j**2 + 4*j**3 + 3*j**2 + t*j**2 + 2*j**4 - j**2.
2*j**2*(j + 1)**2
Let d(g) be the third derivative of -g**8/420 + 4*g**7/525 + 3*g**2. Factor d(v).
-4*v**4*(v - 2)/5
Let c(p) = p - 5. Let i be c(-8). Let k = -49/4 - i. Factor k*n**2 - 9/4*n + 3/2.
3*(n - 2)*(n - 1)/4
Let c(v) = v**4 - v**3 + v**2 - v - 1. Let y(g) = -23*g**4 + 18*g**3 - 2*g**2 - 2*g - 2. Let o(q) = -6*c(q) + 3*y(q). Factor o(h).
-3*h**2*(5*h - 2)**2
Let f be 2 + (-4)/6*6. Let d be 1*(-6 + 2)/f. Determine a so that -2*a + 3*a**4 + 2*a**3 + 0*a + d - 5*a**2 + a - a**3 = 0.
-1, 2/3, 1
Let z(s) be the third derivative of s**8/840 - s**7/105 + 2*s**6/75 - 2*s**5/75 - 7*s**2. Factor z(n).
2*n**2*(n - 2)**2*(n - 1)/5
Let q(k) be the second derivative of 5*k**4/12 + 5*k**3/3 + 5*k**2/2 + 14*k. Factor q(h).
5*(h + 1)**2
Let w(c) be the third derivative of 0 + 1/168*c**8 - 3/70*c**7 + 1/12*c**4 + 7/60*c**6 + 6*c**2 + 0*c**3 - 3/20*c**5 + 0*c. Factor w(h).
h*(h - 2)*(h - 1)**2*(2*h - 1)
Let r = -14003/36 - -389. Let f(l) be the second derivative of 1/6*l**2 + 0 - 1/18*l**3 - 3*l + 1/60*l**5 - r*l**4. Factor f(i).
(i - 1)**2*(i + 1)/3
Let m(g) be the third derivative of -g**7/8820 + g**6/1260 - 3*g**4/8 - 4*g**2. Let q(n) be the second derivative of m(n). Determine z so that q(z) = 0.
0, 2
Suppose 5 = -4*z + x + 14, 2*x - 6 = 0. Find s such that -4*s**4 + 4*s**2 - 2*s + 2*s**5 + s**3 + s**z - 2*s**3 = 0.
-1, 0, 1
Let h(n) be the first derivative of 3*n**5/10 - 5*n**4/6 - 2*n**3/3 - 4*n - 1. Let w(j) be the first derivative of h(j). Factor w(o).
2*o*(o - 2)*(3*o + 1)
Let p(w) be the third derivative of -w**9/7560 + w**8/3360 - w**4/8 - w**2. Let g(a) be the second derivative of p(a). Suppose g(u) = 0. Calculate u.
0, 1
Let o = -294 + 1183/4. Factor -1 + o*n**2 + 3*n.
(n + 2)*(7*n - 2)/4
Let l(i) be the first derivative of 3*i**4/4 - 9*i**2/2 + 6*i - 7. Factor l(v).
3*(v - 1)**2*(v + 2)
Factor 2/5*q**2 + 0 - 8/5*q.
2*q*(q - 4)/5
Suppose 256*h**3 - 4 - 49*h - 62*h - 192*h**2 + 159*h = 0. Calculate h.
1/4
Let c = 36 - 14. Let w = 24 - c. Factor -3/2*y + 3*y**w + 0 - 3/2*y**3.
-3*y*(y - 1)**2/2
Let j(i) be the second derivative of -i**7/14 + i**6/10 + 3*i**5/10 + 20*i. Let j(t) = 0. Calculate t.
-1, 0, 2
Let z = 7 + -4. Let v(i) = i**2 + i. Let k(l) = l**2 + 3*l. Let o(h) = z*k(h) - 5*v(h). Factor o(a).
-2*a*(a - 2)
Let h(j) be the first derivative of j**6/720 - j**5/120 + j**4/48 + 2*j**3 - 6. Let d(y) be the third derivative of h(y). Factor d(f).
(f - 1)**2/2
Solve -2/3 - 10/3*a - 25/6*a**2 = 0.
-2/5
Suppose -5 = 2*q - 3*i, i = -5*q - 8 + 21. Factor 4*c**2 + q*c - 7 - 2*c**2 + 0*c + 3.
2*(c - 1)*(c + 2)
Let s(p) be the third derivative of p**5/30 + 11*p**4/36 - 4*p**3/9 + 7*p**2. Let s(j) = 0. What is j?
-4, 1/3
Let m(t) be the third derivative of t**6/300 + 3*t**5/10 + 45*t**4/4 + 225*t**3 + 2*t**2 + 2*t. Determine c so that m(c) = 0.
-15
Let s(z) be the third derivative of z**6/900 + z**5/150 + z**3/2 + 5*z**2. Let p(u) be the first derivative of s(u). Find h such that p(h) = 0.
-2, 0
Find a, given that -436/3*a**2 - 48*a - 16/3 - 196/3*a**4 - 168*a**3 = 0.
-1, -2/7
Let h be (-4)/(-12) - 4/(-6). Let i be 10/25*h*15. Factor 2*v**2 + 2*v + 2*v**2 - i*v**3 + 0*v**2.
-2*v*(v - 1)*(3*v + 1)
Let w(x) be the third derivative of -x**2 + 0*x**5 + 0*x**3 + 0 + 0*x - 1/120*x**6 + 1/24*x**4. Suppose w(i) = 0. Calculate i.
-1, 0, 1
Let o(n) be the second derivative of n**8/63 + 4*n**7/63 + n**6/10 + 7*n**5/90 + n**4/36 + 3*n**2/2 + n. Let f(m) be the first derivative of o(m). Factor f(z).
2*z*(z + 1)*(2*z + 1)**3/3
Let d(w) be the first derivative of -w**3/12 - w**2/8 + 3*w/2 - 14. What is q in d(q) = 0?
-3, 2
Let d(g) be the first derivative of -g**8/7560 + g**7/1890 + g**6/540 - g**5/135 - g**4/27 - g**3/3 + 4. Let z(r) be the third derivative of d(r). Factor z(k).
-2*(k - 2)**2*(k + 1)**2/9
Let z(q) be the second derivative of -q**5/100 + q**4/60 + q**3/15 - 4*q. What is c in z(c) = 0?
-1, 0, 2
Let o be (-10)/(-2)*4/10. Factor -3*u**o - 4 + u**2 - 6*u + 4*u**2 - 4*u**2.
-2*(u + 1)*(u + 2)
Suppose 14 = 4*v - 2. Suppose -q + v + 1 = 0. What is d in -14*d**q + 0 + d - 57/2*d**4 + 3/2*d**2 - 14*d**3 = 0?
-1, -2/7, 0, 1/4
Let f be 32/6 - (-27)/((-567)/84). Factor 20/3*k**3 - f + 8/3*k**4 - 14*k**2 + 23/3*k.
(k + 4)*(2*k - 1)**3/3
Let d be 2 - ((1 - 0) + -3). Let i(q) be the second derivative of 0*q**2 + q + 0 - 1/24*q**d + 1/12*q**3. Factor i(l).
-l*(l - 1)/2
Let a(o) be the third derivative of -o**7/350 + o**6/100 - o**2. Factor a(d).
-3*d**3*(d - 2)/5
Find o such that -3/8*o**2 + 0 - 33/8*o**4 + 33/8*o**3 + 9/8*o**5 - 3/4*o = 0.
-1/3, 0, 1, 2
Let l = -46/5 - -382/35. What is c in -12/7*c**2 - l - 40/7*c = 0?
-3, -1/3
Solve -1/4 + 0*x + 1/4*x**2 = 0.
-1, 1
Let l(t) be the first derivative of 3*t**4/28 - 2*t**3/7 + 3*t**2/14 + 3. Factor l(d).
3*d*(d - 1)**2/7
Let w(f) be the third derivative of -f**6/140 + f**5/105 + f**4/12 + 2*f**3/21 - f**2. Factor w(x).
-2*(x - 2)*(x + 1)*(3*x + 1)/7
Let w be (-17)/(-12) + (-27)/36. Factor -10/3*u**3 - w*u - 4/3 + 16/3*u**2.
-2*(u - 1)**2*(5*u + 2)/3
Suppose 7*q - 2 = 6*q. Suppose 0 = q*g - 3*g. Determine u, given that 0*u + 2/5*u**2 + g = 0.
0
Let k(n) be the third derivative of -n**7/735 + 4*n**6/105 - 32*n**5/105 - 47*n**2. Factor k(t).
-2*t**2*(t - 8)**2/7
Let t(v) = 4*v**3 - 12*v - 16. Let f(w) = w**2 + w + 1. Suppose 11 = 4*u - 21. Let j(k) = u*f(k) + t(k). Determine a so that j(a) = 0.
-2, -1, 1
Let g(y) be the third derivative of 3/5*y**3 + y**2 + 0*y + 2/75*y**5 + 1/5*y**4 + 0. Solve g(w) = 0.
-3/2
Let l = 3 - 1. Solve i - i**2 + 1 - 3 + 1 - i**3 + l*i**2 = 0 for i.
-1, 1
Let d(j) be the second derivative of 3*j**5/100 - 3*j**4/10 + 6*j**3/5 - 12*j**2/5 - 3*j. Factor d(a).
3*(a - 2)**3/5
Let k(j) be the second derivative of j**5/80 - j**4/48 - j**3/24 + j**2/8 + 11*j. Let k(q) = 0. What is q?
-1, 1
Let x(s) = s**3 - 4*s**2 - 4*s - 6. Let b be x(5). Let v = 5/3 + b. Factor -2/3*j**5 + 4/3*j**2 + 4/3*j**3 - v*j**4 - 2/3*j - 2/3.
-2*(j - 1)**2*(j + 1)**3/3
Factor -16*d**2 - 9*d + 5*d**3 - 8 + 6*d**4 - 15*d - 7*d**3 - 6*d**2 + 2*d**5.
2*(d - 2)*(d + 1)**3*(d + 2)
Factor -1/4*l**2 - 1/2 - 3/4*l.
-(l + 1)*(l + 2)/4
Let w be (-67)/(-90) + 12/(-40). Factor -2/9 - 2/9*m**2 + w*m.
-2*(m - 1)**2/9
Let w = 11 + 4. Find y such that -3*y + 9*y + 4 - 9*y**2 + 14*y**3 - w*y**2 = 0.
-2/7, 1
Let q(b) be the third derivative of b**5/4 + 3*b**4/2 + 2*b**3 - 6*b**2. Factor q(y).
3*(y + 2)*(5*y + 2)
Let s(l) be the first derivative of 0*l**2 - l + 1/4*l**5 - 2/3*l**3 - 1 + 2/3*l**4. Let m(t) be the first derivative of s(t). Find f, given that m(f) = 0.
-2, 0, 2/5
Let d(x) = x**2 - 2. Let v be d(2). Let f(w) = -2*w**3 + 8*w**2 + 2*w - 6. Let z(u) = -u**4 - u**2 + 1. Let n(p) = v*z(p) + f(p). What is t in n(t) = 0?
-2, -1, 1
Let f = -5829/5 - -1170. Factor -9/5*a + 36/5*a**2 - 6/5 - f*a**3.
-3*(a - 1)**2*(7*a + 2)/5
Suppose -2*m - 16 = -6*m. Let k(c) be the second derivative of -1/15*c**3 - c + 0*c**2 + 0 - 1/30*c**m. What is p in k(p) = 0?
-1, 0
Let h = 743 - 2923/4. Let o(t) be the first derivative of 8*t - h*t**4 - 1 - 98/3*t**3 + 2*t**2. Solve o(y) = 0.
-2, -2/7, 2/7
Let h = 9/20 - 59/220. Factor 0 - 2/11*y - h*y**2.
-2*y*(y + 1)/11
Suppose 1/3*c + 4/3*c**2 - 2/3 - c**3 = 0. Calculate c.
-2/3, 1
Factor 1/5*p**2 + 6/5 - 7/5*p.
(p - 6)*(p - 1)/5
Let b(m) = m**3 + 5*m**2 - m - 2. Let n = -8 + 3. Let y be b(n). Solve 4/3*c**y + 0 + 0*c**2 + 0*c**4 - 2/3*c - 2/3*c**5 = 0 for c.
-1, 0, 1
Let s(t) be the first derivative of t**7/3780 - t**5/540 + t**3 - 2. Let n(w) be the third derivative of s(w). Solve n(u) = 0 for u.
-1, 0, 1
Let s(y) be the third derivative of y**7/840 + y**6/180 + y**5/120 - y**3 + y**2. Let o(i) be the first derivative of s(i). Determine p so that o(p) = 0.
-1, 0
Factor -2/9*n**3 - 8/9*n**2 + 0 - 8/9*n.
-2*n*(n + 2)**2/9
Let y = -271 - -4067/15. Solve -2/15*k**3 - 2/15*k**2 + 2/15*k + y*k**4 + 0 = 0 for k.
-1, 0, 1
Let z(x) be the third derivative of -x**5/390 + x**3/39 - 23*x**2. Find m such that z(m) = 0.
-1, 1
Let v = -6 + 9. Let r = 1 - -1. Determine q so that -9*q + 4 - 6*q**v - 5*q + 11*q**2 + 5*q**r = 0.
2/3, 1
Let u(o) be the second derivative of 1/165*o**6 - 1/33*o**4 + 1/11*o**2 + 0*o**5 + 0*o**3 + 4*o + 0. Factor u(q).
2*(q - 1)**2*(q + 1)**2/11
