nd derivative of 1/30*z**5 - 1/12*z**4 + 0 + 0*z**3 - z**2 - z. Let h(i) be the first derivative of p(i). Factor h(f).
2*f*(f - 1)
Let k(h) be the third derivative of -h**4/8 - h**3/6 - h**2. Let q be k(-1). Factor 0 + 2/5*f**4 + 0*f + 1/5*f**3 + 1/5*f**5 + 0*f**q.
f**3*(f + 1)**2/5
Let h(j) be the third derivative of j**6/420 - j**5/70 + j**4/42 + 54*j**2. Factor h(l).
2*l*(l - 2)*(l - 1)/7
Suppose 3*s - 4*m + 9 = -5, 5*m - 21 = 2*s. Solve 2*a**3 + 4*a**2 + 4*a + 0*a**2 - s*a = 0 for a.
-1, 0
Let c(y) be the second derivative of y**5/150 - y**3/15 + 7*y**2/2 + 6*y. Let g(n) be the first derivative of c(n). Factor g(d).
2*(d - 1)*(d + 1)/5
Let a(j) = 7*j**5 + 3*j**4 + 5*j**3 + 9. Let t(g) = -3*g**5 - g**4 - 2*g**3 - 4. Let o(x) = 4*a(x) + 9*t(x). Let o(s) = 0. What is s?
-2, -1, 0
Let j(l) = -l. Let z be j(1). Let h be (1 - 1)/((-1)/z). Factor 0*c**2 - 2*c**4 + 3/2*c**5 + 0*c + h + 1/2*c**3.
c**3*(c - 1)*(3*c - 1)/2
Let w(y) be the first derivative of -y**4/2 - 2*y**3 - 2*y**2 + 15. Suppose w(s) = 0. Calculate s.
-2, -1, 0
Let p be 16/(-14)*46*(-56)/96. Determine z so that 52/3*z**3 - 16/3 + p*z**4 - 80/3*z + 28/3*z**5 - 76/3*z**2 = 0.
-2, -1, -2/7, 1
Let l(j) be the third derivative of -j**8/90720 + j**5/60 - j**2. Let m(f) be the third derivative of l(f). Factor m(b).
-2*b**2/9
Factor -334*z**2 + 329*z**2 + 10*z + 2 - 2.
-5*z*(z - 2)
Suppose n + 7 = -1. Let j be 2*1 - 0/n. Solve 4*w**5 + 33*w**3 + 3 + 42*w**j + 27*w**4 - 9*w**5 - 81*w**3 - w**5 - 18*w = 0.
1/2, 1
Suppose 3 = c - j, -2 = -4*j + 2. Suppose -4*o = -c - 4. Factor 0*p - o*p**2 - 8*p**4 - 2*p**5 - 6*p**2 - 2*p - 12*p**3.
-2*p*(p + 1)**4
Let b(g) = g + 1. Let d be b(8). Factor -3*l**2 - 3*l + d - 9.
-3*l*(l + 1)
Factor -2*u**2 - 2*u - 2/3*u**3 - 2/3.
-2*(u + 1)**3/3
Solve -12/5*o**2 + 0 + 6/5*o + 6/5*o**3 = 0 for o.
0, 1
Let t(k) be the third derivative of k**8/6720 - k**6/1440 - k**3/3 + 5*k**2. Let s(h) be the first derivative of t(h). Suppose s(f) = 0. Calculate f.
-1, 0, 1
Let y(p) = -6*p**2 - 16*p - 16. Let l(g) = 1. Let k(w) = -8*l(w) - y(w). What is r in k(r) = 0?
-2, -2/3
Let p(b) = -2*b**3 - 9*b**2 - 2*b - 5. Let t be (-7)/21 - (-14)/(-3). Let f(k) = k**3 + 5*k**2 + k + 3. Let u(a) = t*f(a) - 3*p(a). What is d in u(d) = 0?
-1, 0
Let d(w) be the third derivative of -1/360*w**6 + 0*w**3 - 1/60*w**5 + 0*w - 1/36*w**4 + 0 + 9*w**2. Factor d(s).
-s*(s + 1)*(s + 2)/3
Factor -44/7*f**3 - 14641/7 - 1/7*f**4 - 726/7*f**2 - 5324/7*f.
-(f + 11)**4/7
Suppose 5*l = -5, -f + 5*f + 4 = -4*l. Factor -2/5*w**2 - 4/5*w + f.
-2*w*(w + 2)/5
Let p(c) = -5*c**2 + 5*c - 2. Let u(f) = 21*f**2 - 21*f + 8. Let i(y) = 22*p(y) + 6*u(y). Factor i(k).
4*(2*k - 1)**2
Let t(j) be the first derivative of j**6/69 + 2*j**5/115 - 3*j**4/46 - 2*j**3/69 + 2*j**2/23 + 2. Determine i so that t(i) = 0.
-2, -1, 0, 1
Factor 1 + 2 + 2*p - 3 + 2*p**2.
2*p*(p + 1)
Let w be (-4)/10 + (-2)/(-5). Let 2/5*g**5 - 2/5*g**3 + 0*g**2 + 0 + w*g + 0*g**4 = 0. Calculate g.
-1, 0, 1
Let m(u) be the third derivative of u**5/12 + 5*u**4/24 + 20*u**2. Factor m(t).
5*t*(t + 1)
Let n(g) be the first derivative of -7*g**4/20 + 2*g**3/15 + 7*g**2/10 - 2*g/5 - 4. Solve n(t) = 0.
-1, 2/7, 1
Let l be (-2)/((-4)/(-6)) + 5/1. Factor -2/9*n**3 + 4/9*n**l - 4/9 + 2/9*n.
-2*(n - 2)*(n - 1)*(n + 1)/9
Factor -3 - 3*j**3 + 3*j**4 + 6*j - 14*j**3 + 11*j**3.
3*(j - 1)**3*(j + 1)
Let q(d) be the first derivative of d**7/105 - d**6/60 - d**5/30 + d**4/12 - d**2 - 4. Let h(n) be the second derivative of q(n). Determine m so that h(m) = 0.
-1, 0, 1
Let i(k) be the first derivative of -k**4/10 - 2*k**3/15 + k**2/5 + 2*k/5 + 2. Factor i(h).
-2*(h - 1)*(h + 1)**2/5
Let v = 1156/15 + -77. Let j(y) be the first derivative of -v*y**3 + 0*y - 2 - 1/5*y**2. Suppose j(a) = 0. Calculate a.
-2, 0
Suppose 0 = 4*o - 2*o - 10. Suppose -2*x = -o*x. Let 2/5*j**2 + x + 2/5*j = 0. What is j?
-1, 0
Let h(q) be the third derivative of 0*q**5 + 0 + 1/120*q**6 - 1/210*q**7 + 0*q + 0*q**4 - 2*q**2 + 0*q**3. Find a, given that h(a) = 0.
0, 1
Solve 4*a**2 - 9*a**2 + 2 - 7 + 10*a = 0 for a.
1
Let t(d) = -d + 6. Let o be t(4). Suppose -8 = -2*k + 3*s, 2*k - 2*s = 4 + 4. Suppose z - z**k + 0*z**3 - z**3 + z**o + 0*z**4 = 0. What is z?
-1, 0, 1
Let c be (-2)/15 - (-68)/85. Factor 0*w - c*w**4 - 2/3*w**5 + 2/3*w**3 + 0 + 2/3*w**2.
-2*w**2*(w - 1)*(w + 1)**2/3
Let i(p) be the third derivative of p**7/105 - p**6/20 + p**5/15 + 22*p**2. Determine m so that i(m) = 0.
0, 1, 2
Suppose 17*h - 21*h = -8. Factor -p + 0 - 1/2*p**h.
-p*(p + 2)/2
Let o(v) = 7*v**5 + v**4 + 7*v**3 + 5. Let h(i) = 3*i**5 + 3*i**3 + 2. Let y(u) = 5*h(u) - 2*o(u). Factor y(j).
j**3*(j - 1)**2
Let p(u) be the third derivative of -u**8/2520 + 4*u**7/1575 + u**6/450 - 4*u**5/225 - u**4/180 + 4*u**3/45 + 11*u**2 - 2. What is i in p(i) = 0?
-1, 1, 4
Let w = -3 - -3. Factor w*l**2 - 2*l + 4*l**2 + 0*l**2 + 2*l**3 - 4.
2*(l - 1)*(l + 1)*(l + 2)
Let h(t) be the second derivative of -1/60*t**5 + 0*t**3 + t + 0*t**2 + 0*t**4 + 0*t**6 + 0 + 1/126*t**7. Factor h(l).
l**3*(l - 1)*(l + 1)/3
Let u(t) be the first derivative of t**3/6 - t**2/4 + 3. Factor u(c).
c*(c - 1)/2
Let t(r) be the first derivative of -25*r**6/24 - 17*r**5/2 - 53*r**4/2 - 116*r**3/3 - 26*r**2 - 8*r + 9. Determine p so that t(p) = 0.
-2, -2/5
Let w(q) = 11*q**2 - 162*q + 1119. Let x(z) = 12*z**2 - 164*z + 1118. Let s(f) = 7*w(f) - 6*x(f). Factor s(p).
5*(p - 15)**2
Let j = 3 + -1. Let g(t) be the third derivative of -1/12*t**4 + 1/20*t**5 + 0 + 0*t + 0*t**3 + t**j. Factor g(l).
l*(3*l - 2)
Let -l + 1/2*l**2 - 1/2*l**4 + 0 + l**3 = 0. Calculate l.
-1, 0, 1, 2
Solve 11*s**4 - 6*s**2 - 3*s**3 + 2 - 7*s**2 - 16*s**3 + 5*s + 14*s**5 = 0 for s.
-1, -2/7, 1/2, 1
Let s(q) = -q + 3. Let j be s(3). Suppose r + j*r - 3 = 0. Factor -3/2*x**2 + 9/2*x - 9/2 + 1/6*x**r.
(x - 3)**3/6
Factor -26/3*w**2 + 0 + 4/3*w + 40/3*w**3 - 6*w**4.
-2*w*(w - 1)**2*(9*w - 2)/3
Let n(s) be the first derivative of 2*s**3/33 + 4*s**2/11 - 10*s/11 - 32. Find b, given that n(b) = 0.
-5, 1
Let w(b) be the third derivative of b**7/13860 - b**5/660 + b**4/8 - b**2. Let i(v) be the second derivative of w(v). Factor i(f).
2*(f - 1)*(f + 1)/11
Suppose 1 = -3*h + 7. Suppose h*m - 3 = p - 2, 2*m - 4 = 0. Factor -4*i**4 - 5*i**3 - 2*i**5 + 0*i**3 + p*i**3.
-2*i**3*(i + 1)**2
Let t(a) be the third derivative of -a**8/56 + a**7/15 - 7*a**6/180 - 17*a**5/90 + 4*a**4/9 - 4*a**3/9 - 23*a**2. Solve t(y) = 0.
-1, 2/3, 1
Let u(g) be the third derivative of -g**7/945 + g**6/270 + g**5/270 - g**4/54 + 7*g**2. What is d in u(d) = 0?
-1, 0, 1, 2
Factor -8/5*p + 0 + 14/5*p**3 - 24/5*p**2.
2*p*(p - 2)*(7*p + 2)/5
Let k be (-85)/(-119)*3/5. Factor -3/7*b**5 + 0*b**2 + 6/7*b**3 - k*b + 0*b**4 + 0.
-3*b*(b - 1)**2*(b + 1)**2/7
Let c be (-3)/(-3) + (-65)/7. Let n = -8 - c. Factor 0 + n*f**2 - 2/7*f**3 + 0*f.
-2*f**2*(f - 1)/7
Let c(n) be the second derivative of n**5/90 - n**4/18 + 4*n**2/9 + 2*n. Let c(d) = 0. What is d?
-1, 2
Suppose -4*a + 3*a = -4. Let t be a/6*3/4. Let 0 - 1/2*n + t*n**3 + 7/4*n**4 - 7/4*n**2 = 0. What is n?
-1, -2/7, 0, 1
Let w(r) be the third derivative of -r**6/540 + r**4/108 + 5*r**2. Factor w(x).
-2*x*(x - 1)*(x + 1)/9
Factor 0*d + d**2 + 0 + 1/2*d**3.
d**2*(d + 2)/2
Let z(x) = 7*x**4 - x**3 - x**2 - 5*x. Suppose 0*f - 12 = 2*f. Let y(s) = -6*s**4 + s**3 + s**2 + 4*s. Let i(m) = f*y(m) - 5*z(m). Factor i(a).
a*(a - 1)**2*(a + 1)
Factor -1/5*t**2 + 1/5*t**3 - t - 3/5.
(t - 3)*(t + 1)**2/5
Suppose 3*y = 2*y. Let l(w) be the third derivative of 1/120*w**5 + 0*w + y + 1/48*w**4 - 3*w**2 - 1/6*w**3. Factor l(q).
(q - 1)*(q + 2)/2
Let m be (1/27)/(85/510). Let 0*t - m*t**3 + 0 - 2/9*t**2 = 0. What is t?
-1, 0
Let f(a) be the third derivative of -a**9/60480 - a**8/20160 + a**5/20 - 3*a**2. Let o(h) be the third derivative of f(h). Factor o(s).
-s**2*(s + 1)
Let n = 29 - 24. Suppose 6*o - n*o = 3. Determine t so that 1/4*t**5 + 4*t**o - 7/4*t**4 + 4 - 2*t**2 - 4*t = 0.
-1, 2
Factor -84/5 + 88/5*r - 4/5*r**2.
-4*(r - 21)*(r - 1)/5
Let i = 24 - 21. Let o(j) be the first derivative of -1/2*j**2 - j + 1/4*j**4 + 1/3*j**i + 1. Factor o(l).
(l - 1)*(l + 1)**2
Suppose 4*j - 2*v = -20, -5*j - 26 = -0*j - 3*v. Let a = -3 - j. Solve a + 2*i**3 - 6*i**3 - 3 + 4*i + 2*i**4 = 0.
-1, 1
Let s be (-1)/(((-140)/(