 such that t(z) = 0.
0, 1, 2
Let l(q) be the first derivative of -q**5/20 + q**4/4 - q**3/2 + 5*q**2/2 - 3. Let o(k) be the second derivative of l(k). Let o(m) = 0. Calculate m.
1
Let t be 1/((4/24)/1). Let z(u) be the third derivative of 0*u**3 + 0*u**5 + 0 + 1/48*u**4 - 1/240*u**t + 0*u - 2*u**2. Factor z(f).
-f*(f - 1)*(f + 1)/2
Let t(u) be the third derivative of u**5/120 - u**4/12 - 13*u**2. Factor t(w).
w*(w - 4)/2
Let q be (-2 + 2)/(1/2*-4). Let v(n) be the second derivative of -1/12*n**3 - n - 1/8*n**2 + 1/120*n**6 + q*n**4 + 1/40*n**5 + 0. Find x such that v(x) = 0.
-1, 1
Let l be 2/10*1*-1*-1. Factor l*w + 0 - 1/5*w**2.
-w*(w - 1)/5
Suppose 0 = -i + 3*i - 8. Factor -2*w**3 + 5*w**4 - 61*w**2 - 4 - 28*w - 14*w**i - 40*w**3.
-(w + 2)**2*(3*w + 1)**2
Let g(p) be the third derivative of p**5/420 - p**4/21 + 8*p**3/21 + 2*p**2. Solve g(y) = 0 for y.
4
Let b(o) be the first derivative of -2*o**3 - 13*o**2 - 8*o - 6. Suppose b(j) = 0. Calculate j.
-4, -1/3
Determine x so that 0 + 16/3*x - 7/3*x**3 + 8/3*x**2 + 1/3*x**4 = 0.
-1, 0, 4
Let n(k) be the first derivative of -k**4/4 + 5*k**3/3 - 4*k**2 + 4*k + 6. Factor n(b).
-(b - 2)**2*(b - 1)
Suppose 0 = -6*u + 22 - 4. Solve -8*w + w**3 - w**2 - w**2 + 3*w**u - 2*w**2 = 0 for w.
-1, 0, 2
Solve 1/2*w**3 - 1/2*w + 3/4 + 1/4*w**4 - w**2 = 0 for w.
-3, -1, 1
Let p(l) = 6*l**4 - 29*l**3 + 10*l**2 + 4. Let w(r) = -5*r**4 + 30*r**3 - 10*r**2 - 5. Let v(z) = 5*p(z) + 4*w(z). Solve v(h) = 0.
0, 1/2, 2
Solve 0 + 2/11*k**2 + 4/11*k = 0 for k.
-2, 0
Let t be ((-4)/24)/(16/(-24)). Factor -1/4*b + t*b**2 - 1/2.
(b - 2)*(b + 1)/4
Let m(x) be the third derivative of x**7/280 + x**6/160 - x**5/20 - x**4/8 - 31*x**2. Factor m(t).
3*t*(t - 2)*(t + 1)*(t + 2)/4
Let p(n) = n + 2. Let f be p(0). Suppose 18 - 12*b + b**2 + 3*b**2 - f*b**2 = 0. What is b?
3
Suppose 6 = -5*p + 4*u - 0, 5*u = p - 3. Let k be 2/p + 3 - 2. Factor -1/5*b**5 + k + 0*b + 0*b**3 + 1/5*b**4 + 0*b**2.
-b**4*(b - 1)/5
Let f(q) be the first derivative of -q**6/45 + 2*q - 3. Let u(s) be the first derivative of f(s). Suppose u(a) = 0. Calculate a.
0
Let h be (-1)/(16/(-12) - -1). Let d be (-5)/((-75)/4)*10. Solve -d*s + 0 - 70/3*s**h + 44/3*s**2 + 25/3*s**4 = 0 for s.
0, 2/5, 2
Factor -10/9*p + 4/9 - 2/3*p**2.
-2*(p + 2)*(3*p - 1)/9
Let n(p) be the first derivative of p**5/30 - p**4/18 - p**3/9 + p**2/3 + 2*p + 3. Let r(m) be the first derivative of n(m). Factor r(t).
2*(t - 1)**2*(t + 1)/3
Let z(p) = p**3 - 4*p**2 + 2*p - 6. Let t be z(4). Let v be (-3 + t)/(1/(-13)). Factor 2*u - 8*u**2 - 3*u**3 + v*u**3 - 8*u**4 + 2*u**5 + 2*u**3.
2*u*(u - 1)**4
Let q be 2/(-3) - (-154)/33. Let u(y) be the second derivative of 0 + 0*y**2 - 1/30*y**6 + 1/10*y**5 + 0*y**3 - 1/12*y**q - y. Suppose u(m) = 0. Calculate m.
0, 1
Let i(n) be the third derivative of n**6/90 - n**5/15 + n**4/6 + 4*n**3/3 - 6*n**2. Let f(y) be the first derivative of i(y). Factor f(k).
4*(k - 1)**2
Let x(n) = -n**3 + n + 1. Let g(l) = 3*l**3 + 20*l**2 + 27*l + 12. Let y(b) = g(b) - 2*x(b). Find m such that y(m) = 0.
-2, -1
Let n be -6 + (-10)/(-2) - -4. Let h(f) be the first derivative of 0*f + 0*f**2 + 1 - 2/3*f**n. Suppose h(k) = 0. What is k?
0
Let g(b) = -60*b**3 + 260*b**2 - 304*b + 96. Let u(m) = -12*m**3 + 52*m**2 - 61*m + 19. Let i(a) = -3*g(a) + 16*u(a). Factor i(c).
-4*(c - 2)**2*(3*c - 1)
Let l(x) = -x**2 - 7*x - 3. Let p be l(-6). Let y be 8/(-14)*28/(-12). Factor -y - 8/3*s - 5/3*s**2 - 1/3*s**p.
-(s + 1)*(s + 2)**2/3
Solve 2/15*p**3 - 2/15*p**4 + 2/15*p**2 + 0 - 2/15*p = 0.
-1, 0, 1
Let n(k) be the third derivative of -k**7/105 + k**6/60 + k**5/10 - 5*k**4/12 + 2*k**3/3 - 8*k**2. Factor n(c).
-2*(c - 1)**3*(c + 2)
Factor 0 + 2/11*i**2 + 4/11*i.
2*i*(i + 2)/11
Let h(r) be the third derivative of -r**5/120 - 5*r**4/24 - 25*r**3/12 + 2*r**2. Solve h(z) = 0 for z.
-5
Let g be ((-5)/((-50)/(-4)))/((-26)/130). Let -8/11 - 2/11*j**g - 14/11*j**3 + 16/11*j + 10/11*j**4 - 2/11*j**5 = 0. What is j?
-1, 1, 2
Let m(x) be the third derivative of -1/45*x**6 + 0*x + 1/135*x**7 + 1/54*x**4 - 7*x**2 + 1/90*x**5 + 0*x**3 + 0. Factor m(w).
2*w*(w - 1)**2*(7*w + 2)/9
Let o(c) be the first derivative of -c**7/560 + c**6/120 - c**5/80 + c**3/3 + 7. Let u(j) be the third derivative of o(j). Factor u(q).
-3*q*(q - 1)**2/2
Let f(p) be the second derivative of 1/10*p**5 - 2*p + 1/3*p**3 + 1/3*p**4 + 0 + 0*p**2. Factor f(k).
2*k*(k + 1)**2
Let u be -1 + 5 + (-14)/4. Let p(h) = h + 5. Let w be p(-5). Factor u - 1/2*b**2 + w*b.
-(b - 1)*(b + 1)/2
Let v(b) = -6*b**3 - 8*b**2 - 8*b - 6. Let p(u) = -u**3 - u**2 - u - 1. Let h(g) = -5*p(g) + v(g). Factor h(n).
-(n + 1)**3
Suppose -3*m + 0*m = -2*v + 4, 2*v - 6 = 2*m. What is x in 27/5*x**4 + 0 - 4/5*x + 8/5*x**m + 39/5*x**3 = 0?
-1, -2/3, 0, 2/9
Let g(z) be the first derivative of -z**5/5 + z**4/2 - z**2 + z - 20. Determine a, given that g(a) = 0.
-1, 1
What is t in -5/4*t**3 + 5/4*t - 5/4*t**2 + 5/4 = 0?
-1, 1
Factor 2/5*s**5 + 44/5*s**3 + 0 - 48/5*s**2 + 18/5*s - 16/5*s**4.
2*s*(s - 3)**2*(s - 1)**2/5
Let y(l) be the second derivative of -l**7/126 - 2*l**6/45 - l**5/10 - l**4/9 - l**3/18 + 7*l. Factor y(z).
-z*(z + 1)**4/3
Let i = -6 + 6. Find r such that 117*r**2 - 113*r**2 - 4*r + i*r = 0.
0, 1
Let l(f) be the second derivative of 1/12*f**4 + 1/2*f**5 - 3*f - 7/6*f**3 + f**2 + 0. Factor l(y).
(y + 1)*(2*y - 1)*(5*y - 2)
Suppose -2*d = c - 3 + 22, 2*d - 4*c + 14 = 0. Let m be 3 - ((-44)/d - 3). Factor 8/9*n**4 + 2/9*n**2 + 0*n + 0 - m*n**3.
2*n**2*(n - 1)*(4*n - 1)/9
Let z(v) = v**5 - v**4 - v**3 - v**2 + v - 1. Let q(f) = f**5 - 2*f**4 - 2*f**3 - 2*f**2 + 2*f - 2. Let b(g) = -q(g) + 2*z(g). Suppose b(h) = 0. Calculate h.
0
Let n(h) be the first derivative of 2*h**5/35 + 5*h**4/7 + 26*h**3/21 - 60*h**2/7 + 72*h/7 - 35. Solve n(j) = 0.
-6, 1
Let z(n) be the second derivative of -n**7/21 + 16*n**6/105 - 11*n**5/70 + n**4/21 - 9*n. Factor z(v).
-2*v**2*(v - 1)**2*(7*v - 2)/7
Let f(q) be the third derivative of q**6/240 + q**5/60 - q**4/12 - 2*q**3/3 + 18*q**2. Let f(l) = 0. Calculate l.
-2, 2
Let z(i) be the third derivative of i**6/360 - i**5/45 + i**4/18 + 28*i**2. Factor z(x).
x*(x - 2)**2/3
Let t(q) = q**5 + q**5 + 4*q**3 - q - 2*q**4 - 5*q**5. Let s(k) = -7*k**5 - 5*k**4 + 9*k**3 - 2*k. Let d(r) = -4*s(r) + 10*t(r). Factor d(m).
-2*m*(m - 1)**2*(m + 1)**2
Let i be 10/15 - (4/3)/2. Determine u so that 0*u**2 - 12/5*u**4 - 3/5*u**3 + 0 - 9/5*u**5 + i*u = 0.
-1, -1/3, 0
Suppose -4*w + 0*z - 5*z + 97 = 0, 3*w - 69 = -3*z. Let s = -16 + w. Determine o so that -2/5*o - 2/5*o**s + 0 = 0.
-1, 0
Let c(a) be the second derivative of -a**6/80 - 3*a**5/80 + a**3/8 + 3*a**2/16 + 8*a. Factor c(p).
-3*(p - 1)*(p + 1)**3/8
Let t(s) be the first derivative of 3*s**2 - s**3 - 10 - 3*s + 9 - 6*s**2. Find c such that t(c) = 0.
-1
Let z(q) be the third derivative of q**5/210 - q**4/21 + 4*q**3/21 - 6*q**2. Solve z(p) = 0.
2
Let f(r) be the third derivative of 0 + 1/140*r**7 + 0*r**5 - r**2 + 0*r**3 - 1/80*r**6 + 0*r**4 + 0*r. Solve f(a) = 0 for a.
0, 1
Let h(i) = i - 16. Let u be h(18). Suppose -3*d = -2*d. Factor 1/2*y - 1/2*y**u + d.
-y*(y - 1)/2
Let d(w) be the second derivative of -w**4 - 3*w**2 - 3/20*w**5 - 5/2*w**3 + 0 + 7*w. Factor d(t).
-3*(t + 1)**2*(t + 2)
Let n be -7*(77/245 + 3/(-5)). What is w in -1/7*w**3 + 3/7*w + 2/7 + 0*w**n = 0?
-1, 2
Let i(m) be the third derivative of -m**8/2880 - m**7/3780 - m**4/8 + m**2. Let o(b) be the second derivative of i(b). Let o(w) = 0. What is w?
-2/7, 0
Let y(u) = -u**4 - u**3 + u**2 - u - 1. Let i(d) = 5*d**5 - 2*d**4 + 7*d**3 - 5*d**2 + 5*d + 5. Let x(h) = -4*i(h) - 20*y(h). Factor x(g).
-4*g**3*(g - 1)*(5*g - 2)
Let d(m) be the first derivative of -m**4/16 + m**3/4 + 3*m**2/4 - 2*m - 61. Factor d(s).
-(s - 4)*(s - 1)*(s + 2)/4
Let p(j) be the second derivative of 9*j**5/20 - j**4/4 - 3*j**3/2 + 3*j**2/2 - 6*j. Factor p(w).
3*(w - 1)*(w + 1)*(3*w - 1)
Suppose -5*y = -0*y. Let -3*g**2 + 9*g**4 + 7*g - 7*g + y*g**4 - 12*g**3 + 6*g = 0. Calculate g.
-2/3, 0, 1
Factor 2/5*q - 2/5*q**2 + 4/5.
-2*(q - 2)*(q + 1)/5
Let g(b) be the second derivative of b**6/10 + 3*b**5/20 - 3*b**4/4 - b**3/2 + 3*b**2 + b. Factor g(v).
3*(v - 1)**2*(v + 1)*(v + 2)
Suppose -p = -3*a + 2 - 7, 0 = -p + 2*a + 5. Factor -5*t + 4*t**2 + p*t**3 + 14 