et s = p - 12/5. Factor -2/3 + s*c + 2/3*c**2 - 1/3*c**3.
-(c - 2)*(c - 1)*(c + 1)/3
Let w be 4/(-2)*25/(-30). Let -2/3 - 1/3*m**4 - 3*m**2 - 7/3*m - w*m**3 = 0. Calculate m.
-2, -1
Factor d**3 + 0*d**3 + 3*d**4 - d**5 - 8*d**2 + 4 + 0*d**2 + d**2.
-(d - 2)**2*(d - 1)*(d + 1)**2
Let v(w) be the third derivative of -w**8/6720 + w**7/210 - w**6/15 - w**5/15 + w**2. Let q(j) be the third derivative of v(j). Determine m so that q(m) = 0.
4
Let g be (-2 - 1/(-24)) + 2. Let a(u) be the third derivative of 0 - 1/16*u**4 - 1/6*u**3 + g*u**5 + 0*u + u**2. Factor a(f).
(f - 1)*(5*f + 2)/2
Let s = -35 + 169/5. Let g = 28/15 + s. Factor -4/3*w**3 + g*w**4 + 2/3*w - 4/3*w**2 + 2/3 + 2/3*w**5.
2*(w - 1)**2*(w + 1)**3/3
Let u(y) be the third derivative of -y**6/420 - y**5/105 + y**4/84 + 2*y**3/21 + 19*y**2. Suppose u(t) = 0. Calculate t.
-2, -1, 1
What is b in 6/7*b**4 - 8/7*b**3 + 0 - 2/7*b**2 + 4/7*b = 0?
-2/3, 0, 1
Let g(p) = 4*p**3 + 2*p**2 - 2*p - 4. Let d(n) = 9*n**3 + 4*n**2 - 4*n - 9. Let q be (-4)/2 + 5/(-5). Let j = 2 - q. Let y(o) = j*g(o) - 2*d(o). Factor y(i).
2*(i - 1)*(i + 1)**2
Let m(u) = -u**3 + u**2 - u - 1. Let w(o) = 3*o**3 - 3*o**2 + 4*o + 3. Let n = -37 - -58. Let g(j) = n*m(j) + 6*w(j). Factor g(r).
-3*(r - 1)**2*(r + 1)
Let x(d) be the first derivative of 25*d**6/9 + 28*d**5/3 + 23*d**4/2 + 56*d**3/9 + 4*d**2/3 - 6. Factor x(s).
2*s*(s + 1)**2*(5*s + 2)**2/3
Let p(m) be the first derivative of m**4/4 - m**3 + m**2 + 2*m - 7. Let y be p(2). Determine j so that 0 + 0*j - 2/7*j**3 - 2/7*j**y = 0.
-1, 0
Let a(k) be the third derivative of k**5/390 + k**4/39 + k**3/13 - k**2. Factor a(m).
2*(m + 1)*(m + 3)/13
Let i(b) = 23*b**4 + 11*b**3 + 17*b - 17. Let o(h) = -8*h**4 - 4*h**3 - 6*h + 6. Let x(m) = 6*i(m) + 17*o(m). Factor x(j).
2*j**3*(j - 1)
Let k(f) be the third derivative of f**6/48 + f**5/4 - 10*f**2. Factor k(y).
5*y**2*(y + 6)/2
Suppose -y = -5*d - 3*y + 30, 3*d - 17 = -y. Factor 5/2*k**d + 0*k**2 - 7/2*k**5 + k**3 + 0 + 0*k.
-k**3*(k - 1)*(7*k + 2)/2
Suppose -3*b - 251 = -92. Let u = -157/3 - b. Suppose u*g**3 + 0*g - 2/3*g**2 + 0 = 0. What is g?
0, 1
Suppose 0 = 3*z + i - 3, 21*i = 3*z + 17*i - 18. What is f in -2/13*f**4 + 0*f - 2/13*f**z - 4/13*f**3 + 0 = 0?
-1, 0
Solve -1/8*p + 0*p**2 + 1/8*p**3 + 0 = 0 for p.
-1, 0, 1
Let b(a) be the third derivative of a**7/1260 + a**6/360 - a**5/30 + a**4/12 - 4*a**2. Let m(w) be the second derivative of b(w). Determine y so that m(y) = 0.
-2, 1
Let w be (-6)/(-4)*(-11 - -12). Let w*t**2 + 0*t + 0 = 0. Calculate t.
0
Let k(n) be the first derivative of n**4/10 - n**2/5 - 6. Suppose k(u) = 0. What is u?
-1, 0, 1
Let k be (-38)/4*-5 - -4. Let a = 54 - k. Solve -1/2*n - 2*n**3 + 0 - a*n**2 = 0.
-1, -1/4, 0
Let u = 127/288 + -7/32. Suppose 0*v**2 + 0*v + u*v**4 + 0 - 2/9*v**3 = 0. Calculate v.
0, 1
Determine c, given that -6*c**3 + 5*c**2 - 117 - c + 117 = 0.
0, 1/3, 1/2
Solve 0 + 2/3*k**2 - 4*k**3 + 4*k - 2/3*k**4 = 0 for k.
-6, -1, 0, 1
Let b be -4 + 2 + -1 + 5. Let d be (4 + -3 - 0)*b. Factor 0*g**d + 0*g**3 + 0 - 1/3*g**4 + 0*g.
-g**4/3
Let h(y) = -5*y**3 - 2*y**2 - 5*y + 4. Let r(b) = 6*b**3 + 3*b**2 + 6*b - 5. Let j(t) = -5*h(t) - 4*r(t). Factor j(g).
g*(g - 1)**2
Let r(f) be the third derivative of f**5/80 + 3*f**4/32 + f**3/4 + 14*f**2. Factor r(g).
3*(g + 1)*(g + 2)/4
Suppose -2*x - 1 = -l + 11, x + 5 = 0. Find w, given that w**l - 6*w + 3*w**2 - w**2 - 9 = 0.
-1, 3
Let c(d) be the third derivative of d**6/480 - d**5/120 + d**4/96 - 3*d**2. Factor c(g).
g*(g - 1)**2/4
Let l(p) = p**3 + 5*p**2 - 4*p - 7. Let w be l(-5). Suppose -4*x + w - 1 = 0. Factor 4*v**2 - x*v**2 + v + 0*v**2.
v*(v + 1)
Let g(f) be the third derivative of 0 - 13/10*f**5 - 10*f**2 - 10/3*f**4 - 3/20*f**6 - 4*f**3 + 0*f. Factor g(j).
-2*(j + 3)*(3*j + 2)**2
Let c(l) be the second derivative of -l**4/4 - 2*l**3 - 6*l**2 + 7*l. Factor c(o).
-3*(o + 2)**2
Factor x**3 + 0*x**4 + 0 + 0*x**2 - 1/2*x**5 - 1/2*x.
-x*(x - 1)**2*(x + 1)**2/2
Let m(z) be the second derivative of 3*z + 1/120*z**6 - 1/24*z**4 + 0*z**2 + 1/80*z**5 + 0*z**3 + 0. Determine v so that m(v) = 0.
-2, 0, 1
Suppose -5*o = 5, -2*y + y - 2*o = -2. Let g be -2 + y*(-4)/(-8). Factor -8/9*h**3 - 2/9*h**5 + g + 0*h**2 + 0*h - 8/9*h**4.
-2*h**3*(h + 2)**2/9
Let m(b) be the second derivative of -b**4/12 - 5*b**3/6 - 11*b. Factor m(t).
-t*(t + 5)
Let x(c) be the second derivative of 4/105*c**6 + 0*c**2 - 1/147*c**7 + 0 - 3/35*c**5 + 2/21*c**4 - 1/21*c**3 - 3*c. What is o in x(o) = 0?
0, 1
Suppose 0 = a + 2*a. Let d(y) be the third derivative of 0*y - 2*y**3 + 3*y**2 + a + 1/4*y**5 - y**4. What is t in d(t) = 0?
-2/5, 2
Let p(m) be the third derivative of -m**2 + 1/60*m**5 + 1/24*m**4 + 0*m + 0 + 0*m**3. Factor p(y).
y*(y + 1)
Let p(i) be the third derivative of -i**7/63 - 29*i**6/360 - i**5/6 - 13*i**4/72 - i**3/9 + 31*i**2. Solve p(z) = 0.
-1, -1/2, -2/5
Let t be (-8)/(-3) + (-3)/(-9). Let l(h) = h**2 - 3*h + 3. Let j be l(t). Factor -v**j + 3*v**3 + 0*v**3 - 3*v**4 + v**2.
-v**2*(v - 1)*(3*v + 1)
Let g(j) be the first derivative of 5*j**4/8 - 5*j**3 + 45*j**2/4 - 10*j + 9. Suppose g(z) = 0. What is z?
1, 4
Let w be (-5)/(-15) - (-4)/12. Factor -2/3*k + 0 + w*k**2.
2*k*(k - 1)/3
Let a(s) be the third derivative of -1/210*s**5 + 2/21*s**3 + 0 - 3*s**2 + 0*s + 1/84*s**4. Suppose a(u) = 0. Calculate u.
-1, 2
Suppose 0 = -7*r + 3*r. Factor 4*m**3 - 3*m**4 + 5*m**4 + 0*m + r*m + 2*m**2.
2*m**2*(m + 1)**2
Suppose -4*s - 72 = -72. Factor -3/5*p**3 + 9/5*p**2 + s - 6/5*p.
-3*p*(p - 2)*(p - 1)/5
Let a(r) be the first derivative of -4*r**3/9 - 1. Let a(s) = 0. Calculate s.
0
Let f be (0 - 0) + 4/8. Let m be 3/2 + (0 - 1). Factor -f*t**3 - 1/2*t**2 + 1/2 + m*t.
-(t - 1)*(t + 1)**2/2
Factor -2/3*t**2 + 0 + 0*t - 1/3*t**3 + 2/3*t**4 + 1/3*t**5.
t**2*(t - 1)*(t + 1)*(t + 2)/3
Let j(r) = -r**2 + 2*r - 1. Let c be -4*((-22)/(-8) - 3). Let a be j(c). Solve 2/9*b**2 + 0*b + a = 0.
0
Suppose 4*u - 25 = -u + 5*i, 0 = u + 3*i - 5. Determine d so that -27/4*d**2 - 3*d**3 + 81/4*d**4 + 15*d**u + 0 + 3/2*d = 0.
-1, 0, 1/4, 2/5
Let q = -17 - -19. What is l in l**2 + 3*l**q + 26*l - 18*l = 0?
-2, 0
Let s(z) be the first derivative of 0*z**2 + 2*z - 3 - 1/21*z**3 + 1/7*z**4 - 9/70*z**5. Let l(x) be the first derivative of s(x). Factor l(b).
-2*b*(3*b - 1)**2/7
Let z be 2 + 1 + 1/(-1). Suppose 0 = -3*a + z*a. Let -j**3 + a*j**4 + 0*j**2 + 1/2*j + 1/2*j**5 + 0 = 0. Calculate j.
-1, 0, 1
Let x(b) be the second derivative of -b**4/18 + 4*b**3/9 - 4*b**2/3 - 17*b. What is d in x(d) = 0?
2
Let c(y) be the first derivative of -5*y**5/4 + 15*y**4/8 + 11*y**3/12 - 3*y**2/2 - y + 13. What is v in c(v) = 0?
-2/5, 1
Let f = 20979 + -18440539/879. Let m = 7054/9669 - f. Suppose 0*p + 0 + 50/11*p**5 - m*p**2 + 48/11*p**3 - 90/11*p**4 = 0. What is p?
0, 2/5, 1
Let o(v) = v**3 + v + 1. Let x(w) = 4*w**3 - 6*w**2 + 4*w + 1. Let u(g) = -o(g) + x(g). Find j, given that u(j) = 0.
0, 1
Factor -2/7*f**2 + 6/7*f**3 - 6/7*f**4 + 2/7*f**5 + 0*f + 0.
2*f**2*(f - 1)**3/7
Let h(g) = 4*g. Let u be h(2). Suppose -3*r = -u + 2. What is v in -4*v + 5*v - 2*v**2 + 3*v**r + 4 + 3*v = 0?
-2
Let w = 23 + -10. Let b(z) = -8 - 9 - w*z - 2 - z**2. Let t(x) = -x**2 + x + 1. Let d(v) = b(v) + t(v). Let d(j) = 0. What is j?
-3
Let d be ((-11)/(-2) - 4) + -1. Determine s, given that -1/2*s**2 - d*s**4 + 0 - s**3 + 0*s = 0.
-1, 0
Let y = 531 + -529. What is v in 6/13*v - 4/13 - 2/13*v**y = 0?
1, 2
Factor 5/6*m**4 - 5/6*m**2 + 0 + 5/6*m**3 - 5/6*m.
5*m*(m - 1)*(m + 1)**2/6
Let d(x) be the first derivative of 0*x**4 + 5 + 0*x**2 - 2/5*x**5 + 0*x + 2/3*x**3. Factor d(w).
-2*w**2*(w - 1)*(w + 1)
Suppose 31 = 2*z - 5*q, 3*z - 2*q - 3*q - 59 = 0. Factor -z*v**4 + 28*v**4 - 2*v**5 + 2*v**3.
-2*v**3*(v - 1)*(v + 1)
Factor h**3 + 5*h**2 + 3*h**5 + 3*h**4 - 8*h**2 - 4*h**3.
3*h**2*(h - 1)*(h + 1)**2
Let g(z) be the second derivative of -z**4/3 + 8*z**3/3 - 8*z**2 + 45*z. Let g(b) = 0. Calculate b.
2
Let i(z) be the first derivative of 3*z**6/2 + 3*z**5 - 21*z**4/4 - 21*z**3 - 24*z**2 - 12*z + 4. Factor i(a).
3*(a - 2)*(a + 1)**3*(3*a + 2)
Suppose 0*b + 5 = b. Factor -1 - 3*r**2 - 3*r - b - 6*r.
-3*(r + 1)*(r + 2)
Let g(f) be the third derivative of -1/18*f**4 + 0*f - 5*f**2 + 3/40*f**6 - 2/45*f**5 + 0*f**3 + 1/252*f**8 - 19/630*f**7 + 0