- 1)/7
Let m(t) be the second derivative of 1/10*t**5 + 0 + 0*t**2 + 1/6*t**4 - t + 0*t**3. Factor m(f).
2*f**2*(f + 1)
Let l(o) be the third derivative of 1/60*o**6 - 2/5*o**5 + 0 + 4*o**4 + 0*o - 64/3*o**3 - 3*o**2. Factor l(r).
2*(r - 4)**3
Let o(g) = -5*g**2 - 18*g - 117. Let p(f) = f**2 - f - 1. Let j(b) = o(b) + 4*p(b). Factor j(u).
-(u + 11)**2
Suppose 2*i = i + 5*p + 28, -3*i + 3*p = -24. Let q be 3 + -2 + (-1)/2. Solve -q*z**i + 0 + 0*z - z**2 = 0 for z.
-2, 0
Let p(v) be the third derivative of -8*v**7/1575 + v**6/45 - v**5/25 + 7*v**4/180 - v**3/45 - 6*v**2. Factor p(t).
-2*(t - 1)*(2*t - 1)**3/15
Let b(h) be the second derivative of -h**7/168 - h**6/60 + 3*h**5/80 + 8*h. Let b(y) = 0. What is y?
-3, 0, 1
Let b be 8/3 - 4/6. Solve 11 - 11 + 0*w**b + w**2 = 0 for w.
0
Let m(i) be the third derivative of i**6/540 + i**5/90 + i**4/36 + i**3/27 + 12*i**2. Factor m(v).
2*(v + 1)**3/9
Let d(q) be the third derivative of 1/96*q**6 + 4*q**2 - 1/30*q**5 - 1/24*q**4 + 0*q + 0*q**3 + 0. Determine a so that d(a) = 0.
-2/5, 0, 2
Let f(j) be the second derivative of -j**9/90720 - j**8/40320 + j**7/7560 - j**4/3 + 6*j. Let s(l) be the third derivative of f(l). Solve s(q) = 0 for q.
-2, 0, 1
Let t(n) be the first derivative of -n**7/84 + n**6/60 - 2*n + 1. Let z(u) be the first derivative of t(u). Factor z(h).
-h**4*(h - 1)/2
Factor 32/3*x**2 + 20*x**3 + 16/9*x + 100/9*x**4 + 0.
4*x*(x + 1)*(5*x + 2)**2/9
Let i(w) = 6*w**3 - 2*w**2 + 2*w - 1. Let p be i(1). Determine s so that 3*s**4 - 4*s**3 - p*s**4 + 3*s**2 + s**2 + 2*s**3 = 0.
-2, 0, 1
Let r(z) be the third derivative of 0*z**6 + 0*z**3 + 0 + 0*z + 0*z**4 - 6*z**2 + 1/60*z**5 - 1/210*z**7. Factor r(j).
-j**2*(j - 1)*(j + 1)
Let q(v) be the second derivative of -v**4/24 + 3*v**3/2 - 81*v**2/4 + 45*v. Factor q(t).
-(t - 9)**2/2
Suppose -7 - 7 = -7*t. Factor -1/3*a**5 + 0 + 1/3*a**4 - 1/3*a**t + 0*a + 1/3*a**3.
-a**2*(a - 1)**2*(a + 1)/3
Suppose 5*m - 127 = -3*d, -2*m + 4*d = 2 - 32. Let x = -21 + m. Factor 0 + 2/3*w + 2/3*w**x.
2*w*(w + 1)/3
Suppose 0 = -3*d + 3*d + 3*d. Suppose d + 2/13*r**2 + 0*r = 0. Calculate r.
0
Let p(c) be the third derivative of 0*c**3 - 1/525*c**7 + 0*c**4 - 1/840*c**8 + 0*c + 0*c**5 + 0 + 0*c**6 + 5*c**2. Factor p(h).
-2*h**4*(h + 1)/5
Let u(p) = p + 2. Let v be u(3). Suppose -6 = -v*m + 4. Factor -3*a**2 - 5*a**m + 10*a - 5 + 2*a**3 + 1.
2*(a - 2)*(a - 1)**2
Suppose 5 - 11 = -3*d. Suppose 2/3*l**3 + d*l**2 + 2/3 + 2*l = 0. What is l?
-1
Let h(s) = 2 + 2 - 3 + 0. Let k(r) = r**2 + 2*r - 2. Let i(g) = -6*h(g) - 2*k(g). Factor i(v).
-2*(v + 1)**2
Let u(w) be the second derivative of -w**6/120 - w**5/20 + 3*w**4/8 - 2*w**3/3 - 2*w. Let a(d) be the second derivative of u(d). Find r such that a(r) = 0.
-3, 1
Suppose -3*a = 1 - 4. Suppose -v = -3 + a. What is p in 0 + 0*p**3 + 1/5*p - 1/5*p**5 + 2/5*p**4 - 2/5*p**v = 0?
-1, 0, 1
Let b(z) be the first derivative of 1/5*z**2 + 2/15*z**3 - 2/5*z - 1/10*z**4 - 4. Factor b(u).
-2*(u - 1)**2*(u + 1)/5
Let v be 1/(-3) - (-25)/(-15). Let f be (2/(-6))/(v/4). Factor 2/3 - 2/3*i**5 - 2/3*i - 4/3*i**2 + 4/3*i**3 + f*i**4.
-2*(i - 1)**3*(i + 1)**2/3
Suppose 4/9*q + 2/9 - 4/9*q**3 + 0*q**2 - 2/9*q**4 = 0. What is q?
-1, 1
Suppose -5*o + 5*y = 40, 5*o + y = -14 + 4. Let r(f) = f**2 + f - 4. Let z be r(o). Factor 1/3*l**4 + 4/3*l**3 + z*l**2 + 4/3*l + 1/3.
(l + 1)**4/3
Let n(d) = -28*d**4 + 20*d**3 - 56*d**2 + 40*d + 24. Let g(v) = v**4 + v**2 - v - 1. Let r(x) = 24*g(x) + n(x). Find j such that r(j) = 0.
0, 1, 2
Let d(b) be the first derivative of -b**5/10 + b**4/8 + b**3/6 - b**2/4 - 3. Factor d(l).
-l*(l - 1)**2*(l + 1)/2
Let p be (21 + -15)*2/54. Suppose p*l**2 - 2/3*l + 4/9 = 0. What is l?
1, 2
Let -26*t**2 + 30*t**4 - 12*t**3 - 13*t - 38*t**2 + 28*t**5 + 34*t**4 - 3*t = 0. Calculate t.
-2, -1, -2/7, 0, 1
Let w(h) be the second derivative of -2*h**7/21 - 8*h**6/15 - 4*h**5/5 + 2*h**4/3 + 10*h**3/3 + 4*h**2 + 25*h. Factor w(s).
-4*(s - 1)*(s + 1)**3*(s + 2)
Let o(w) = w**4 - 2*w**3 - 3*w. Let m(q) = -2*q**4 + 2*q**3 + 4*q. Suppose -i = -3, -k - 5*i = 3*k - 27. Let l(d) = k*m(d) + 4*o(d). Let l(z) = 0. Calculate z.
-1, 0
Let d be (-5 - (-332)/68) + (-10)/(-85). Let 0*a**2 - 2/15*a**3 + d + 2/15*a**4 + 0*a = 0. What is a?
0, 1
Let x(b) be the first derivative of 3*b**4/14 - 2*b**3/21 + 2*b - 3. Let j(i) be the first derivative of x(i). Factor j(m).
2*m*(9*m - 2)/7
Let u(g) = g**3 - 6*g**2 - 16*g + 2. Let r be u(8). Find z such that 1/3*z**3 + z**r + 1/3 + z = 0.
-1
Suppose 0 = -s + t + 3, 5*s = 3*t - 1 + 10. Let o = 19/3 - 23/6. Suppose -2*l**4 - 1/2*l**2 - o*l**3 + s*l + 0 = 0. Calculate l.
-1, -1/4, 0
Let v = -1/56 - -23/840. Let r(i) be the second derivative of 0 - 1/21*i**3 + i - v*i**6 + 0*i**2 + 1/70*i**5 + 1/42*i**4. Factor r(o).
-2*o*(o - 1)**2*(o + 1)/7
Let p(w) be the second derivative of -5*w**4/12 + 10*w**3/3 - 10*w**2 + 5*w. Let p(a) = 0. What is a?
2
Let l(h) be the first derivative of 2*h**3/27 + 7*h**2/9 - 16*h/9 - 55. Find t such that l(t) = 0.
-8, 1
Let c(k) be the third derivative of 0*k**3 - 1/12*k**4 - 2*k**2 + 0*k - 1/30*k**5 + 0. Factor c(s).
-2*s*(s + 1)
Let n(r) be the second derivative of -2*r**6/3 - 12*r**5/5 + r**4/3 + 8*r**3 + 8*r**2 - 9*r. Solve n(m) = 0.
-2, -1, -2/5, 1
Let f be ((3/2)/(1 - 4))/(-1). Determine d so that -f*d + 0 - 1/2*d**3 - d**2 = 0.
-1, 0
Let g(p) = -p**2 + 22*p + 3. Let f be g(22). Factor -2/7*i**f + 2/7*i**5 - 2/7*i**2 + 2/7*i**4 + 0 + 0*i.
2*i**2*(i - 1)*(i + 1)**2/7
Let z = -120 + 122. Find j such that -14/5*j**z + 0 - 4/5*j = 0.
-2/7, 0
Let m = -25 + 83/3. Solve -m*x**2 + 0*x + 0*x**3 + 2/3*x**5 + 0 + 2*x**4 = 0.
-2, 0, 1
Suppose -2*x = -h - x + 1, 5 = x. Let g(w) be the first derivative of 0*w**4 + 0*w - w**2 + 1/3*w**h + 4/5*w**5 - 4/3*w**3 + 1. Factor g(z).
2*z*(z - 1)*(z + 1)**3
Let q be (-45)/(-18)*(3 + (-27)/15). Find m such that 1/4*m**2 - 1/2*m**q + 0 + 1/2*m - 1/4*m**4 = 0.
-2, -1, 0, 1
Let z(h) be the second derivative of h**6/180 - h**5/40 + h**4/24 - h**3/36 + 10*h. Solve z(i) = 0.
0, 1
Let a be 10/6*5*52/325. Find z such that 4/3*z**2 + 1/3*z + 0 - a*z**4 - 1/3*z**3 = 0.
-1, -1/4, 0, 1
Suppose -5*m - 5*b + 10 = 0, 0 = -2*m - 7*b + 2*b - 2. Let h = m + -2. Factor -1 - 4*v**3 + 0*v**5 + 2*v**5 + h*v + 1.
2*v*(v - 1)**2*(v + 1)**2
Let v be (6/8)/(6/24). Suppose 1 + 0*b**2 - v - b**2 - 5*b**2 + 2*b**3 + 6*b = 0. Calculate b.
1
Let h(j) be the third derivative of 0*j**4 - 3*j**2 + 0*j + 0 + 0*j**3 + 1/315*j**7 + 0*j**6 - 1/90*j**5. Factor h(v).
2*v**2*(v - 1)*(v + 1)/3
Solve 14*l**3 - 5/2*l**4 - 24*l**2 + 8 + 8*l = 0.
-2/5, 2
Let a(m) be the third derivative of -m**6/840 + m**5/140 - 2*m**3/21 - 6*m**2. Factor a(v).
-(v - 2)**2*(v + 1)/7
Let j(k) = -k - 1. Suppose -9 = 4*t + 3. Let z be j(t). Factor 18*r**3 + 6 - z*r + 8*r**5 - 6 - 22*r**4 - 2*r**2.
2*r*(r - 1)**3*(4*r + 1)
Let a(o) be the second derivative of 7*o**5/40 - 5*o**4/16 - o**3/2 + 5*o**2/2 + o. Let x(s) be the first derivative of a(s). Factor x(n).
3*(n - 1)*(7*n + 2)/2
Let h = 25/27 + -7/27. Factor -2/3*q + 0 - h*q**2.
-2*q*(q + 1)/3
Let h = 18 + -539/30. Let d(u) be the third derivative of -1/3*u**3 + 3*u**2 + 0 - 1/6*u**4 + 0*u - h*u**5. Factor d(m).
-2*(m + 1)**2
Let f = 21 + -29. Let x be (1/6)/(f/(-16)). Factor 1/3*z**2 + x + 2/3*z.
(z + 1)**2/3
Solve -27*h**2 + 13*h**2 - 22*h + 15*h**2 + 121 = 0 for h.
11
Factor 0 + 1/3*y**3 - 1/3*y + 0*y**2.
y*(y - 1)*(y + 1)/3
Let a(p) be the first derivative of p**5/40 + p**4/16 + 2*p**2 - 6. Let d(h) be the second derivative of a(h). Suppose d(g) = 0. What is g?
-1, 0
Let o(n) = -n + 6. Let p be o(6). Let m be ((-31)/(-93))/(1/15). Factor -1/2*y + p*y**4 - 1/2*y**m + y**3 + 0 + 0*y**2.
-y*(y - 1)**2*(y + 1)**2/2
Let f(g) be the third derivative of -g**6/30 - g**5/15 + g**4/6 + 2*g**3/3 - g**2 + 2. Determine j so that f(j) = 0.
-1, 1
Determine y so that 18*y**4 - 24*y**3 + 0*y - 12 - 19*y**2 + 13*y**2 + 27*y - 3*y**5 = 0.
-1, 1, 4
Let x(k) = -k - 21. Let d be x(-21). Let l(o) be the first derivative of -3/4*o**4 + d*o**2 - 5/18*o**6 + 4/5*o**5 - 3 + 0*o + 2/9*o**3. Factor l(j).
-j**2*(j - 1)**2*(5*j - 2)/3
Suppose -d = -p + 3*d + 12, -2*p + 45 = -d. Let l be 14/8 + 6/p. Factor -3*s + s**3 + s**2 + 2*s - 2*s**3 - 3*s**l.
-s*(s + 1)**2
Suppose 0 = -0*g + g - 10. Find z