7*x + 12*x**2 - 92/7*x**3.
4*(x - 1)**3*(8*x + 1)/7
Let j(m) be the first derivative of 5/9*m**3 - 1/3*m**4 + 0*m - 1/3*m**2 - 1 + 1/15*m**5. Find o such that j(o) = 0.
0, 1, 2
Let t(s) = s**2 - 10*s - 5. Let d be t(11). Find k, given that -15*k**5 + d*k**4 - 4*k + 12*k**5 - 6*k**2 + 7*k = 0.
-1, 0, 1
Let l(r) = -r**2 + 6*r + 4. Let u be l(6). Solve 2*h**5 - 2*h + 6*h**u + 2*h - 2*h**4 + 2*h**3 = 0.
-1, 0
Let y(u) = 7*u - 14. Let d be y(8). Let n = d - 83/2. Factor 1/2*o**5 - 1/2*o**3 + 0 + 0*o + n*o**2 - 1/2*o**4.
o**2*(o - 1)**2*(o + 1)/2
Let i = 1811 + -12653/7. Solve -i*l + 24/7*l**3 - 10/7*l**2 + 18/7*l**4 - 8/7 = 0 for l.
-1, -2/3, 1
Let n(x) be the third derivative of x**7/560 - 3*x**6/320 - x**5/40 - 24*x**2. Determine g so that n(g) = 0.
-1, 0, 4
Let r(c) be the first derivative of c**8/840 - c**7/84 + c**6/30 + c**5/15 - 2*c**4/3 - 5*c**3/3 + 3. Let i(z) be the third derivative of r(z). Solve i(o) = 0.
-1, 2
Let b(w) be the second derivative of -2*w**6/135 - 2*w**5/45 - w**4/27 - 23*w. Solve b(r) = 0.
-1, 0
Suppose 2*j + 6 = i, 2*i + 2 = -j + 14. Find p, given that -p**2 - 1 + p - 5*p + i*p = 0.
1
Let q(j) = -j**3 + 29*j**2 + 31*j - 28. Let k be q(30). Solve 1 + 7/2*f + 3/2*f**k = 0 for f.
-2, -1/3
Let z(r) = -9*r**2 - 18*r + 3. Let q(k) = k**2 + k - 1. Let y(f) = 12*q(f) + z(f). Factor y(g).
3*(g - 3)*(g + 1)
Factor 6*t**3 - 12*t**5 + 24*t**2 - 4*t - 29*t**3 - 25*t**3 + 40*t**4.
-4*t*(t - 1)**3*(3*t - 1)
Factor -4*i**3 + 20*i + 0*i**2 + 2*i**3 - i**2 - 17*i**2.
-2*i*(i - 1)*(i + 10)
Let p = 16 - 19. Let a(q) = -2*q**3 + 6*q**2 + 2*q + 2. Let f(t) = -t**3 + 5*t**2 + t + 1. Let d(z) = p*a(z) + 4*f(z). Find g such that d(g) = 0.
-1, 1
Let r = 5 - 2. Let h(b) be the second derivative of -1/6*b**r - 2*b + 0 - 1/4*b**2 - 1/24*b**4. Determine d, given that h(d) = 0.
-1
Factor m**4 - 2*m**2 + 7*m**2 - 3*m**3 - 6*m**2 + 3*m**2.
m**2*(m - 2)*(m - 1)
Let c(r) be the first derivative of r**4/5 - 16*r**3/15 + 6*r**2/5 - 13. Factor c(i).
4*i*(i - 3)*(i - 1)/5
Let a(r) be the first derivative of -1/24*r**6 + 1/20*r**5 + 0*r**2 - 3 - 1/12*r**3 + 0*r + 1/16*r**4. Factor a(w).
-w**2*(w - 1)**2*(w + 1)/4
Let g = 10 - 5. Let f = g + -2. Factor 0*w**f + 0*w + 4/7*w**2 - 2/7*w**4 - 2/7.
-2*(w - 1)**2*(w + 1)**2/7
Let o(n) be the third derivative of -n**5/12 - 5*n**4/24 - 14*n**2. What is k in o(k) = 0?
-1, 0
Let p(o) = -2*o**3 - 5*o**2. Let h be (-13)/2 - 6/(-12). Let u = h + 3. Let q(j) = j**3 + 3*j**2. Let c(t) = u*p(t) - 5*q(t). Determine n, given that c(n) = 0.
0
Let m(s) be the first derivative of -s**4/4 + s**3/3 - 1. Let c(j) = j**4 + 4*j**3 - 3*j**2. Suppose -3*z - 1 = -2*z. Let a(r) = z*c(r) - 3*m(r). Factor a(n).
-n**3*(n + 1)
Suppose -3*z - c = 18, -c - 6 = c. Let o be ((-4)/70)/(1/z). Factor 6/7*h**2 + 2/7 + 6/7*h + o*h**3.
2*(h + 1)**3/7
Let u(w) be the third derivative of -w**8/26880 - w**7/2240 - w**6/480 + w**5/60 - 5*w**2. Let f(b) be the third derivative of u(b). Factor f(k).
-3*(k + 1)*(k + 2)/4
Let s(f) be the second derivative of -f**8/3360 - f**4/12 - f. Let q(i) be the third derivative of s(i). What is x in q(x) = 0?
0
Let t(s) be the third derivative of -s**6/150 + s**4/10 + 4*s**3/15 - 7*s**2. Factor t(o).
-4*(o - 2)*(o + 1)**2/5
Suppose 0 = 3*j - 5*j. Suppose r + j*r = 0. Factor 3*b**4 + 6*b**3 + r*b**3 - 5*b**4 - 8*b + 0*b**4.
-2*b*(b - 2)**2*(b + 1)
Suppose 0*p + p = 0. Let l(d) be the third derivative of 0*d + 1/9*d**3 - 1/90*d**5 + d**2 + p*d**4 + 0. Suppose l(u) = 0. What is u?
-1, 1
Let d be (-1*1/2)/(108/(-24)). Let c(v) be the third derivative of -d*v**3 + 1/90*v**5 + 0*v**4 + 0 - 2*v**2 + 0*v. Factor c(a).
2*(a - 1)*(a + 1)/3
Let s(p) be the second derivative of -p**7/14 + p**6/10 + 9*p. Factor s(x).
-3*x**4*(x - 1)
Let w(u) be the first derivative of -u**4 + 4*u**3 - 6*u**2 + 4*u + 2. Solve w(g) = 0.
1
Let v(p) be the third derivative of 49*p**6/720 + 28*p**5/45 + 29*p**4/36 + 4*p**3/9 + 6*p**2. Determine m so that v(m) = 0.
-4, -2/7
Suppose -3/4*z**2 + 1/6*z + 0 = 0. Calculate z.
0, 2/9
Let a be ((-30)/(-9) - 3)*-6. Let g be 0/1 - a/3. Solve g*d**4 - 4/3*d**3 + 0 + 2/3*d**2 + 0*d = 0 for d.
0, 1
Let j(l) be the third derivative of -l**8/168 - l**7/105 + l**6/60 + l**5/30 + 16*l**2. Factor j(v).
-2*v**2*(v - 1)*(v + 1)**2
Let b = 17/22 + -3/11. Factor -1/2 + b*u**2 + 1/2*u**3 - 1/2*u.
(u - 1)*(u + 1)**2/2
Determine h, given that -32*h - 5 - 13*h - 1 - 84*h**2 = 0.
-2/7, -1/4
Factor -2/15*a**2 + 8/5*a - 24/5.
-2*(a - 6)**2/15
Let f(w) be the third derivative of 1/200*w**6 - 1/10*w**3 + 0 + 0*w + 1/100*w**5 - 5*w**2 - 1/40*w**4. Factor f(k).
3*(k - 1)*(k + 1)**2/5
Let u(b) = 2*b**3 + 11*b**2 - 7*b - 6. Let l be u(-6). Determine j, given that -2/5*j**3 + 0*j + l - 2/5*j**2 = 0.
-1, 0
Let a(y) = -2*y + 10. Let i be a(4). Determine d, given that 0 - 6*d**3 + 6*d**5 - 3/2*d**i + 0*d + 3/2*d**4 = 0.
-1, -1/4, 0, 1
Let 18 + 24*q + 1/2*q**3 + 13/2*q**2 = 0. What is q?
-6, -1
Let t(b) be the third derivative of -b**5/12 + 5*b**4/6 + 10*b**3 + 48*b**2. Suppose t(z) = 0. Calculate z.
-2, 6
Let z(k) be the third derivative of 0*k + 4/3*k**3 + 4*k**2 - 1/60*k**6 - 1/10*k**5 + 0 + 0*k**4. Factor z(q).
-2*(q - 1)*(q + 2)**2
Let a be ((-4)/(-16))/(1/8). Find g, given that -2/9*g**3 + 0 + 2/9*g + 0*g**a = 0.
-1, 0, 1
Let n(z) be the second derivative of z**6/15 - z**5/5 + z**4/6 - 17*z. Factor n(b).
2*b**2*(b - 1)**2
Let y(x) = -4*x + 21. Let v be y(5). Let v + 3/2*b - 5/2*b**2 = 0. Calculate b.
-2/5, 1
Factor 2/15*j**3 - 2/5*j**2 + 0 + 4/15*j.
2*j*(j - 2)*(j - 1)/15
Let c(i) be the first derivative of i**3/3 - i - 10. Determine q so that c(q) = 0.
-1, 1
Let i(m) be the first derivative of -2*m**3 - m**2 - 3. Solve i(j) = 0.
-1/3, 0
Let h(f) = 21*f**2 + 4*f + 3. Let q be h(-1). Let i be (q/(-15) + 1)/(-1). Factor -i + 0*s + 1/3*s**2.
(s - 1)*(s + 1)/3
Let s = -2 - -5. Suppose 3*u = -s*i + 8 + 7, -u - 5*i = 15. Find m such that -2*m**2 + u - 10 - 2*m**3 = 0.
-1, 0
Factor -1/4*o**3 - o + o**2 + 0.
-o*(o - 2)**2/4
Let f(l) be the third derivative of l**7/630 + l**6/90 - l**5/10 + l**4/8 + 4*l**2. Let k(h) be the second derivative of f(h). Determine a so that k(a) = 0.
-3, 1
Let j(q) be the second derivative of -q**6/60 - q**5/20 + q**3/6 + q**2/4 + 8*q. Factor j(v).
-(v - 1)*(v + 1)**3/2
Let c(g) = -4*g**4 + 6*g**3 + 4*g**2 - 6*g - 2. Let p(m) = -m**3 + m - 1. Let r(x) = c(x) - 2*p(x). Suppose r(f) = 0. Calculate f.
-1, 0, 1, 2
Suppose u - 13 = q - 4*u, 4 = -q + 2*u. Find x such that -42*x - 3*x**5 - 3*x**q + 42*x - 9*x**3 - 9*x**4 = 0.
-1, 0
Let l be 8/16 + (-6)/(-4). Factor 5/2*p - 1 + 1/2*p**3 - l*p**2.
(p - 2)*(p - 1)**2/2
Let u(b) be the second derivative of b**5/40 + b**4/4 + 3*b**3/4 - 4*b. Factor u(a).
a*(a + 3)**2/2
Let y be (-2)/4*(-90)/(-48) + 1. Let a(f) be the first derivative of 3 - 1/12*f**3 + 1/4*f - y*f**4 + 1/8*f**2. Find w such that a(w) = 0.
-1, 1
Let r(z) be the third derivative of -z**5/20 - 3*z**4/10 - 2*z**3/5 + 22*z**2. Let r(m) = 0. Calculate m.
-2, -2/5
Let n(b) be the second derivative of 0*b**3 + 0 - 3/2*b**2 + 1/4*b**4 + 2*b. What is h in n(h) = 0?
-1, 1
Let m be 1 - 1*(-3 + -2). Factor 4*x**2 + 0*x**3 + x**4 + m*x**3 + x + x**4 + 2*x**4 + x**5.
x*(x + 1)**4
Let r(l) be the second derivative of l**7/2 + 8*l**6/5 - 9*l**5/20 - 4*l**4 - 2*l**3 - 2*l. Find f such that r(f) = 0.
-2, -1, -2/7, 0, 1
Let k(z) be the first derivative of -z**7/70 - z**6/20 + 3*z**5/20 + z**4/2 - 2*z**3 - 3*z**2 - 1. Let t(u) be the second derivative of k(u). Factor t(b).
-3*(b - 1)**2*(b + 2)**2
Let q(x) be the second derivative of x**6/100 + x**5/150 - x**3/3 - x. Let m(v) be the second derivative of q(v). Find w, given that m(w) = 0.
-2/9, 0
Suppose 8 + 8 = 2*f. Let v be (-1)/(-3 + (-8)/(-3)). Let -7*s + 21*s**2 - 2 - f*s - v - 1 = 0. Calculate s.
-2/7, 1
Let m(k) be the third derivative of -k**6/1440 - k**5/240 - k**3/3 - 5*k**2. Let r(p) be the first derivative of m(p). Factor r(y).
-y*(y + 2)/4
Suppose 34 - 69 = -7*c. Factor 0*q**4 - 1/5*q + 0 - 1/5*q**c + 2/5*q**3 + 0*q**2.
-q*(q - 1)**2*(q + 1)**2/5
Let w(k) = 11*k**3 - 12*k**2 + k - 5. Let t(x) = -6*x**3 + 6*x**2 + 3. Let b(y) = 5*t(y) + 3*w(y). Suppose b(d) = 0. Calculate d.
0, 1
Let f = 100/7 - 199/14. Let m(t) be the second derivative of 0*t**3 - 1/5*t**6 + 3*t + 0 + 0*