) = 0. What is u?
-1, 0, 1
Let o be (-112)/(-180) + (-2 - 8/(-5)). Find t such that 4/9*t + 2/9 + o*t**2 = 0.
-1
Let g(f) = 3*f**2 - 2*f - 5. Let i = -4 + 5. Let t(y) = y**2 - y - 1. Let s(k) = i*g(k) - 4*t(k). Suppose s(q) = 0. Calculate q.
1
Suppose k - 3*o + 3 = 0, 0 = k + k + 2*o - 10. Let d = 6 - 2. Factor -5*v + d*v + 3*v**2 - k*v**2 + v**2.
v*(v - 1)
Let j(z) be the second derivative of -4/15*z**6 - z + z**5 - z**4 + 2*z**2 - 2/3*z**3 + 0. Factor j(x).
-4*(x - 1)**3*(2*x + 1)
Suppose -n - 4 = -6. Factor -4*x + 6*x + 0*x**n + 2*x**2.
2*x*(x + 1)
Factor -2*g - 1/6*g**3 - g**2 - 4/3.
-(g + 2)**3/6
Let k = 282 - 279. Factor 0*h - 1/3*h**k + 0 + 1/3*h**2.
-h**2*(h - 1)/3
Let u(d) = -d**2 - 85*d + 400. Let o(n) = -4*n**2 - 256*n + 1200. Let w(i) = 5*o(i) - 16*u(i). Determine r so that w(r) = 0.
10
Let s(g) be the second derivative of -g**7/525 - g**6/150 - g**5/150 - g**2/2 - 2*g. Let x(a) be the first derivative of s(a). Factor x(k).
-2*k**2*(k + 1)**2/5
Let j(n) = -22*n**2 + 38*n + 6. Let f(v) = 110*v**2 - 189*v - 29. Let b(r) = -2*f(r) - 11*j(r). Determine m so that b(m) = 0.
-2/11, 2
Let x(w) be the first derivative of -9*w**4 + 0*w + 14/5*w**5 - 8*w**2 + 7 - 1/3*w**6 + 40/3*w**3. Find g, given that x(g) = 0.
0, 1, 2
Let i(g) be the first derivative of -1/4*g**4 + 1/3*g**2 - 1/15*g**5 - 1 + 1/18*g**6 + 0*g + 1/9*g**3. Factor i(n).
n*(n - 2)*(n - 1)*(n + 1)**2/3
Let o = -77/12 + 247/36. Factor -2/9*f - 2/9*f**2 + o.
-2*(f - 1)*(f + 2)/9
Let g(p) be the first derivative of p**5/10 - 3*p**4/8 + p**3/3 - 8. What is x in g(x) = 0?
0, 1, 2
Suppose 2*l**2 + l - 1/2*l**4 - l**3 - 3/2 = 0. Calculate l.
-3, -1, 1
Let u(y) be the second derivative of -y**4/12 + 4*y**3/3 - 8*y**2 + 11*y. Determine n so that u(n) = 0.
4
Find m such that -2/3 + 4/3*m - 2/3*m**2 = 0.
1
Let c(m) be the first derivative of -7 + 1/35*m**5 - 1/7*m**2 + 5/21*m**3 - 1/7*m**4 + 0*m. Solve c(w) = 0.
0, 1, 2
Let h = 11996/22815 + -15/169. Let r = h + -1/27. Factor 3/5*m - 1/5*m**2 - r.
-(m - 2)*(m - 1)/5
Let h(v) = v + 3. Let u be (-4)/18 + 4/18. Let a be h(u). Factor 1/3*s**a - 1/3 + s - s**2.
(s - 1)**3/3
Let l(s) = 2*s**3 + s**2. Let i be l(1). Suppose 2*o + 5*x - 4 = 0, -o - 4*x = x - 2. Factor 0*q**3 + i*q**3 - q**3 - 4*q**o + 4*q - 2*q.
2*q*(q - 1)**2
Let p = 7 - 5. Let t = -168 + 171. Let 3/2*u**p + t*u + 3/2 = 0. What is u?
-1
Find o such that -4/5 + 1/5*o**2 + 0*o = 0.
-2, 2
Suppose n + 20 = 4*b + 5, -3*n - 12 = -b. Solve -2*r + 2*r**4 + 9*r**3 + 4*r + 6*r**2 - b*r**3 + 0*r = 0 for r.
-1, 0
Let v be (2/(-4))/1*-4. Suppose 20 = -h - 4*s, v*h + 5*s + 25 = h. Solve -10*j**3 + h*j**2 - 3*j**5 + 8*j**4 + 4*j**2 + j**5 = 0 for j.
0, 1, 2
Let h(x) = 6*x**2 - 39*x + 23. Let a be h(6). What is s in -8/7*s**2 + 24/7*s**3 + 20/7*s**4 - 4*s + 4/7*s**a - 12/7 = 0?
-3, -1, 1
Suppose 9 - 3 + 8*b + 33*b**2 - 42*b**2 + 7*b = 0. Calculate b.
-1/3, 2
Suppose -2*g = -0*a + 5*a - 2, -2*a - 12 = 4*g. Factor 7*z**a + 8*z**2 - 12*z**2 + 12 - 12*z.
3*(z - 2)**2
Factor -1/5*y**2 - 1/5 - 2/5*y.
-(y + 1)**2/5
Let k(a) be the second derivative of -3*a**6/20 - 3*a**5/20 + a**4/8 + 2*a. Factor k(u).
-3*u**2*(u + 1)*(3*u - 1)/2
Suppose -4 = -5*n + n. Let x = 3 - n. Solve p**x + 0 + 0 - p**3 - p**4 + p = 0.
-1, 0, 1
Let h(q) = q - 3. Let p be h(5). Let f = p + 1. Factor -o**5 - o + 2*o + 2*o**4 - f*o**2 + o**2.
-o*(o - 1)**3*(o + 1)
Let d(t) be the second derivative of -t**5/20 - t**4/6 + t**3/2 - 15*t. Factor d(w).
-w*(w - 1)*(w + 3)
Let y = -8 - -10. Let o be 3 + 1 + 0/y. Solve -2/3*g**o + 0*g**2 + 0*g**3 - 2/3*g**5 + 0 + 0*g = 0.
-1, 0
Let r(u) be the third derivative of -u**8/40320 + u**6/1440 - u**5/30 - 3*u**2. Let a(f) be the third derivative of r(f). Factor a(m).
-(m - 1)*(m + 1)/2
Let y(l) be the second derivative of 1/18*l**4 - 1/90*l**5 - 3/2*l**2 + 0*l**3 - 1/60*l**6 + 0 - l. Let d(p) be the first derivative of y(p). Solve d(b) = 0.
-1, 0, 2/3
Let v(n) be the second derivative of -n**7/21 + n**6/45 + n**5/15 - 4*n. Determine r, given that v(r) = 0.
-2/3, 0, 1
Let z be (7/(-14))/(-1 - (-3)/4). Find j such that -2/3*j**3 + 0 + 2/3*j + 0*j**z = 0.
-1, 0, 1
Let o = 221/5 + -43. Factor o*t - 2/5*t**2 - 4/5.
-2*(t - 2)*(t - 1)/5
Let m(o) be the first derivative of o**2/2 + 5*o + 1. Let j be m(-5). Factor j + s**3 + 0*s**3 + 0.
s**3
Let p(w) = 64*w**3 - 7*w - 3. Suppose -4*g + 2*f - 20 = -3*f, 5*f = 0. Let i be ((-3)/12)/((-1)/4). Let m(l) = l - 1. Let c(y) = g*m(y) + i*p(y). Factor c(a).
2*(2*a + 1)*(4*a - 1)**2
Find x such that -8/3*x + 0*x**2 + 8/3*x**3 - 4/3*x**4 + 4/3 = 0.
-1, 1
Let s(n) be the second derivative of -3/70*n**5 + 3*n + 0 + 1/7*n**3 + 1/7*n**2 - 1/42*n**4. Let s(b) = 0. What is b?
-1, -1/3, 1
Let h(u) be the third derivative of u**6/160 - u**5/20 + 5*u**4/32 - u**3/4 + u**2. Factor h(n).
3*(n - 2)*(n - 1)**2/4
Let h be (17 + -15)*(-10)/(-16). Factor -1/4 - 3/2*z**2 + h*z.
-(2*z - 1)*(3*z - 1)/4
Let o(v) be the first derivative of -1 + 2/3*v**3 + 8*v - 4*v**2. Solve o(k) = 0.
2
Let j be 4/14*(-11 + 12). Let t(g) be the first derivative of -j*g**2 + 0*g - 2/21*g**3 - 1. Find c such that t(c) = 0.
-2, 0
Let g(x) be the second derivative of x**6/105 - x**5/10 + 17*x**4/42 - 17*x**3/21 + 6*x**2/7 - 20*x. Find a such that g(a) = 0.
1, 2, 3
Let d(t) be the third derivative of 1/630*t**7 + 0*t**4 + 1/180*t**5 + 0*t**3 + 7*t**2 + 0*t - 1/180*t**6 + 0. Solve d(f) = 0 for f.
0, 1
Let v(z) = -z**2 + 8*z + 9. Let b(d) = -d - 1. Let s(x) = 40*b(x) + 5*v(x). Factor s(m).
-5*(m - 1)*(m + 1)
Let j(w) be the first derivative of w**5/10 + w**4/6 - 3*w + 3. Let t(l) be the first derivative of j(l). Let t(f) = 0. Calculate f.
-1, 0
Let v(w) be the first derivative of -2*w**5/15 - w**4/3 + 10*w**3/9 + 2*w**2 - 33. Suppose v(m) = 0. Calculate m.
-3, -1, 0, 2
Suppose -2*x + 10 = 2. Factor 6*y**2 + 0*y**3 - 2*y**2 + y**x - 4*y**3.
y**2*(y - 2)**2
Suppose -4*u = 2*f + 10, -4*f + 2*f = -3*u - 18. Let q be 0 + (0 - f/(-1)). Suppose -1/4*i**q + 1/4*i + 1/4*i**2 - 1/4 = 0. What is i?
-1, 1
Let d(b) = -b**3 - b**2 - b. Let j(q) = -q**3 - 2*q**2 - 2*q. Let o(x) = -2*d(x) + j(x). What is h in o(h) = 0?
0
Suppose 0 = 4*n - n, -n = -o + 2. Let r be (-24)/(-140) + 1/10*4. Find c, given that -22/7*c + r - 8/7*c**4 - 16/7*c**3 + 6/7*c**5 + 36/7*c**o = 0.
-2, 1/3, 1
Let g(q) be the first derivative of q**4/4 - 5*q**3/3 + 4*q**2 - 4*q + 4. Determine x so that g(x) = 0.
1, 2
Suppose 1/3*s**3 + 1/3 - 1/3*s**2 - 1/3*s = 0. What is s?
-1, 1
Suppose -x - 6 = n - 0*n, 5*x - n = -24. Let m be (4/x)/((-18)/15). Solve 2*b**2 - m*b + 0 + 2/3*b**4 - 2*b**3 = 0 for b.
0, 1
Let m(z) be the third derivative of z**6/240 + z**5/300 - z**4/48 - z**3/30 + 9*z**2. Factor m(k).
(k - 1)*(k + 1)*(5*k + 2)/10
Let k(g) = -30*g**4 + 33*g**3 + 33*g**2 - 30*g + 12. Let u(q) = 12*q**4 - 13*q**3 - 13*q**2 + 12*q - 5. Let p(r) = -5*k(r) - 12*u(r). Solve p(a) = 0.
-1, 0, 1/2, 2
Let q(j) be the second derivative of -j**7/840 - j**6/120 + 3*j**5/40 - 5*j**4/12 - 2*j. Let o(x) be the third derivative of q(x). Determine r so that o(r) = 0.
-3, 1
Let i(n) be the third derivative of n**8/6 + 12*n**7/35 + n**6/4 + n**5/15 - 8*n**2. Let i(h) = 0. What is h?
-1/2, -2/7, 0
Let w(m) = 14*m - 3. Let i(g) = -9*g + 2. Let v(u) = 8*i(u) + 5*w(u). Let l be v(-1). Suppose -1/3*h**l - 1/3*h**2 + 1/3*h + 0 + 1/3*h**4 = 0. Calculate h.
-1, 0, 1
Factor 0*x**2 - 4*x**3 - 4*x**3 - 16*x**2 + 4*x**3.
-4*x**2*(x + 4)
Let u(n) = 6*n**3 - 17*n**2 - 7*n + 17. Let p(l) = -l**3 + 3*l**2 + l - 3. Let h(v) = -34*p(v) - 6*u(v). Factor h(a).
-2*a*(a - 2)*(a + 2)
Determine j, given that 0*j**4 + 0 + 0*j**2 - 1/2*j + j**3 - 1/2*j**5 = 0.
-1, 0, 1
Let j(w) = -4*w**2 - 3*w + 11. Let i(u) = -u - 2. Let x be i(-3). Let z(l) = -l - 2 - l**2 + 4 + x. Let c(d) = 6*j(d) - 22*z(d). Solve c(b) = 0 for b.
0, 2
Let i(g) be the third derivative of 0 - 1/480*g**6 - 2*g**2 + 0*g + 0*g**5 + 1/32*g**4 - 1/12*g**3. Suppose i(l) = 0. Calculate l.
-2, 1
Let j be ((-10)/(-25))/(5/25). Let p(d) be the first derivative of 18*d + 1 + 2/3*d**3 - 6*d**j. Suppose p(a) = 0. Calculate a.
3
Let h(k) be the third derivative of -1/720*k**6 + 11*k**2 + 0 + 0*k - 1/180*k**5 + 0*k**3 - 1/144*k**4. Factor h(s).
-s*(s + 1)**2/6
Let w = 1547 + -371279/240. Let u(o) be the third derivative of -o**2 + 0*o**3 + 1/96*o**