(q) = -4*q**2 + 12*q + 4. Suppose w + 3*c - 9 = 0, -2*c - 7 - 3 = -2*w. Let j be 2/((4/w)/(-2)). Let b(v) = j*h(v) + d(v). Factor b(z).
-2*(z - 1)*(2*z - 1)
Let p(f) = f. Let y(d) = -d**2 - d. Suppose 1 = -v + 2*v. Let m(h) = v*p(h) + y(h). Determine k so that m(k) = 0.
0
Let v(q) be the third derivative of -q**8/840 - q**7/210 + q**5/30 + q**4/12 - q**3/3 + 7*q**2. Let b(c) be the first derivative of v(c). Factor b(u).
-2*(u - 1)*(u + 1)**3
Let v(f) = f**3 + 2*f. Let k(a) = -4*a**3 - 10*a. Let g(t) = -6*k(t) - 28*v(t). Suppose g(l) = 0. Calculate l.
-1, 0, 1
Let t(j) = -j**5 + j**3 + j**2 - j + 1. Let k(p) = -8*p**5 + p**4 + 8*p**3 + 6*p**2 - 7*p + 7. Let z(s) = -2*k(s) + 14*t(s). Let z(f) = 0. Calculate f.
-1, 0, 1
Let d(k) be the first derivative of 0*k + 2/3*k**3 + 0*k**2 - 8/5*k**5 + 1 + 3/2*k**4. Suppose d(t) = 0. Calculate t.
-1/4, 0, 1
Let q(s) be the first derivative of -s**5/5 + 2*s**3/3 - s - 7. What is i in q(i) = 0?
-1, 1
Let q be 0 + ((-39)/(-6) - 6). Find x such that 0*x**4 - 1/4*x**5 + 1/2 - 3/4*x + x**3 - q*x**2 = 0.
-2, -1, 1
Let y(r) be the first derivative of r**5/15 - r**4/12 - 2*r**3/9 - 1. Factor y(n).
n**2*(n - 2)*(n + 1)/3
Let s(n) be the third derivative of 4*n**2 + 0*n**3 - 1/420*n**6 + 0 + 0*n - 1/42*n**4 - 1/70*n**5. Factor s(a).
-2*a*(a + 1)*(a + 2)/7
Let a(n) be the third derivative of 1/10*n**3 - 1/40*n**4 + 0*n + 1/200*n**6 - 2*n**2 + 0 - 1/100*n**5. Determine z, given that a(z) = 0.
-1, 1
Let -y**4 + 1/2*y**3 + y**2 - 1/2*y + 0 = 0. Calculate y.
-1, 0, 1/2, 1
Solve -12*u + 1 - 9 + 48*u**2 + 18*u**3 - 46*u**3 = 0.
-2/7, 1
Let z(i) be the third derivative of -i**2 + 0*i + 0 - 1/60*i**6 - 1/12*i**3 + 1/105*i**7 + 1/12*i**4 - 1/40*i**5. Suppose z(t) = 0. What is t?
-1, 1/2, 1
Let 2*q**2 + 5*q**2 - 2*q**2 + 15*q = 0. What is q?
-3, 0
Factor -2/9*k**3 + 8/9*k + 0 - 2/3*k**2.
-2*k*(k - 1)*(k + 4)/9
Let f be (-6)/(-1*12/8). Let x(c) be the third derivative of -1/48*c**f - 1/280*c**7 + 0*c**3 - 1/60*c**6 - 7/240*c**5 + 0 + 0*c + c**2. Factor x(d).
-d*(d + 1)**2*(3*d + 2)/4
Suppose -2*n - 7 = -3*n. Suppose 0 = h + d + 1, 3*h - d - n = 10. Factor -4*o**2 + o - h*o - 2*o - 2 - o**3.
-(o + 1)**2*(o + 2)
Suppose -3*h + 3 + 3 = 0. Let n be ((-14 + 2)/(-2))/h. Solve 3 - p**3 - n = 0.
0
Let q(j) be the first derivative of -j**2/2 + 8*j + 4. Let g be q(4). Factor 0 + 3/4*z**2 + 3/4*z**g - 3/2*z**3 + 0*z.
3*z**2*(z - 1)**2/4
Let k(q) be the third derivative of q**7/70 + 17*q**2. Determine c, given that k(c) = 0.
0
Suppose -4/5*q**3 + 12/5 + 4/5*q**2 + 4*q = 0. What is q?
-1, 3
Let g(s) be the first derivative of s**7/140 + s**6/24 + s**5/20 - 2*s**3/3 - 2. Let x(u) be the third derivative of g(u). Factor x(b).
3*b*(b + 2)*(2*b + 1)
Suppose -10 = -4*k - 2*r, 5*k + 3*r - r - 13 = 0. Find x, given that 10/3*x**k + 0 + 4/3*x**2 + 0*x = 0.
-2/5, 0
Suppose y + 0 = 4. Determine a, given that -2*a**5 + 3*a**3 - 15*a**y + 5*a**5 + 21*a**3 - 12*a**2 = 0.
0, 1, 2
Let f = 641/285 + 8/95. Determine q, given that 11/3*q**2 + 0 + f*q**4 - 16/3*q**3 - 2/3*q = 0.
0, 2/7, 1
Let m(r) be the first derivative of 3 - 1/7*r**2 + 2/7*r - 2/21*r**3 + 1/14*r**4. What is f in m(f) = 0?
-1, 1
Let z(i) be the first derivative of i**6/42 + 2*i**5/35 - 2*i**3/21 - i**2/14 + 1. Factor z(o).
o*(o - 1)*(o + 1)**3/7
Let k(v) be the first derivative of 0*v - 3 + 2/15*v**3 + 0*v**2. Factor k(r).
2*r**2/5
Let t(y) = -3*y**3 - 3*y - 2. Let n(z) = 16*z**3 + z**2 + 16*z + 11. Let v = 0 - -4. Let o(x) = v*n(x) + 22*t(x). Solve o(a) = 0 for a.
0, 1
Let j(m) = m - 2. Let f be j(2). Let c = 1 - f. Factor 5*x**2 - x**3 - 8*x - 3 + 8 + 0 - c.
-(x - 2)**2*(x - 1)
Let h(m) be the second derivative of -m**6/360 + m**3/2 - 3*m. Let j(a) be the second derivative of h(a). Factor j(l).
-l**2
Suppose -2/13*k**3 - 4/13*k**2 + 0 - 2/13*k = 0. Calculate k.
-1, 0
Let t(u) = u**2 + 4*u - 6. Let k be t(-5). Let f = 3 + k. What is q in q**f + q**3 + 0*q**3 + q**2 + q = 0?
-1, 0
Let c(w) be the second derivative of -4*w + 3/10*w**5 - 1/14*w**7 + 0 - 1/10*w**6 - 1/2*w**3 - 3/2*w**2 + 1/2*w**4. Determine h, given that c(h) = 0.
-1, 1
Let b = 16/25 + 4/25. Suppose -6/5*q + 0*q**4 - 2/5*q**5 + 4/5*q**2 + 8/5*q**3 - b = 0. Calculate q.
-1, 1, 2
Let m(k) be the third derivative of 3*k**6/40 + k**5/10 - 4*k**2. Let m(h) = 0. What is h?
-2/3, 0
Let g be -7 + (-120)/(-104) + 6. Suppose -2/13*i**4 + 0*i - 2/13*i**5 + 2/13*i**3 + 0 + g*i**2 = 0. Calculate i.
-1, 0, 1
Let h(x) = x + 3. Let m be h(-3). Suppose 0 = 5*d - 4 - 6. Suppose -1/5*c - 1/5*c**3 + m + 2/5*c**d = 0. What is c?
0, 1
Let y(h) = 3*h**2 + 2*h + 1. Let k(q) = -q**2 - q. Let z(c) = 2*k(c) + y(c). Let m be z(-1). Let 0*v + 0*v**4 + 0 - 2/3*v**5 + 0*v**m + 2/3*v**3 = 0. What is v?
-1, 0, 1
Let c(q) be the first derivative of q**6/240 - q**5/60 - q**4/48 + q**3/6 - q**2 - 1. Let z(j) be the second derivative of c(j). Find f, given that z(f) = 0.
-1, 1, 2
Let c(v) be the second derivative of -v**6/75 + v**5/25 - v**4/30 - 8*v. Factor c(w).
-2*w**2*(w - 1)**2/5
Let c(z) = 4 - 2 - 5 + 2*z + 4 + z**2. Let l be c(-3). Factor 2/5*n**l + 2/5*n + 0 - 2/5*n**2 - 2/5*n**3.
2*n*(n - 1)**2*(n + 1)/5
Let l(y) = -17*y - 17. Let p be l(-1). Let -2/5*f**3 + 4/5*f**2 - 2/5*f + p = 0. What is f?
0, 1
Let s(c) be the third derivative of c**6/120 + c**5/20 + c**4/8 + c**3/6 + 4*c**2. Let s(m) = 0. What is m?
-1
Let v(n) = n**3 + 10*n**2 + 10*n + 11. Let f be v(-9). Factor -6/5*k + 4/5 - 6/5*k**3 - 16/5*k**f.
-2*(k + 1)*(k + 2)*(3*k - 1)/5
Let m(n) be the second derivative of n - 1/60*n**4 + 0*n**2 + 0 + 1/15*n**3. Determine k so that m(k) = 0.
0, 2
Let f(u) be the first derivative of 0*u**2 + 2 - 2*u + 1/24*u**4 + 1/12*u**3. Let g(c) be the first derivative of f(c). Find y such that g(y) = 0.
-1, 0
Let 73 - 32 - 31 + 15*x**5 + 40*x**4 - 15*x - 50*x**2 = 0. Calculate x.
-2, -1, 1/3, 1
Let n be (9/(-8))/(-9)*2*2. Factor -7/4*t**2 - 9/4*t - n.
-(t + 1)*(7*t + 2)/4
Let a = -505 + 507. Suppose -10/3*h - 2 - 2/3*h**a + 2/3*h**3 = 0. What is h?
-1, 3
Let l(h) be the first derivative of h**5/10 + h**4/3 + h**3/3 - 2*h - 1. Let a(s) be the first derivative of l(s). Factor a(q).
2*q*(q + 1)**2
Determine p so that -27/2*p + 3 + 15*p**2 - 9/2*p**3 = 0.
1/3, 1, 2
Let s be (4 - 36/8)*6 + 6. Let -2/11*t**s - 2/11*t + 0 - 4/11*t**2 = 0. Calculate t.
-1, 0
Find z such that -2*z**2 + 0*z**2 + 72*z - 73*z - z**3 + 0*z**2 = 0.
-1, 0
Let a = 23 + -21. Let u(j) be the second derivative of 0 + 0*j**a + 1/30*j**6 - 1/12*j**4 + 0*j**3 + 2*j + 1/42*j**7 - 1/20*j**5. Suppose u(h) = 0. Calculate h.
-1, 0, 1
Factor 31*f + 25*f**2 - 6*f - 15*f - 70*f + 20.
5*(f - 2)*(5*f - 2)
Let x(f) be the first derivative of 0*f + f**3 - 1/8*f**4 - 2*f**2 - 2 - 1/20*f**5. Let r(k) be the second derivative of x(k). Find a such that r(a) = 0.
-2, 1
Let h(t) = 13*t**3 + 79*t**2 + 281*t + 391. Let s(x) = -7*x**3 - 40*x**2 - 140*x - 196. Let v(m) = 4*h(m) + 7*s(m). Find u, given that v(u) = 0.
-4
Let i(c) be the third derivative of -c**6/200 - 3*c**5/100 + c**4/40 + 3*c**3/10 + 15*c**2. What is b in i(b) = 0?
-3, -1, 1
Let i(d) = -d**2 + 8*d + 13. Let p be i(9). Factor 0*l**p - 4/3 + 4/3*l**2 + 2/3*l**5 - 8/3*l**3 + 2*l.
2*(l - 1)**3*(l + 1)*(l + 2)/3
Let a = -4 - -10. Suppose 10*u**2 - 16*u - a*u**3 + 4*u**3 + 0*u**3 + 8 = 0. Calculate u.
1, 2
Let p(m) be the first derivative of 2*m**5/25 - 2*m**4/5 + 2*m**3/3 - 2*m**2/5 - 23. Factor p(y).
2*y*(y - 2)*(y - 1)**2/5
Suppose 0*i - 3*i + 4*n = -18, -2 = 5*i + 4*n. Factor 7*p**2 + p**4 - i*p**3 + p**2 - 3*p**4 - 4*p**2.
-2*p**2*(p - 1)*(p + 2)
Let g be 1 + 1 + (-1172)/588. Let u(i) be the second derivative of 0*i**2 + 1/70*i**5 - g*i**7 + i + 0 + 1/105*i**6 - 1/42*i**4 + 0*i**3. Factor u(o).
-2*o**2*(o - 1)**2*(o + 1)/7
Let l(v) = -180*v**2 + 422*v - 245. Let q(c) = -c. Let y(f) = -l(f) - 2*q(f). Solve y(k) = 0.
7/6
Determine t so that -t**3 - 1/2*t**4 - 1/2*t**2 + 0*t + 0 = 0.
-1, 0
Let f(g) = -8*g - 10*g**3 - 3*g - 1 - 10 - g**3 + 8*g**4. Let w(n) = -3*n**4 + 4*n**3 + 4*n + 4. Let a(j) = 4*f(j) + 11*w(j). Determine z so that a(z) = 0.
0
Let c(a) be the first derivative of 6 + 0*a - 1/7*a**2 + 0*a**3 + 1/14*a**4. Factor c(d).
2*d*(d - 1)*(d + 1)/7
Let q(k) = 3*k**2 + 18*k + 5. Let n(x) = 2*x**2 + 18*x + 4. Let h(t) = 5*n(t) - 4*q(t). What is v in h(v) = 0