15 + 2*k**6/45 - k**5/45 - 2*k**4/9 + 21*k**2. Find v, given that z(v) = 0.
-4, -1, 0, 1
Factor -1/3*d**2 + 0 + 0*d - 1/3*d**3.
-d**2*(d + 1)/3
Find v, given that -5/3*v**3 - 115/3*v + 65/3*v**2 + 55/3 = 0.
1, 11
Let 12*z + 0*z - 4*z**5 + 24*z**3 - z**2 - 31*z**2 + 0*z**3 = 0. What is z?
-3, 0, 1
Suppose -28 = -4*b - 8. Suppose -v - 3 = -2*f - 5, -17 = -5*v + 3*f. Determine k, given that 3*k**2 + 2*k**5 - k**b - k**3 - 2*k**2 - k**v = 0.
-1, 0, 1
Let r be (2 - 4)/(2 + -14). Factor -r*v**2 + 1/3 - 1/6*v.
-(v - 1)*(v + 2)/6
Let g(c) be the third derivative of 1/70*c**5 - 1/28*c**4 - 1/420*c**6 + 1/21*c**3 + 0*c - 3*c**2 + 0. Find o such that g(o) = 0.
1
Let c(w) be the first derivative of 1/3*w**2 + 10/9*w**3 + 0*w - 6/5*w**5 - 2 + 1/2*w**4. Factor c(h).
-2*h*(h - 1)*(3*h + 1)**2/3
Let -3*h**4 + 0*h**3 + 3/2*h + 3*h**2 - 3/2*h**5 + 0 = 0. Calculate h.
-1, 0, 1
Let f(m) = -7*m**3 + 3*m**2 + 4*m + 3. Let g(x) = 20*x**3 - 8*x**2 - 12*x - 8. Let j(p) = 8*f(p) + 3*g(p). Factor j(d).
4*d*(d - 1)*(d + 1)
Let v = 15 - 27/2. Solve 1/2*w**2 + 1/2*w**5 + 0 + v*w**3 + 3/2*w**4 + 0*w = 0 for w.
-1, 0
Let k(f) = -5*f**3 - 3*f**2 - 2*f + 2. Let g = 8 - 5. Let m(d) = -15*d**2 - 11*d + 19*d**g - 4 - 45*d**3 + 15. Let q(o) = -11*k(o) + 2*m(o). Factor q(s).
3*s**2*(s + 1)
Let x(f) be the second derivative of 5*f**4/3 - 35*f**3/6 - 5*f**2 + 2*f. Find r such that x(r) = 0.
-1/4, 2
Let d be 7*1*(10 + -5). Let w be 8/14 + (-20)/d. Factor w + 2/5*a**2 - 2/5*a**4 + 0*a - 2/5*a**3 + 2/5*a**5.
2*a**2*(a - 1)**2*(a + 1)/5
Let m(r) = 3*r**3 + 4*r**2 + 4*r - 2. Let q(x) = 7*x**3 + 8*x**2 + 8*x - 5. Let t(y) = 15*m(y) - 6*q(y). Factor t(n).
3*n*(n + 2)**2
Let o(k) be the third derivative of 1/40*k**6 + 1/20*k**5 + 3*k**2 + 0*k + 0 - 1/4*k**4 + 0*k**3. Solve o(u) = 0.
-2, 0, 1
Let d(p) = -2*p**2 - 2*p - 4. Let y(b) = -b**3 + b**2 + 1. Let k(i) = d(i) - y(i). Let z be k(4). Find m such that -2*m**4 - 4 - 2*m + 4 + 2*m**2 + 2*m**z = 0.
-1, 0, 1
Let f be (-15)/(-9) + 3/9. Let m(o) be the first derivative of 3/10*o**5 - 1 + 0*o**f + 5/8*o**4 + 0*o + 1/3*o**3. What is s in m(s) = 0?
-1, -2/3, 0
Let c(y) be the third derivative of -y**8/840 - y**7/175 - y**6/150 + y**5/75 + y**4/20 + y**3/15 + 3*y**2. Factor c(x).
-2*(x - 1)*(x + 1)**4/5
Let a(r) = r**3 + 3*r**2 + r. Suppose z + 4 = -z. Let f be a(z). Factor 2*d - 1 + d**f + 0*d - 3*d**3 + 4*d**3 - 3*d.
(d - 1)*(d + 1)**2
Let -15*h**3 + 11*h**3 + 2*h**4 + 4*h**2 + 10*h**3 = 0. Calculate h.
-2, -1, 0
Suppose 0 = -2*f - f. Let d(i) be the third derivative of 1/42*i**4 - 1/210*i**5 - 1/21*i**3 + 0*i + f + i**2. Factor d(r).
-2*(r - 1)**2/7
Factor -b**4 - 4*b**2 + 6*b**4 + b - 5*b**5 - 2*b**3 + 2 - 3*b**4 + 6*b**5.
(b - 1)**2*(b + 1)**2*(b + 2)
Suppose 0 = 3*x - 2*v - 3*v + 11, -4*x + 4*v - 28 = 0. Let a be (-33)/x - (-1)/4. Factor 2*s**2 - 2 + 4*s + 2*s**3 + 0*s**3 - 6*s**a.
-2*(s - 1)*(s + 1)*(2*s - 1)
Let y = -1/55 - -57/110. Determine w, given that -y + 3/4*w + 5/4*w**2 = 0.
-1, 2/5
Let a be 8/(-4)*(-1 + 0). Let v = 0 - -2. Factor 1 + l**a - 4*l**2 + v*l**2.
-(l - 1)*(l + 1)
Let d = 17 + -15. Factor 3*c**d - 6 + 2*c + 0*c**2 - 5*c.
3*(c - 2)*(c + 1)
Factor -16/3 + 54*j**3 + 88/3*j - 60*j**2 - 18*j**4.
-2*(j - 1)*(3*j - 2)**3/3
Let t(h) be the first derivative of -2*h**6 - 29*h**5/5 - 5*h**4 - h**3/3 + h**2 + 4. Solve t(v) = 0.
-1, -2/3, 0, 1/4
Let f be (-3)/(1 - 23/2). Let p = -186 - -188. Factor 6/7*i**p + 10/7*i - f*i**4 - 2/7*i**3 + 4/7.
-2*(i - 2)*(i + 1)**3/7
Let o(r) be the first derivative of -1/10*r**4 + 1/30*r**6 - 2/15*r**3 + 6 + 1/5*r + 1/25*r**5 + 1/10*r**2. Find v such that o(v) = 0.
-1, 1
Suppose -3*l = 5*n - 16, -18 = -5*n - 6*l + 2*l. Let m = -3 - -5. Factor -n*p**3 + 6*p + m*p**2 + 0*p - 2*p.
-2*p*(p - 2)*(p + 1)
Factor 0 + 1458/11*d + 2/11*d**4 + 486/11*d**2 + 54/11*d**3.
2*d*(d + 9)**3/11
Let k(f) = 4*f**2 + 9*f + 7. Let m(o) = o**2 + 3*o + 2. Let w(l) = 4*k(l) - 14*m(l). Factor w(b).
2*b*(b - 3)
Let p(x) be the second derivative of 8*x**7/147 + 44*x**6/105 - 47*x**5/140 + x**4/14 + 17*x. Factor p(f).
f**2*(f + 6)*(4*f - 1)**2/7
Determine t so that -2/15*t**2 - 512/15 + 64/15*t = 0.
16
Let w be 2/(2/(8/2)). Factor b**4 + 0*b**3 - b**3 + 4*b**w + 0*b**4 - 4*b**5.
-b**3*(b - 1)*(4*b - 1)
Suppose -13 = -5*y - 3. Suppose -8*i + 7*i**2 - 3*i**3 + 7*i**3 + 5*i**y + i**4 - 10*i**3 = 0. What is i?
0, 2
Factor 2/3*l - 1/3*l**2 + 0 - 1/3*l**3.
-l*(l - 1)*(l + 2)/3
Find u, given that -66*u - 20*u**3 + 60*u - 4*u**2 + 8*u**3 - 3*u**4 - 11*u**2 = 0.
-2, -1, 0
Let w be (2 - -1)*(-48)/18. Let k = w + 10. Factor -1/5*v**4 - 1/5*v**3 + 0*v**k + 0*v + 0.
-v**3*(v + 1)/5
Suppose 2*v - 2 = 0, 0 = c + 5*v - 4 - 5. Let j be (c/(-5))/((-16)/40). Factor -1/6*y + 0 - 1/6*y**j.
-y*(y + 1)/6
Solve -2 + 12 - 3*g**3 + 12*g**2 - 4 - 15*g = 0.
1, 2
Suppose 187*v + 16 = 191*v. Determine m so that -4/3*m + 2/9*m**v + 16/9*m**2 + 4/3*m**3 - 2 = 0.
-3, -1, 1
Let v(t) be the second derivative of t**7/2940 + t**6/1260 - t**5/210 - t**3/3 + t. Let h(b) be the second derivative of v(b). Factor h(u).
2*u*(u - 1)*(u + 2)/7
Let o(u) be the third derivative of 1/12*u**4 + 0*u + 0 - 3*u**2 + 2/3*u**3 - 1/30*u**5. Let o(w) = 0. Calculate w.
-1, 2
Let i be (-4)/(-3) + (-12)/(-18). Factor -12 + 3*t**3 - 2*t**i + 9*t**2 + 2*t**2.
3*(t - 1)*(t + 2)**2
Factor -3/5*c**4 + 6/5*c - 6/5*c**3 + 0*c**2 + 3/5.
-3*(c - 1)*(c + 1)**3/5
Let s = 18 + -15. Let j(x) be the second derivative of -2/11*x**2 - 3*x - 1/66*x**4 - 1/11*x**s + 0. Factor j(w).
-2*(w + 1)*(w + 2)/11
Factor 1/4*h**4 + 0 + 0*h - 3/4*h**3 + 1/2*h**2.
h**2*(h - 2)*(h - 1)/4
Factor 0 - 10/3*w + 2/3*w**2.
2*w*(w - 5)/3
Let z = -1 + 4. Suppose -22 = -z*c - 16. Factor -2/9*w - 2/9*w**4 + 2/9*w**c + 0 + 2/9*w**3.
-2*w*(w - 1)**2*(w + 1)/9
Let p = -13 - -18. Suppose -5*f - p*y - 3 = 12, f + 2*y = -8. Factor -1 + f + b**4 - b**2 - b**2.
(b - 1)**2*(b + 1)**2
Let o(x) be the second derivative of 4*x - 1/30*x**4 - 1/75*x**6 + 0*x**2 - 1/25*x**5 + 0 + 0*x**3. Find y such that o(y) = 0.
-1, 0
Suppose 4*v + 0*v + 5*a = 27, -v - a + 6 = 0. Solve 3*x + x + 8*x**2 - 10 - 4*x**v + 2 = 0 for x.
-1, 1, 2
Suppose -3*t - 7 = -25. Factor -16*a**3 + 5*a + t - 3 + 7*a + 1.
-4*(a - 1)*(2*a + 1)**2
Let f = -61 - -63. Factor 2/7*z**3 + 0 + 2/7*z + 4/7*z**f.
2*z*(z + 1)**2/7
Let j(o) = 5*o**4 + 5*o**3 - 5*o**2 - 5*o + 3. Let x(n) = -n**4 - n**3 + n**2 + n - 1. Let c(d) = -j(d) - 3*x(d). Factor c(i).
-2*i*(i - 1)*(i + 1)**2
Let 0*y**4 - 6/11*y + 8/11*y**3 - 2/11*y**5 - 4/11*y**2 + 4/11 = 0. What is y?
-2, -1, 1
Let b be 2 - (3 - 1) - 12/(-32). Let d(r) be the first derivative of 1/3*r**3 - 1/4*r + b*r**2 + 2. Let d(z) = 0. Calculate z.
-1, 1/4
Solve 10/9*c**3 + 0 - 8/3*c**2 + 8/9*c = 0 for c.
0, 2/5, 2
Let z(n) be the first derivative of n**3/3 - n - 6. Factor z(w).
(w - 1)*(w + 1)
Let k(x) be the first derivative of -x**6/14 + 3*x**5/7 - 27*x**4/28 + x**3 - 3*x**2/7 - 7. Let k(u) = 0. Calculate u.
0, 1, 2
Suppose -4*l - 12 = 2*h, -2*h + 5*l = 1 - 7. Let z be 2 + 3 - (-2)/h. Find b, given that 0 + 0*b + 5/4*b**5 - 1/2*b**2 - 5/4*b**3 + 1/2*b**z = 0.
-1, -2/5, 0, 1
Let y(v) = 8*v**3 + 8*v**2 - 8*v - 4. Let o(h) = h**3 + h**2 - h. Let m(u) = -4*o(u) + y(u). Factor m(l).
4*(l - 1)*(l + 1)**2
Suppose -6*d + 69 = -9*d. Let q = d + 29. Factor 6/5*k**4 + 4/5 - 22/5*k**3 + q*k**2 - 18/5*k.
2*(k - 1)**3*(3*k - 2)/5
Let k(z) = 4*z**5 + 2*z**4 - z**3 - 2*z**2 + 3. Let p = -15 + 16. Let n(s) = -s**5 - s**4 + s**2 - 1. Let u(w) = p*k(w) + 3*n(w). Let u(l) = 0. What is l?
-1, 0, 1
Let t(h) = 3*h**4 - 3*h**3 - 3*h**2 - 5*h. Let v(q) = -q**4 + q**3 + q**2 + q. Let j(c) = t(c) + 4*v(c). Factor j(k).
-k*(k - 1)**2*(k + 1)
Let t(w) be the second derivative of 1/3*w**3 + 3/5*w**5 + 4*w - 2/3*w**4 + 0*w**2 + 0 - 4/15*w**6 + 1/21*w**7. Find z, given that t(z) = 0.
0, 1
Let c(l) be the first derivative of l**5/10 + l**4/8 - 25. Find p, given that c(p) = 0.
-1, 0
Let v be (-9)/24*(-4)/6. Let i = 9 + -5. Suppose 1/4*f**5 + 3/4*f**3 + v*f**2 + 3/4*f**i + 0 + 0*f = 0. Calculate f.
-1, 0
Let q be 35/(-30) + (-3)/(-6). Let j = -4/15 - q. Factor 0 - j*h**2 - 2/5*h.
-2*h*(h + 1)/5
Let y(f) be the second derivative of f**6/225 + f**5/75 - 2*f**3/45 - f**2/15 + 9*f. Find n such that y(n) = 0.
-1, 1
Let v = -1 - -4. Let c = 5 - v. What is k in -4 - 3*k - c*k**2 