- 1)**3*(w + 1)/3
Let g(k) = 4*k**4 - 27*k**3 - 11*k**2. Let t(u) = -u**4 + 7*u**3 + 3*u**2. Let m(s) = -6*g(s) - 22*t(s). Factor m(r).
-2*r**3*(r - 4)
Let x(h) be the second derivative of h**6/180 - 2*h**3/3 + 3*h. Let v(o) be the second derivative of x(o). Let v(n) = 0. What is n?
0
Let k(n) be the second derivative of -n**8/504 + n**7/105 - n**6/60 + n**5/90 + 3*n**2/2 + 2*n. Let f(x) be the first derivative of k(x). Factor f(z).
-2*z**2*(z - 1)**3/3
Let n(t) = -t + 1. Let i be n(-1). Factor 14*k**4 + 0*k**i + 0*k - 24*k**3 + 6*k**2 + 4*k.
2*k*(k - 1)**2*(7*k + 2)
Suppose k + 4 = 2*k + 2*n, k + 4*n = 6. What is u in 1 - 4*u**k - 9*u + u**2 + 11 = 0?
-4, 1
Determine g so that 0*g + 0 - 14/5*g**3 + 4/5*g**2 = 0.
0, 2/7
Let -2*p**5 - 8*p**3 + 19*p**4 - 26*p**5 - 55*p**4 = 0. What is p?
-1, -2/7, 0
Let y be 12/20 - 3/45*3. Factor y*x**2 - 2/5*x - 4/5.
2*(x - 2)*(x + 1)/5
Let p(w) be the third derivative of w**7/945 - w**6/108 + w**5/90 + w**4/12 - 9*w**2. Factor p(z).
2*z*(z - 3)**2*(z + 1)/9
Let m(q) be the second derivative of q**5/80 - q**4/48 - q**3/12 - 6*q. Factor m(z).
z*(z - 2)*(z + 1)/4
Suppose -7 = 2*a - 1. Let y be (a/(-1))/(0 - -1). Factor -r**2 - r**2 - r**3 + 8*r**4 - y*r**5 - 2*r**5.
-r**2*(r - 1)**2*(5*r + 2)
Let p(h) = -11*h**4 - 41*h**3 + 43*h**2 + 36*h - 47. Let v(r) = -5*r**4 - 20*r**3 + 22*r**2 + 18*r - 23. Let d(u) = 2*p(u) - 5*v(u). Factor d(g).
3*(g - 1)**2*(g + 1)*(g + 7)
Let l(j) be the third derivative of 0*j**5 + 0 + 2*j**2 + 1/1512*j**8 + 0*j**7 + 0*j**3 + 0*j + 0*j**6 + 0*j**4. Factor l(s).
2*s**5/9
Let f(a) = 29*a**5 + 29*a**4 - 24*a**3 + 17*a + 17. Let y(x) = -5*x**5 - 5*x**4 + 4*x**3 - 3*x - 3. Let k(i) = 6*f(i) + 34*y(i). Find d such that k(d) = 0.
-2, 0, 1
Factor 3/4*r - 3/4*r**2 + 3/2.
-3*(r - 2)*(r + 1)/4
Suppose -2*y = -3*y + 4. Suppose -f + 0 = -3, y*f = -j + 15. Solve a**j + a**2 + 5*a - 6*a + 0*a**2 - 1 = 0.
-1, 1
Let p(c) = c**3 + 7*c**2 + c + 9. Let w be p(-7). Let l(s) be the second derivative of 1/5*s**2 + 0 + 1/5*s**3 + 1/10*s**4 + 1/50*s**5 + w*s. Factor l(d).
2*(d + 1)**3/5
Let x(v) = 2*v + 25. Let y be x(-11). Factor -4*o**3 - 2*o**4 + 2*o**2 - 2*o**3 + 8*o**y - 2*o.
-2*o*(o - 1)**2*(o + 1)
Suppose -p = 4*p - 4*p. Let w(m) be the third derivative of p + 0*m**3 - 1/480*m**6 + 3*m**2 - 1/120*m**5 + 0*m - 1/96*m**4. Suppose w(z) = 0. What is z?
-1, 0
Let b be -3 - (4/6)/(8/(-60)). Factor -1/4*k**b + 0*k + 0.
-k**2/4
Solve -6*g**3 + 3*g + 0 + 6 - 12*g**2 + 5*g**3 + 3*g**5 + 6*g**4 - 5*g**3 = 0.
-2, -1, 1
Let z = 19 - 1. Let i = -15 + z. Find x such that 2/7*x**2 - 2/7*x + 2/7*x**i - 2/7 = 0.
-1, 1
Let m(u) be the second derivative of u**7/42 + 2*u**6/15 + 3*u**5/20 - u**4/3 - 2*u**3/3 - 2*u. Factor m(i).
i*(i - 1)*(i + 1)*(i + 2)**2
Let u(p) = p**2 - p - 1. Let q be -3 + (-3)/6*6. Let c = 7 + q. Let o(d) = 3*d**2 - 6*d - 12. Let h(s) = c*o(s) - 12*u(s). Find g, given that h(g) = 0.
0, 2/3
Factor 3/5*x**3 - 9/5*x**2 + 0 + 6/5*x.
3*x*(x - 2)*(x - 1)/5
Let c be 18/(-3) + 3 - -3. Determine w, given that -2/5*w + 2/5*w**2 + c = 0.
0, 1
Let a(k) be the second derivative of k**9/4536 + k**8/2520 - k**3/6 - 3*k. Let i(c) be the second derivative of a(c). Solve i(d) = 0.
-1, 0
Suppose -2*o + 6*o = 5*l - 41, 0 = -o - 3*l + 11. Let r be (-2)/2*o/20. What is f in 0 - r*f**4 + 0*f**3 + 3/5*f**2 - 2/5*f = 0?
-2, 0, 1
Let o be 0 - (-1 + 21/27). Suppose -2/3*g - o*g**3 - 2/3*g**2 - 2/9 = 0. Calculate g.
-1
Let x(t) be the third derivative of t**6/1080 - t**5/360 - t**3/2 - 3*t**2. Let j(d) be the first derivative of x(d). Let j(l) = 0. What is l?
0, 1
Let r be (1/(1/(-1)))/(-1). Solve -r - n**2 + 3 - n**2 = 0.
-1, 1
Determine b so that -25/4*b**5 - 1 + 6*b + 1/4*b**3 + 45/4*b**4 - 41/4*b**2 = 0.
-1, 2/5, 1
Let j = -334/15 - -67/3. Let b(i) be the third derivative of 0*i - j*i**6 + i**2 - 1/30*i**5 + 0*i**3 + 0*i**4 + 0. Factor b(g).
-2*g**2*(4*g + 1)
Suppose 18 = 3*g - 3*d, -5*g + 28 = -g - 5*d. Find c, given that -8/7 + 40/7*c + 6/7*c**g - 14*c**4 - 20*c**3 = 0.
-1, 2/7
Let r(n) be the third derivative of n**5/30 + n**4/36 - 2*n**3/9 - 4*n**2. Solve r(l) = 0 for l.
-1, 2/3
Let y(q) be the third derivative of -q**7/525 + q**5/75 - q**3/15 + 12*q**2. Let y(x) = 0. What is x?
-1, 1
Suppose p - 10 = -4*p. Suppose -3*r + u = -p*u - 6, -2*r + u = -5. Suppose -5/2*w**4 - 1/2 - 5*w**r - 5/2*w - 1/2*w**5 - 5*w**2 = 0. Calculate w.
-1
Let s(u) = 3*u - 3. Let h be s(2). Suppose 2*t - 5 = -2*g + t, 5*g - 18 = h*t. Factor 0 - 1/5*a + 0*a**2 + 1/5*a**g.
a*(a - 1)*(a + 1)/5
Suppose 0 = -3*f - 28 - 29. Let r = f + 22. Factor 0 - 2/3*j**2 + 4/3*j**r - 2/3*j**4 + 0*j.
-2*j**2*(j - 1)**2/3
Let n = -2/721 - -208/721. Suppose 4/7*m + n + 2/7*m**2 = 0. Calculate m.
-1
Factor 0*u**2 + 3*u + 1 + 5 + u**2 - 4*u**2.
-3*(u - 2)*(u + 1)
Suppose 7*v - 10 = 2*v. Let o be v*4*(-1)/(-2). Determine f so that -f**3 - 6*f**4 - 3*f**5 - f**3 + f**o = 0.
-1, -2/3, 0
Let -6*w**3 - 22*w**2 - 2*w**4 + 3*w**4 - 7*w**4 - 2*w**5 + 20*w**2 = 0. What is w?
-1, 0
Let f(t) = t - 1 + 2*t**2 - 6*t**2 - t**3 + 2*t**2. Let w(j) = -j**3 - 5*j**2 + 3*j - 2. Let v be 2/(0 - (-8)/(-12)). Let r(h) = v*w(h) + 5*f(h). Factor r(z).
-(z - 1)**2*(2*z - 1)
Let s(h) be the second derivative of -3*h**5/20 + 3*h**4/4 - 3*h**3/2 + 3*h**2/2 - 5*h. Let n(y) = y - 1. Let q(a) = 12*n(a) + s(a). Factor q(o).
-3*(o - 3)*(o - 1)*(o + 1)
Let q(h) = -116*h**2 + 1196*h - 3996. Let a(u) = -u**3 + 117*u**2 - 1197*u + 3997. Let i(b) = 4*a(b) + 3*q(b). Determine m so that i(m) = 0.
10
Let d(x) be the second derivative of 5*x**4/12 - 10*x**3/3 - 32*x. Solve d(a) = 0.
0, 4
Let w(n) be the second derivative of -1/2*n**4 + 0*n**2 + 0 + 4*n + 0*n**3 - 9/20*n**5. Solve w(g) = 0.
-2/3, 0
Let a(q) be the first derivative of 16/9*q - 20/3*q**2 + 3 + 28/3*q**3 - 49/18*q**4. Suppose a(v) = 0. Calculate v.
2/7, 2
Let b(p) be the first derivative of 1/9*p**3 - 6 + 0*p - 1/3*p**2. Let b(h) = 0. What is h?
0, 2
Let p be (-2)/10 + 55/25. Determine i, given that 2*i + 16*i**2 - 6*i - 2*i**p = 0.
0, 2/7
Let i be (-9)/(-4) + 0 + -2. Factor -1/4*k**5 - i*k + 0*k**2 + 0*k**4 + 0 + 1/2*k**3.
-k*(k - 1)**2*(k + 1)**2/4
Let q(x) be the first derivative of -3 - 2/5*x**3 + 0*x - 2/5*x**2 - 1/10*x**4. Determine u so that q(u) = 0.
-2, -1, 0
Let u = 1543 + -918. Let r = 1115 - u. Determine c so that 2 + 40*c - 8 + 196*c**2 - r*c**3 - 10 = 0.
-2/7, 2/7, 2/5
Suppose -4*t + 9 + 44 = 5*z, -3*z - 33 = -3*t. Let y = -12 + t. Factor -2/5*w - 2/5*w**3 - 4/5*w**2 + y.
-2*w*(w + 1)**2/5
Let v(d) be the third derivative of -2*d**7/525 + d**5/25 - d**4/15 + 6*d**2. Factor v(y).
-4*y*(y - 1)**2*(y + 2)/5
Let g = -19 - -9. Let b(m) = 5*m**4 - 7*m**3 - m**2. Let h(v) = 9*v**4 - 13*v**3 - v**2. Let l(t) = g*b(t) + 6*h(t). Factor l(w).
4*w**2*(w - 1)**2
Find a, given that -12/5 - 2/5*a**2 - 2*a = 0.
-3, -2
Let w(x) be the third derivative of -x**5/90 + x**4/18 - x**3/9 - 10*x**2 - x. Find v such that w(v) = 0.
1
Let f(x) be the second derivative of -x**7/630 - x**6/120 - x**5/60 - x**4/72 + x**3/6 + x. Let w(n) be the second derivative of f(n). Factor w(h).
-(h + 1)**2*(4*h + 1)/3
Let u(g) = -g**3 + 3*g**2 - g - 1. Let m be u(2). Determine f so that 9/2*f**2 + 7/2*f - m = 0.
-1, 2/9
Suppose -3*z + 2*z + 2 = 0. Suppose -q - 12 = 3*q, -3 = -3*w - q. What is m in m**3 + z - w - m = 0?
-1, 0, 1
Let o = -4 + 6. Let z = 1 + o. What is w in 32/7*w**4 + 4/7 + 30/7*w**5 - 32/7*w**z - 36/7*w**2 + 2/7*w = 0?
-1, -2/5, 1/3, 1
Factor 3/4*m**5 - 3/2 - 3*m**3 + 9/4*m + 3/2*m**2 + 0*m**4.
3*(m - 1)**3*(m + 1)*(m + 2)/4
Let z(n) = -n - 1. Let b be z(-9). Factor -y**5 + 3*y**3 - 4*y**4 - y**3 - b*y**3 - 4*y**2 - y.
-y*(y + 1)**4
Let v(y) = 11*y**2 + 4*y**3 + 13*y - 3*y**3 - 8 - 2*y**3. Let x be v(12). Solve -1/5*a - 4/5*a**3 + a**5 + 2/5 - 2*a**2 + 8/5*a**x = 0.
-1, 2/5, 1
Let n = 1/17 - -25/153. Factor -2/9*z**5 + 0 + 4/9*z**4 + 0*z**2 - n*z**3 + 0*z.
-2*z**3*(z - 1)**2/9
Let s(q) be the first derivative of q**6/120 - 3*q**5/20 + 9*q**4/8 - 9*q**3/2 + 5*q**2/2 - 5. Let f(b) be the second derivative of s(b). Solve f(a) = 0 for a.
3
Factor 194*j**5 + 29*j**5 - 34*j**5 + 5*j**3 + 7*j**3 + 96*j**4.
3*j**3*(7*j + 2)*(9*j + 2)
Let n(c) be the third derivative of -c**5/210 + 5*c**4/84 - 4*c**3/21 + 15*c**2. Factor n(j).
-2*(j - 4)*(j - 1)/7
Suppose 7*o = -