+ 0*r**2 - 1/24*r**m - 1/12*r**3. Determine o, given that u(o) = 0.
-1, 0
Let l = 67 - 65. Suppose 5*d**4 + 0*d - 17*d + 40*d**l - 25*d**3 + d - 4*d = 0. Calculate d.
0, 1, 2
Let j = 674 + -664. Let f(y) be the first derivative of 0*y**4 + y**3 + j + 0*y**2 - 3/5*y**5 + 0*y. Factor f(l).
-3*l**2*(l - 1)*(l + 1)
Let u(y) be the first derivative of y**5 - 5*y**4/2 - 55*y**3/3 + 30*y**2 + 277. Factor u(k).
5*k*(k - 4)*(k - 1)*(k + 3)
Let v be -15*(-20)/(-50) - -8. Factor 11/2*c - 3/4 + 4*c**4 - 31/4*c**v - 10*c**3.
(c - 3)*(c + 1)*(4*c - 1)**2/4
Let z(g) = -17*g**4 - 10*g**3 + 21*g**2 + 16*g + 5. Let o(y) = 18*y**4 + 11*y**3 - 20*y**2 - 15*y - 4. Let r(d) = -3*o(d) - 2*z(d). Let r(i) = 0. What is i?
-1, -2/5, -1/4, 1
Let u be 9*3/9 - (-72)/(-81)*3. Determine x, given that 0*x**3 - 1/3*x**5 - u*x**4 + 0 + 0*x + 0*x**2 = 0.
-1, 0
Let v(q) = -657*q - 1971. Let j be v(-3). Suppose j - 2/7*r**2 - 4/7*r = 0. What is r?
-2, 0
Let r be 6/(-112)*126/(-3240). Let x(o) be the third derivative of 0 - r*o**6 + 0*o + o**2 - 1/840*o**7 + 0*o**5 + 0*o**4 + 0*o**3. Factor x(i).
-i**3*(i + 1)/4
Suppose 55 = -4*f + 9*f. Suppose -5*b + 4*b**3 - 10*b**3 + f*b**3 = 0. What is b?
-1, 0, 1
Suppose 2*q + 3 + 1/3*q**2 = 0. Calculate q.
-3
Let k(o) be the third derivative of o**8/84 + 26*o**7/105 + 21*o**6/10 + 139*o**5/15 + 68*o**4/3 + 32*o**3 - 5*o**2 - 50*o. What is v in k(v) = 0?
-4, -3, -1
Let g(r) be the first derivative of r**4/2 - 32*r**3/3 - 19*r**2 + 68*r + 886. Factor g(q).
2*(q - 17)*(q - 1)*(q + 2)
Let o(b) be the second derivative of -2*b**7/21 + 2*b**6/5 + 2*b**5/5 - 2*b**4 - 2*b**3/3 + 6*b**2 + 6*b - 2. Determine k so that o(k) = 0.
-1, 1, 3
Let z(t) be the first derivative of 4*t**5/35 + 8*t**4/7 + 8*t**3/21 - 64*t**2/7 + 12*t - 182. Factor z(n).
4*(n - 1)**2*(n + 3)*(n + 7)/7
Let x be 32/14 - (-4)/(-14). Let p be (-38)/76*(-9 - -1). Let 2 - 30*b**p + 3*b**3 - 6*b**x - 21*b**3 + 36*b**5 - 14*b**3 + 18*b**2 + 12*b = 0. Calculate b.
-1/2, -1/3, 1
Factor -33/7*q + 78/7 - 3/7*q**2.
-3*(q - 2)*(q + 13)/7
Let h(y) be the third derivative of -y**6/160 + 21*y**5/16 - 3675*y**4/32 + 42875*y**3/8 - 87*y**2. Find c, given that h(c) = 0.
35
Suppose -4*z + 179 - 41 = -d, 4 = 2*d. Let a be 6/(-4)*(1 + z/(-25)). Factor 3/5 - a*h**3 - 3/5*h**2 + 3/5*h.
-3*(h - 1)*(h + 1)**2/5
Let y(q) be the second derivative of 0*q**3 + 0 - 2/45*q**6 - 16*q + 1/63*q**7 + 0*q**4 + 0*q**2 + 1/30*q**5. Factor y(d).
2*d**3*(d - 1)**2/3
Let z(x) be the third derivative of x**6/90 + 2*x**5/45 - x**4/18 - 4*x**3/9 - x**2 - 21. Solve z(g) = 0 for g.
-2, -1, 1
Let q(o) = -o**2 + 50*o - 1. Let a be q(6). Let i = 263 - a. Solve -1/2*v + i + 1/4*v**2 + 1/4*v**3 = 0 for v.
-2, 0, 1
Let q(r) be the third derivative of r**8/560 + r**7/175 - 21*r**6/200 + 9*r**5/50 - 325*r**2. Determine k so that q(k) = 0.
-6, 0, 1, 3
Suppose -6*p + 52 - 28 = 0. Factor -2/3*h**2 - p*h - 6.
-2*(h + 3)**2/3
Determine l, given that 9*l**2 + 15*l**4 + 71/2*l**3 - 9/2*l - 1 = 0.
-2, -1/2, -1/5, 1/3
Let a = 20383/40762 - 1/20381. Suppose 4*u**2 - 8*u - a*u**3 + 0 = 0. Calculate u.
0, 4
Let q(y) = -9*y**4 + 15*y**3 + 32*y**2 + 38*y + 20. Let d(m) = 2*m**4 - m**3 - 1. Let i(j) = -20*d(j) - 4*q(j). Factor i(r).
-4*(r + 1)**2*(r + 3)*(r + 5)
Let i(s) be the first derivative of s**4/4 + 133*s**3 + 53067*s**2/2 + 2352637*s - 73. Factor i(q).
(q + 133)**3
Let g(p) be the third derivative of p**9/18144 - p**8/5040 + p**6/1080 - p**5/720 - 7*p**3/3 + 13*p**2. Let h(i) be the first derivative of g(i). Factor h(n).
n*(n - 1)**3*(n + 1)/6
Let x(q) be the first derivative of -q**7/168 + q**5/8 + 5*q**4/12 + 19*q**3/3 - 11. Let s(m) be the third derivative of x(m). Factor s(l).
-5*(l - 2)*(l + 1)**2
Let k(b) be the first derivative of 1/6*b**4 + 0*b**2 - 2/3*b**3 - 6*b + 1/10*b**5 + 2. Let g(q) be the first derivative of k(q). Factor g(f).
2*f*(f - 1)*(f + 2)
Let m(a) be the second derivative of a**9/756 - a**8/140 + a**7/105 - 2*a**3 + 15*a. Let j(l) be the second derivative of m(l). Factor j(y).
4*y**3*(y - 2)*(y - 1)
Factor -1/6*y**2 - 242/3 + 22/3*y.
-(y - 22)**2/6
Let s(g) be the second derivative of 1/96*g**4 + 0 + 0*g**2 + 9*g + 1/80*g**5 + 1/240*g**6 + 0*g**3. Determine t so that s(t) = 0.
-1, 0
Let c be (-4)/24*3*-6. Factor -31*x + 33*x + 2*x**3 - 4*x**c.
-2*x*(x - 1)*(x + 1)
Suppose 12*x + 8*x**2 - 2*x**3 + 7*x**2 + 28 + 26*x - 7*x**2 = 0. Calculate x.
-2, -1, 7
Let g be (-442)/(-51) - ((-16)/(-6) - 2). Let a be (0*(4/g + 0))/4. Factor -2/3*s**5 + 0*s - 2/3*s**2 + a - 2*s**3 - 2*s**4.
-2*s**2*(s + 1)**3/3
Let g be ((-10)/(-175))/((-96)/(-10)). Let q(u) be the third derivative of -1/420*u**5 + 0 + 0*u**3 - g*u**4 - 5*u**2 + 0*u. Factor q(d).
-d*(d + 1)/7
Factor -8/3*g**2 - 128/3 - 1/3*g**5 + 20/3*g**3 + 2/3*g**4 - 128/3*g.
-(g - 4)**2*(g + 2)**3/3
Factor -6 + 3/5*t - 3/5*t**3 + 6*t**2.
-3*(t - 10)*(t - 1)*(t + 1)/5
Let m(t) = 2*t**3 + 40*t**2 - 71*t + 29. Let k(v) = -3*v**3 - 41*v**2 + 71*v - 27. Let l(y) = 3*k(y) + 4*m(y). Factor l(a).
-(a - 35)*(a - 1)**2
Let o(r) be the first derivative of -12*r**5/25 - 1431*r**4/20 - 23*r**3 + 1431*r**2/10 + 357*r/5 - 71. Find s such that o(s) = 0.
-119, -1, -1/4, 1
Let z be 2*6 + 2812/(-259). What is h in 1/7*h**4 + 4*h + z*h**3 + 23/7*h**2 + 12/7 = 0?
-3, -2, -1
Let r(x) be the second derivative of 16*x**6/45 + 49*x**5/30 + x**4/6 - 160*x. Factor r(m).
2*m**2*(m + 3)*(16*m + 1)/3
Let a = 44 + -37. Factor -a*f**2 - f**2 - 3*f**2 + 8*f**2.
-3*f**2
Let x(s) be the third derivative of s**5/60 - 17*s**4/24 + 8*s**3/3 + 76*s**2 - 2. Factor x(m).
(m - 16)*(m - 1)
Let l(o) be the second derivative of 0*o**2 + 1/6*o**6 - 20/9*o**3 - 25/126*o**7 + 13*o + 11/6*o**5 - 5/3*o**4 - 2. Determine f so that l(f) = 0.
-2, -2/5, 0, 1, 2
Suppose 0 = 4*n - 5*l - 67, -2*n - 5*l = -10 - 1. Let f be (2/6)/(n/195). Suppose -6*k**2 - 12*k**f + 1 - 1 + 4*k + 26*k**4 - 12*k**3 = 0. What is k?
-1/2, 0, 2/3, 1
Let n(p) be the second derivative of -p**4/138 + 16*p**3/69 - 2*p. Factor n(c).
-2*c*(c - 16)/23
Suppose 872 = -x - x. Let k be 4/3*(x/56 + 8). Find y such that 0 - k*y**2 + 0*y = 0.
0
Let b = -34 - -40. Suppose -3*g = -4*d + b, 8*d - 4*g - 4 = 4*d. Factor -11*i**4 - d*i**3 + 10*i**4 - 2*i**2 + 5*i**3 + i**2.
-i**2*(i - 1)**2
Let k = -1 + 3. Find h, given that -187*h**3 + 191*h**3 + 5*h**4 - 3*h**4 + 2*h**k = 0.
-1, 0
Let w be 0*1/1 - 0. Let m(l) = -l**2 + 4*l + 143. Let v be m(-10). Factor w*j + 9/4*j**v + 3/2*j**2 + 3/4*j**4 + 0.
3*j**2*(j + 1)*(j + 2)/4
Find r such that 0*r - 3/7*r**5 + 3/7*r**3 + 9/7*r**4 - 9/7*r**2 + 0 = 0.
-1, 0, 1, 3
Let q(c) be the second derivative of 5*c - 1/25*c**5 + 0*c**4 + 0 - 4/105*c**7 + 0*c**3 - 2/25*c**6 + 0*c**2. What is u in q(u) = 0?
-1, -1/2, 0
Let w(u) be the second derivative of 0*u**2 - 1/33*u**3 - 9*u - 4/33*u**4 - 8/55*u**5 + 0. Let w(t) = 0. Calculate t.
-1/4, 0
Let f(h) be the third derivative of -h**5/30 - h**4/4 + 4*h**3/3 - 74*h**2. Factor f(n).
-2*(n - 1)*(n + 4)
Let z(x) be the second derivative of -89401*x**4/48 + 299*x**3/6 - x**2/2 - 203*x. Factor z(d).
-(299*d - 2)**2/4
Let s be 6 + 0 + (-54)/10. Let g(j) be the second derivative of s*j**2 - 4/15*j**3 + 0 + 5*j + 1/30*j**4. Factor g(t).
2*(t - 3)*(t - 1)/5
Let b(z) = z**3 - 67*z**2 + 194*z - 126. Let j be b(64). Let -2/7*m**3 - 6/7*m + 2/7 + 6/7*m**j = 0. What is m?
1
Let y(u) be the first derivative of -u**5/50 + u**4/30 + 41*u - 7. Let p(s) be the first derivative of y(s). Factor p(x).
-2*x**2*(x - 1)/5
Let 36 - 18*o + 96 - 4*o**2 - 14*o = 0. Calculate o.
-11, 3
Suppose 18*n = -397 + 433. Factor 4/9*q - 2/3*q**n + 2/9*q**3 + 0.
2*q*(q - 2)*(q - 1)/9
Let h(g) be the third derivative of 0 + 5/24*g**4 - 30*g**2 + 0*g**3 + 0*g - 1/6*g**5. Factor h(w).
-5*w*(2*w - 1)
Suppose -4*p + 3*z + 8 = 0, -435*p + 434*p + 2*z = -2. Factor p - 8/3*x + 2/3*x**2.
2*(x - 3)*(x - 1)/3
Let x = -528 - -531. Determine q so that -14/5*q + 2*q**2 + 6/5 - 2/5*q**x = 0.
1, 3
Let b(t) be the second derivative of -5*t**5 - 365*t**4/12 - 205*t**3/6 - 15*t**2 + 159*t. Let b(l) = 0. Calculate l.
-3, -2/5, -1/4
Factor x**2 + 82 + x**2 - 162 + 14*x + 100.
2*(x + 2)*(x + 5)
Suppose 0 = -c + 5*g - 18, 2*g + 1 = 3*c + 3. Let v be c/20 + (-3 - 58/(-20)). Find d, given that v - 4/5*d**2 + 2/5*d**3 + 2/5*d = 0.
0, 1
Let n(u) = -3*u**3 - 7*u - 2.