0)/(-11) - 12/(-66). Let o be 4/22 - (-42)/h. Determine w so that 0*w + o*w**4 + 1/4*w**5 + 0 + 0*w**2 + 1/4*w**3 = 0.
-1, 0
Let h(j) = -j**3 + 12*j**2 - 20*j + 2. Let z be h(10). Let a(p) be the third derivative of 1/24*p**4 - 1/30*p**5 + 0*p - 3*p**z + 0 + 0*p**3. Factor a(q).
-q*(2*q - 1)
Let w(r) = -3*r**2 + 7*r + 2. Let q(y) = 7*y**2 - 14*y - 4. Let g(c) = -6*q(c) - 11*w(c). Suppose g(x) = 0. What is x?
-2/9, 1
Let p = 205/68 - 30/17. Let k(o) be the first derivative of 1 + 1/12*o**6 - 1/2*o - 1/2*o**5 + p*o**4 - 5/3*o**3 + 5/4*o**2. Factor k(u).
(u - 1)**5/2
Let o(d) be the first derivative of -d**5/25 + d**4/10 + d**3/15 - d**2/5 + 29. Factor o(q).
-q*(q - 2)*(q - 1)*(q + 1)/5
Solve 10/9*h**4 + 2*h**2 + 8/3*h**3 + 0 + 4/9*h = 0 for h.
-1, -2/5, 0
Solve 12*q**4 - 56*q**3 + 29*q**3 + 23*q**3 = 0 for q.
0, 1/3
Let m(o) = -o**2 + 12*o + 2. Let x be m(12). Factor 3 - 6*s - 11*s**x + 9*s**2 + 5*s**2.
3*(s - 1)**2
Let x(r) be the first derivative of 0*r**3 + 0*r**4 + 1/20*r**5 + 0*r**2 + r + 1. Let y(a) be the first derivative of x(a). Let y(n) = 0. What is n?
0
Let g(b) = -11*b**2 + 6*b + 5. Let j(q) = 10*q**2 - 5*q - 5. Let h(v) = -5*g(v) - 6*j(v). Let h(k) = 0. What is k?
-1, 1
What is i in 3/5*i**2 + 0 - 6/5*i = 0?
0, 2
Let f(i) be the second derivative of i**4/6 + 7*i**3/15 + 2*i**2/5 + 6*i. Factor f(y).
2*(y + 1)*(5*y + 2)/5
Let a(g) = 8*g**3 + 19*g**2 + 11*g. Let k(f) be the first derivative of -f**4/2 - 5*f**3/3 - 3*f**2/2 - 5. Let v(m) = -6*a(m) - 22*k(m). Factor v(l).
-4*l**2*(l + 1)
Determine c, given that -1/5*c**2 + 0 + 2/5*c**3 - 1/5*c**4 + 0*c = 0.
0, 1
Let u(n) be the first derivative of 3*n**4/8 - n**3 - 15*n**2/4 + 9*n - 35. Determine a so that u(a) = 0.
-2, 1, 3
Factor -16*i**2 - 4*i - 45*i**3 - 4*i + 5*i - 8*i**2.
-3*i*(3*i + 1)*(5*i + 1)
Let l(i) = i**5 - 2*i**4 - i**3 + 2*i**2 - 2*i. Let o(r) = -r**4 + r**2 - r. Let d(w) = -l(w) + 2*o(w). Factor d(g).
-g**3*(g - 1)*(g + 1)
Let r = 22 + -21. Suppose 2 - 2*o**3 + 2*o + r + 1 + 2*o**4 - 6*o**2 + 0*o**4 = 0. What is o?
-1, 1, 2
Suppose -6*p + p + 10 = 0. Let h be ((-12)/(-3))/(p/4). Factor 8*a**2 - 2*a**2 + h + a**3 - 10*a - 2*a - 2*a**3.
-(a - 2)**3
Let x(w) be the second derivative of -3*w**6/35 - 3*w**5/35 + 10*w**4/21 - 8*w**3/21 + 35*w. Factor x(y).
-2*y*(y + 2)*(3*y - 2)**2/7
Factor 1/3*l**2 + 0*l + 0 + 1/3*l**4 - 2/3*l**3.
l**2*(l - 1)**2/3
Let k(y) = -10*y**2 + 4*y. Let w be (10/(-3) + 1)*3. Let p(a) = 3*a**2 - a. Suppose -4*d = d + 10. Let i(n) = d*k(n) + w*p(n). Solve i(z) = 0 for z.
-1, 0
Suppose 0 = -5*z + 4*v + 124 + 43, -4*z - 2*v = -144. Suppose -2*c + 2 = -0*w + w, -5*w = -5*c + z. Factor -c*x**2 + 2*x**2 + x**3 + 3*x**2.
x**2*(x + 2)
Let b(f) = 2*f**2 + 1. Let o be b(-1). What is n in -o*n**3 + 10*n**4 + 0*n**3 - n**3 = 0?
0, 2/5
Suppose -l + 2*l = 2. Suppose 0 = 2*a - 4*o, 0 = l*a - o - 1 - 2. Factor -4/5*t**a - 2/5*t + 0 - 2/5*t**3.
-2*t*(t + 1)**2/5
Solve -5 + 2 - 7*o**2 + 12*o**3 - 12*o + 3*o**2 + 7 = 0 for o.
-1, 1/3, 1
Let v(q) be the second derivative of q**7/280 - q**6/160 - 3*q**2 + 6*q. Let h(s) be the first derivative of v(s). Factor h(n).
3*n**3*(n - 1)/4
Let a(m) be the second derivative of -5/24*m**4 + 1/40*m**5 + 6*m + 2/3*m**3 + 0 - m**2. Factor a(v).
(v - 2)**2*(v - 1)/2
Let m(d) be the third derivative of d**6/900 - d**5/450 - d**4/180 + d**3/45 - 36*d**2. Factor m(c).
2*(c - 1)**2*(c + 1)/15
Let z = 3 + -2. Let x(b) = 2*b**2 + b - 3. Let s(j) = -j**2 + 1. Let i(h) = -h - 3. Let l be i(-6). Let o(p) = l*s(p) + z*x(p). Factor o(m).
-m*(m - 1)
Let g(u) be the first derivative of 3*u**5/40 - 21*u**4/32 + u**3 + 3*u**2 + 2. Let g(a) = 0. What is a?
-1, 0, 4
Let s = 8 - 1. Let n(m) be the third derivative of 0*m**4 + 2*m**2 + 0 + 1/150*m**5 + 1/525*m**s + 0*m**3 + 0*m - 1/150*m**6. What is u in n(u) = 0?
0, 1
Factor 48/5*c + 2/5*c**3 - 18/5*c**2 - 32/5.
2*(c - 4)**2*(c - 1)/5
Let u(h) = -h**3 + 3*h**2 + 3*h - 4. Let p be u(3). Suppose -p = -4*k - r + 6, -4*k = -3*r - 31. Factor 16*a**3 + 15*a**4 - a + 6*a**3 - 9*a**3 - 3*a**k.
a*(a + 1)*(3*a + 1)*(4*a - 1)
Let -1/12*h**2 - 1/3*h - 1/4 = 0. What is h?
-3, -1
Let v(n) be the third derivative of n**6/60 + n**5/30 - n**4/12 - n**3/3 - 5*n**2. Factor v(y).
2*(y - 1)*(y + 1)**2
Let s be 13 - 4/10*5. Let c = s + -9. Factor -2/3*i**3 + 0 - 4/3*i + c*i**2.
-2*i*(i - 2)*(i - 1)/3
Let o(p) be the third derivative of 5*p**8/336 + p**7/42 - p**6/12 - 34*p**2. Factor o(b).
5*b**3*(b - 1)*(b + 2)
Factor -v**4 + 2*v**2 + 3*v - 2*v + 6*v**3 - 8*v**3 + v**5 - 1.
(v - 1)**3*(v + 1)**2
Let j = -689/12 + 173/3. Factor -3/2*f**3 + 0 - f**4 - 1/4*f**5 - f**2 - j*f.
-f*(f + 1)**4/4
Let p(r) = r**2 - 8*r + 7. Let b be p(6). Let t(g) = g**2 + 4*g - 5. Let w be t(b). Suppose 0*x + 1/2*x**5 + w*x**2 - 1/4*x**3 - 1/4*x**4 + 0 = 0. Calculate x.
-1/2, 0, 1
Let c(s) be the third derivative of s**9/15120 - s**8/3360 + s**4/12 + 3*s**2. Let f(g) be the second derivative of c(g). Determine v, given that f(v) = 0.
0, 2
Let t(l) be the second derivative of 0*l**3 + 0*l**2 + 1/3*l**4 + l + 0 + 9/10*l**5 + 4/15*l**6. Suppose t(i) = 0. Calculate i.
-2, -1/4, 0
Let v be (66/55)/((-27)/(-10)). Factor 0 + 2/9*j**5 - 2/9*j + v*j**4 + 0*j**3 - 4/9*j**2.
2*j*(j - 1)*(j + 1)**3/9
Let y(r) be the third derivative of -r**6/30 + 4*r**5/15 - 2*r**4/3 - 8*r**2. Let y(i) = 0. What is i?
0, 2
Factor 1/4*i**3 - 1/4*i + 1/4*i**2 - 1/4.
(i - 1)*(i + 1)**2/4
Let k = -759/200 + 19/5. Let a(j) be the third derivative of 0*j**3 + 0*j + 2*j**2 + 1/40*j**4 - k*j**6 + 0*j**5 + 0. Suppose a(g) = 0. Calculate g.
-1, 0, 1
What is b in -83*b - b**2 - 83*b + 163*b = 0?
-3, 0
Let t(a) be the third derivative of -a**6/270 - a**5/270 + a**4/54 + a**3/27 - 20*a**2. Factor t(o).
-2*(o - 1)*(o + 1)*(2*o + 1)/9
Factor 26*s**2 - 859*s**4 - 221*s**4 - 95*s - 656*s**2 - 1620*s**3 - 3 - 2.
-5*(s + 1)*(6*s + 1)**3
Let l(x) = -11*x**3 + 6*x**2 + 17*x. Let f(u) = -6*u**3 + 3*u**2 + 9*u. Let c(n) = -5*f(n) + 3*l(n). Determine w, given that c(w) = 0.
-1, 0, 2
Let k(c) be the third derivative of -c**7/525 - c**6/150 - c**5/150 + 11*c**2. Find a such that k(a) = 0.
-1, 0
Let s = -25 - -28. Find u such that 109*u - 2*u**5 + s*u**5 - 2 + 14*u**3 - 16*u**2 - 100*u - 6*u**4 = 0.
1, 2
Let s be 7*2/(-14) + (-3)/(-2). Factor 0 + 1/2*n - 1/2*n**4 + 1/2*n**2 - s*n**3.
-n*(n - 1)*(n + 1)**2/2
Let m = 2 + -1. Factor u + u**2 - m + 1 - 2*u.
u*(u - 1)
Let x(o) = -5*o**2 + 2*o. Let w(j) = 15*j**2 - 4*j. Let l(i) = 6*w(i) + 17*x(i). Solve l(g) = 0 for g.
-2, 0
Factor 10*x**2 + 16 - 13*x**2 + 7*x**2 + 16*x.
4*(x + 2)**2
Let h(d) = -d + 24. Let k be h(10). Solve 2*u - k*u - 2 - 10 - 12*u + 15*u**2 = 0 for u.
-2/5, 2
Let q(w) be the third derivative of -w**6/480 + w**5/240 + w**4/96 - w**3/24 - 6*w**2. Solve q(g) = 0.
-1, 1
Let i = -16 - -22. Suppose 0 = -3*u + i*u. Factor -3/4*y**4 - 1/2*y - 7/4*y**2 - 2*y**3 + u.
-y*(y + 1)**2*(3*y + 2)/4
Factor 10*t**4 + 2*t**5 - 3*t**5 - 4*t**5 + 5*t - 10*t**2.
-5*t*(t - 1)**3*(t + 1)
Suppose d + 4*g - 6 = 0, 0 = d + g - 3. Let h be (2 - 6)*d/(-4). Find j, given that j**h - 2/3 + 1/3*j = 0.
-1, 2/3
Let f(d) be the third derivative of -d**7/560 - d**6/120 + d**3/3 - 5*d**2. Let y(v) be the first derivative of f(v). Factor y(s).
-3*s**2*(s + 2)/2
Let s(j) be the second derivative of 11*j**4/3 - 26*j**3/3 + 4*j**2 + 20*j. Suppose s(x) = 0. What is x?
2/11, 1
Let p(a) = 195*a**4 + 535*a**3 + 288*a**2 + 53*a - 1. Let o(x) = 97*x**4 + 268*x**3 + 144*x**2 + 26*x - 1. Let c(d) = 5*o(d) - 3*p(d). Let c(v) = 0. What is v?
-2, -1/4, -1/5
Let 0*i**2 + 0 - 1/4*i + 1/4*i**3 = 0. What is i?
-1, 0, 1
Let t(h) be the first derivative of 5*h**6/6 - h**5 - 5*h**4/2 + 10*h**3/3 + 5*h**2/2 - 5*h - 11. Factor t(j).
5*(j - 1)**3*(j + 1)**2
Let w(q) be the first derivative of -9*q**4/16 - q**3/4 + 3*q**2 - 3*q + 30. Suppose w(z) = 0. Calculate z.
-2, 2/3, 1
Let d(o) be the second derivative of -o**7/147 - 2*o**6/105 - o**5/70 + 18*o. Solve d(t) = 0.
-1, 0
Suppose 24 + 11 = -5*z. Let o(b) = -3*b**3 - 3*b**2 - 6*b + 6. Let i(t) = -3*t**3 - 4*t**2 - 7*t + 7. Let a(g) = z*o(g) + 6*i(g). Determine m so that a(m) = 0.
0, 1
Factor -7*i**3 - i**5 + 8*i + 36 - 6*i**4 - 32 + i**4 + i**2.
-(i - 1)*(i + 1)**2*(i + 2)**2
Let j(q) be the third derivative of 1/300*q**5 + 6*q**2 + 0*q + 0 + 2/15*