e of 1/6*x**3 + 1/12*x**4 + 0*x**2 + 0 - x. Determine n so that k(n) = 0.
-1, 0
Let n(w) be the third derivative of 0*w - w**2 + 1/360*w**5 + 0*w**3 + 0 + 1/72*w**4. Determine c so that n(c) = 0.
-2, 0
Let x(y) be the third derivative of -y**8/560 - 2*y**7/175 - y**6/40 - y**5/50 + 35*y**2. Factor x(f).
-3*f**2*(f + 1)**2*(f + 2)/5
Let m = -4 - 2. Let v be 1/m + (-4)/(-6). Suppose -t**3 - v*t**4 + 0 - 1/2*t**2 + 0*t = 0. What is t?
-1, 0
Let w(i) = i**3 + 10*i**2 + 7*i - 13. Let s be w(-9). Factor -s*z**4 + z**2 + z**4 - 2*z**3 + 3*z**4 + 2*z.
-z*(z - 1)*(z + 1)*(z + 2)
Let a(n) be the third derivative of -n**5/180 - n**4/24 - 7*n**2. Factor a(x).
-x*(x + 3)/3
Let d(p) be the first derivative of p**7/630 - p**5/180 + 5*p**2/2 - 1. Let t(l) be the second derivative of d(l). Solve t(i) = 0 for i.
-1, 0, 1
Factor 2*m**3 + 120 - 120 - 2*m**2.
2*m**2*(m - 1)
Suppose 3*x + i - 5*i = 18, 5*i + 11 = -2*x. Let k be (4/14)/(6/14). Factor -k*y**3 + 0 - 2/3*y**x + 4/3*y.
-2*y*(y - 1)*(y + 2)/3
Let k(c) = 8*c**4 + 6*c**3 - 15*c**2 - 13*c - 13. Let j(q) = -4*q**4 - 3*q**3 + 7*q**2 + 6*q + 6. Let d(o) = 13*j(o) + 6*k(o). What is u in d(u) = 0?
-1, 0, 1/4
Let u(f) be the third derivative of -f**7/420 + f**6/120 + f**5/120 - f**4/24 - 6*f**2. Determine v so that u(v) = 0.
-1, 0, 1, 2
Let y(o) be the second derivative of o**6/90 - o**5/20 + o**4/12 - o**3/18 - o. Factor y(c).
c*(c - 1)**3/3
Solve 6/5 + 2/5*o**2 + 8/5*o = 0 for o.
-3, -1
Determine l so that 1/5*l**2 + 4/5 - l = 0.
1, 4
Let w be 2/(-6)*-3 - 3. Let n(a) = -4*a**2 - 2*a. Let x(u) = -u**2 - u. Let o be 1*-2 - 1*-8. Let m(z) = o*x(z) + w*n(z). Solve m(r) = 0.
0, 1
Suppose 11*a - 8*a - 6 = 0. Suppose -1/3*f**4 + 0 + 1/3*f**a + 0*f**3 - 1/6*f**5 + 1/6*f = 0. What is f?
-1, 0, 1
Let l(n) = -n + 12. Let d be l(10). Let a be 8/(-20) - d/(-5). What is j in 0*j - 4/3*j**4 - 2/3*j**3 + a + 0*j**2 = 0?
-1/2, 0
Suppose -4*q - 23 + 3 = 0. Let b be q/(-21) + 12/28. Let -1/3*k**2 + k - b = 0. What is k?
1, 2
Let d(m) = -m**2 - m - 2. Let o be d(0). Let g(z) = z**3 + 3*z**2 + 3*z + 2. Let x be g(o). Factor 0 + x*q - 2/3*q**2.
-2*q**2/3
Let a(l) be the first derivative of 4*l**3 + 2*l**2 - 7*l + 7. Let u(j) = j**2 - 1. Let i(t) = -2*a(t) + 22*u(t). Let i(k) = 0. What is k?
-2
Factor i**4 + 2*i**2 - 6*i - i**4 - 4*i**3 + 10*i**3 - 2*i**4.
-2*i*(i - 3)*(i - 1)*(i + 1)
Let a(s) = s**2 - s - 1. Let m(x) = x**3 + 7*x**2 - 7*x - 7. Let u(n) = 6*a(n) - m(n). Factor u(v).
-(v - 1)*(v + 1)**2
Let m be 21/15 + 2/10. Let n be ((-16)/(-10))/(-1 - (-21)/15). Find i such that 4/5*i**n - m*i + 27/5*i**2 - 4/5 - 19/5*i**3 = 0.
-1/4, 1, 2
Suppose 0 = 5*k - 1 - 4. Let v = k - -1. Factor -2*o**4 + o**2 - o**v + 2*o**2.
-2*o**2*(o - 1)*(o + 1)
Let b be (2/(-28))/(2*5/(-20)). Let i(m) be the first derivative of -1/14*m**4 + 0*m + 2/35*m**5 - 2/21*m**3 + b*m**2 + 1. Suppose i(v) = 0. What is v?
-1, 0, 1
Let m(i) = i**3 + 12*i**2 - i - 8. Let h be m(-12). Determine b so that -2*b**5 + 11/4*b**3 - 3/4*b - 1/4 + 7/4*b**2 - 3/2*b**h = 0.
-1, -1/4, 1/2, 1
Let p(d) = 2*d**2 + 6*d + 10. Let b(h) = -4*h**2 - 12*h - 21. Let m(n) = -6*b(n) - 13*p(n). Factor m(l).
-2*(l + 1)*(l + 2)
Let c = -23 + 22. Let h be (c + 5)*(-2)/(-16). Solve -1/4*q**4 + 0*q**2 + h*q**3 + 1/4 - 1/2*q = 0.
-1, 1
Let d be (52/(-50) - -1)/(36/(-135)). Let q(l) be the second derivative of 1/4*l**4 - 1/14*l**7 + 0*l**2 + 0*l**3 + l + d*l**5 - 1/10*l**6 + 0. Factor q(m).
-3*m**2*(m - 1)*(m + 1)**2
Let o(j) be the second derivative of -2*j + 0*j**4 + 1/20*j**5 + 0 + 0*j**2 - 1/6*j**3. Factor o(k).
k*(k - 1)*(k + 1)
Let p = 42 - 77/2. Let m(w) be the first derivative of -7/4*w**4 + 49/20*w**5 - 1 + p*w**2 - w - 15/4*w**3. Factor m(j).
(j - 1)*(j + 1)*(7*j - 2)**2/4
Let t be 11/(-3) - (-3)/(-9). Let x be (-1 - t)*8/6. Factor -3/4*g + 1/2*g**x - 1/4 - 1/4*g**2 + 3/4*g**3.
(g - 1)*(g + 1)**2*(2*g + 1)/4
Let f(o) be the third derivative of 0 + 0*o + 2/21*o**4 - 1/42*o**5 - 4/21*o**3 - o**2 + 1/420*o**6. Determine i, given that f(i) = 0.
1, 2
Suppose -6 = g - 8. Let k(l) be the second derivative of -l**g - 1/10*l**5 + 0 + 1/6*l**4 - 2*l + 1/3*l**3. Factor k(h).
-2*(h - 1)**2*(h + 1)
Let q = 753 + -3764/5. Factor 1/5 - q*p**3 + 1/5*p - 1/5*p**2.
-(p - 1)*(p + 1)**2/5
Suppose 80 = 44*p - 4*p. Determine c so that 3/2*c**p + 0 + 1/2*c**3 + c = 0.
-2, -1, 0
Let t(z) be the second derivative of 1/27*z**4 + 0 - 5/189*z**7 + 0*z**3 - z - 8/135*z**6 - 1/90*z**5 + 0*z**2. Factor t(l).
-2*l**2*(l + 1)**2*(5*l - 2)/9
Let l(f) = -f**3 - f + 1. Let w(j) = 5*j**3 - 24*j**2 + j - 1. Let t(a) = -l(a) - w(a). Find b such that t(b) = 0.
0, 6
Let x(o) be the first derivative of 0*o + 1/180*o**5 + 1/9*o**3 + 2 + o**2 + 1/24*o**4. Let f(v) be the second derivative of x(v). Factor f(p).
(p + 1)*(p + 2)/3
Let p be 3/6 - (-14)/4. Suppose 0*u - 3/5*u**5 + 3/5*u**p + 0*u**3 + 0 + 0*u**2 = 0. Calculate u.
0, 1
Suppose -f + 6*f = 0. Let a be f/(1/1 - 3). Solve 2/7 + 6/7*g - 8/7*g**3 + a*g**2 = 0 for g.
-1/2, 1
Let p(m) = -6*m - 4. Let c(y) = -y**2 - y - 1. Let b(v) = -2*c(v) - p(v). Factor b(j).
2*(j + 1)*(j + 3)
Let l(t) = 20*t**2 - 23*t + 3. Let b(i) = 7*i**2 - 8*i + 1. Let s(r) = -17*b(r) + 6*l(r). Find o such that s(o) = 0.
1
Let z(p) be the second derivative of 7*p**5/90 + p**4/18 + 5*p**2/2 + 5*p. Let q(u) be the first derivative of z(u). Factor q(w).
2*w*(7*w + 2)/3
Suppose -8 = -t - 6. Let h(a) be the second derivative of 0 + 0*a**t - 1/6*a**3 + 1/42*a**7 + 0*a**5 - 1/15*a**6 + 1/6*a**4 - a. What is c in h(c) = 0?
-1, 0, 1
Let f(v) be the second derivative of -v**5/130 + v**3/39 + 3*v. Find w such that f(w) = 0.
-1, 0, 1
Let z(u) = 14*u**2 - 10*u - 6. Let l(h) = -14*h**2 + 11*h + 7. Suppose -24 = -4*o - 0. Let m(n) = o*l(n) + 7*z(n). Determine d, given that m(d) = 0.
0, 2/7
Suppose -3*p + 2 + 52 = 0. Let k be 120/54 + (-4)/p. Factor 1/2*h**k - h + 1/2.
(h - 1)**2/2
Let x be 14/49 + (-2)/((-168)/(-17)). Let p(w) be the third derivative of 3*w**2 + 0*w - x*w**4 + 0*w**5 + 0 + 1/60*w**6 + 0*w**3. Suppose p(o) = 0. What is o?
-1, 0, 1
Let j(f) be the second derivative of 0*f**3 + 0 - 1/30*f**5 - 1/36*f**4 + 3*f - 1/90*f**6 + 0*f**2. Solve j(z) = 0.
-1, 0
Let b(o) = 3*o**3 - 12*o**2 + 3*o. Let h(c) = 9*c**3 - 35*c**2 + 10*c. Let k(s) = -8*b(s) + 3*h(s). Suppose k(x) = 0. What is x?
0, 1, 2
Let o(f) = 4*f**2 - 2*f - 2. Let c(b) = b**3 - 5*b**2 + 2*b + 2. Let r(h) = 2*c(h) + 3*o(h). Find z such that r(z) = 0.
-1, 1
Let n(w) = w**2 + 8*w - 9. Let k be n(-9). Let c be k/(6/(-2 + -1)). Factor 0 + 1/3*s**3 + 0*s + c*s**2.
s**3/3
Let a(w) = w**4 + 9*w**3 + 6*w**2 - 3*w. Let m(x) = -4*x**4 - 35*x**3 - 25*x**2 + 11*x. Let l(h) = -22*a(h) - 6*m(h). Factor l(z).
2*z**2*(z + 3)**2
Let -3 - 4/3*z**3 + 2/3*z**2 + 4*z - 1/3*z**4 = 0. Calculate z.
-3, 1
Let y be (1 + 0)/(6/(-4) - -2). Let v(u) be the third derivative of 0*u + 1/840*u**6 + 0*u**4 + 1/420*u**5 + 0 + u**y + 0*u**3. Factor v(d).
d**2*(d + 1)/7
Let n(u) = -3*u**3 + 4*u**2 + 3*u. Let w(q) = 3*q**3 - 3*q**2 - 3*q. Let a(b) = -3*n(b) - 4*w(b). Factor a(t).
-3*t*(t - 1)*(t + 1)
Let -2*g**2 - 7*g - g**2 - 3 + g = 0. What is g?
-1
Suppose -7*g + 3*g + 39 = -3*d, 9 = 4*g + 3*d. Suppose -g = 5*v - 16. Determine z so that -2/7*z - 2/7*z**v + 2/7*z**3 + 2/7*z**4 + 0 = 0.
-1, 0, 1
Suppose -20*k - k**3 - 13*k + 2*k**2 + 33*k = 0. Calculate k.
0, 2
Let c(b) be the first derivative of 0*b**2 + 1/5*b**5 + 0*b**4 + 0*b - 1/3*b**3 + 4. Factor c(f).
f**2*(f - 1)*(f + 1)
Let v(k) = 7*k**2 + 19*k. Let d(c) = 8*c**2 + 20*c. Let x(o) = -3*d(o) + 4*v(o). Factor x(a).
4*a*(a + 4)
Factor 0 - 1/4*r**2 + 1/4*r.
-r*(r - 1)/4
Factor 7/6*y**2 - 2*y - 2/3.
(y - 2)*(7*y + 2)/6
Let l be 3/4 - (-15)/12. Solve 1/7*i**l - 3/7*i**3 + 0*i - 1/7*i**5 + 3/7*i**4 + 0 = 0 for i.
0, 1
Let -1/3*m**2 + 1/3*m + 2/3 = 0. Calculate m.
-1, 2
Let t = 113/102 + -16/17. Let a(f) be the second derivative of -4*f + 0 + 0*f**3 - 1/5*f**5 - t*f**4 + 0*f**2. Let a(x) = 0. What is x?
-1/2, 0
Let i(f) = 2*f**4 + 6*f**3 - 12*f**2 - 6*f + 10. Let o(b) = b**2 - 1. Let k(x) = -6*x**2 - 3*x + 2. Let m be k(2). Let w(n) = m*o(n) - 2*i(n). Factor w(u).
-4*(u - 1)*(u + 1)**2*(u + 2)
Let j(y) be the third derivative of -y**6/120 + y**5/20 + y**2. Let d be j(2). Factor 2*n**4 + 4*n**d - 7*n - 8*n**2 + 3*n + 4*n**3 + 6 - 4.
2*(