second derivative of r**5/20 + 5*r**4/12 + 5*r**3/6 + r**2/2 - r. Let o(n) = -n**2 - n. Let t(m) = 2*o(m) + z(m). Find g such that t(g) = 0.
-1
Let f(s) be the third derivative of -s**8/56 - 5*s**7/42 - 41*s**6/120 - 11*s**5/20 - 13*s**4/24 - s**3/3 - 8*s**2. Solve f(l) = 0 for l.
-1, -2/3, -1/2
Let y = 7 - 5. Factor -3*u**2 - 9*u + u**2 - u**y - 6.
-3*(u + 1)*(u + 2)
Let t(v) = -19*v**4 + 36*v**3 - 24*v**2 + 7*v - 3. Let a(k) = -56*k**4 + 108*k**3 - 72*k**2 + 20*k - 8. Let f(l) = 3*a(l) - 8*t(l). Let f(x) = 0. What is x?
0, 1/4, 1
Let p be (0 - (-4)/12*0)/2. Suppose p + 2/3*y**2 - 1/3*y - 1/3*y**3 = 0. What is y?
0, 1
Let w(i) be the second derivative of 0 - 4/3*i**3 + i + 2/5*i**6 + 0*i**2 - 3/7*i**7 - 2/3*i**4 + 11/10*i**5. Factor w(q).
-2*q*(q - 1)**2*(3*q + 2)**2
Let m(l) be the second derivative of -l**7/42 - l**6/30 + 3*l**5/20 + l**4/12 - l**3/3 - 14*l. Factor m(o).
-o*(o - 1)**2*(o + 1)*(o + 2)
Let m(q) be the first derivative of 3/16*q**4 + 2 + 0*q + 1/8*q**2 + 1/20*q**5 + 1/4*q**3. Let m(c) = 0. Calculate c.
-1, 0
Let v(m) = -m**3 + 5*m**2 + 6*m + 2. Let r be v(6). Suppose 3 = o + 1. Let -15*p**r - o - 10*p**3 - 9*p - p**3 - p**4 - 2*p**4 = 0. What is p?
-1, -2/3
Let s(p) be the second derivative of -p**5/10 - p**4/6 - 6*p. Suppose s(x) = 0. Calculate x.
-1, 0
Factor 5/2*c**2 - 2 - 1/2*c.
(c - 1)*(5*c + 4)/2
Let m(u) = 7*u**3 - u**2 - 12*u - 2. Let g(y) = -8*y**3 + 12*y + 1. Let f(j) = -2*g(j) - 3*m(j). Find v such that f(v) = 0.
-1, -2/5, 2
Let x(i) = i**2 - i. Let z(n) = 7*n**2 - 7*n + 6. Let y(j) = -8*j**2 + 8*j - 7. Let p(b) = -6*y(b) - 7*z(b). Let u(t) = 5*p(t) + 6*x(t). What is g in u(g) = 0?
0, 1
Let q(b) = -9*b**3 - 8*b**2 + b + 5. Let t(w) = -13*w**3 - 12*w**2 + w + 7. Let g(v) = 7*q(v) - 5*t(v). Factor g(p).
2*p*(p + 1)**2
Let c(i) be the first derivative of -i**6/42 + i**5/5 - 19*i**4/28 + 25*i**3/21 - 8*i**2/7 + 4*i/7 - 6. What is q in c(q) = 0?
1, 2
Let j = -7 + 9. Let m(l) = l**3 - 2*l**2 + l + 2. Let t be m(j). Factor -4/5*i**3 - 2/5*i**2 + 0*i - 2/5*i**t + 0.
-2*i**2*(i + 1)**2/5
Let d be (-18)/(-6) - (-2)/(-1). Let b be 0/((-1 - d) + 4). Factor 0*q + 0 + b*q**3 + 2/5*q**2 - 2/5*q**4.
-2*q**2*(q - 1)*(q + 1)/5
Let c(t) be the first derivative of -t**4/28 + t**3/21 + t**2/7 + 1. Solve c(q) = 0 for q.
-1, 0, 2
Let d(s) be the third derivative of s**8/112 - 4*s**7/35 + 5*s**6/8 - 19*s**5/10 + 7*s**4/2 - 4*s**3 + 27*s**2. What is p in d(p) = 0?
1, 2
Suppose h - 4*y = -0 + 8, 0 = -5*h - 4*y - 8. Factor 8/3*o**3 - 2/3*o**4 + 4/3*o - 10/3*o**2 + h.
-2*o*(o - 2)*(o - 1)**2/3
Let h(g) be the first derivative of -g**7/420 - g**6/120 - g**2/2 + 6. Let r(y) be the second derivative of h(y). Determine m, given that r(m) = 0.
-2, 0
Suppose -o = 4*m + 16, -5*m - 11 - 9 = 3*o. Suppose 0 - 2/7*g**4 + 2/7*g**2 + 0*g + o*g**3 = 0. Calculate g.
-1, 0, 1
Factor -507 + 20*u**2 + 85*u - 23*u**2 - 7*u.
-3*(u - 13)**2
Let c(p) = p**3 - 3*p**2 + 2*p - 3. Let f be c(3). Let d**3 - f*d + 8 - 10 + 0*d = 0. What is d?
-1, 2
Suppose -40 = m - 3*m. Let i be 6/m + 7/14. Factor 0*a + 0 - 2/5*a**4 + i*a**3 - 2/5*a**2.
-2*a**2*(a - 1)**2/5
Let v(t) be the second derivative of t**7/630 + t**6/180 + 5*t**4/12 - 8*t. Let u(s) be the third derivative of v(s). Solve u(i) = 0 for i.
-1, 0
Let r(u) be the first derivative of u**4/14 - 4*u**3/21 - u**2/7 + 4*u/7 + 10. Solve r(l) = 0.
-1, 1, 2
Let l(a) = -4*a**3 + 21*a**2 - 8*a. Let b(z) = z**3 - 5*z**2 + 2*z. Let t(w) = -9*b(w) - 2*l(w). Find s such that t(s) = 0.
0, 1, 2
Let x(t) be the first derivative of t**6/45 - t**5/10 + t**4/6 - t**3/9 - 5*t - 6. Let s(m) be the first derivative of x(m). Factor s(f).
2*f*(f - 1)**3/3
Let n(d) be the second derivative of -d**6/50 - 3*d**5/100 + 3*d**4/20 + d**3/2 + 3*d**2/5 - 40*d. Factor n(p).
-3*(p - 2)*(p + 1)**3/5
Let c(w) = -w**2 + 4*w + 9. Let t be c(5). Let i be t/7 + (-62)/(-14). Suppose -3/2*x**i - 6*x**3 + 5*x**4 + 0 + 3*x**2 - 1/2*x = 0. What is x?
0, 1/3, 1
Suppose 0*w + 16/7*w**4 + 0*w**3 + 0 - 2/7*w**5 + 0*w**2 = 0. Calculate w.
0, 8
Let v(t) be the second derivative of t**8/1344 - t**7/420 - 5*t**2/2 - 2*t. Let z(r) be the first derivative of v(r). Determine a so that z(a) = 0.
0, 2
Suppose w + r - 6 = 0, 3*w + 3*r = -2*w + 30. S