4 = 0. Factor -3*d - 162*d**3 - v*d**5 + 21*d**2 - 10*d**2 + 0*d**2 + 25*d**2 + 324*d**4.
-3*d*(3*d - 1)**4
Factor 101 - 11 + 17*g**2 - 28*g - 15*g**2 + 8.
2*(g - 7)**2
Let s be 24/(-9)*(4 + -1). Let k = s - -8. Factor -3/2*h**4 + 0*h + 0*h**2 + 2*h**5 + k - 1/2*h**3.
h**3*(h - 1)*(4*h + 1)/2
Suppose -1130*f = -1122*f. Factor -3/2*w**4 + 0 + 0*w**3 + f*w + 0*w**2 + 3/2*w**5.
3*w**4*(w - 1)/2
Let h = 6 + -4. Suppose -q - q = -6. Factor -3*k + q*k - k**3 - h*k**2 - k.
-k*(k + 1)**2
Let o = -18 + 9. Let t be (o/18)/(2/(-8)). Factor 0 - 2/11*n - 2/11*n**3 - 4/11*n**t.
-2*n*(n + 1)**2/11
Let c(y) be the first derivative of y**5/20 - y**4/16 - y**3/12 + y**2/8 - 8. Factor c(q).
q*(q - 1)**2*(q + 1)/4
Suppose -4*a + 9*a = 20. Let c(u) be the third derivative of -u**2 + 1/6*u**a - 2/3*u**3 - 1/60*u**5 + 0*u + 0. Factor c(j).
-(j - 2)**2
Let b(p) be the first derivative of -p**6/6 + p**4/2 - p**2/2 - 9. Factor b(y).
-y*(y - 1)**2*(y + 1)**2
Suppose -6*i = -i - 20. Let 5*w**4 + w**3 + w**2 + w**2 + 2*w**3 - 4*w**i = 0. Calculate w.
-2, -1, 0
Let a(b) be the third derivative of b**8/1680 + b**7/150 + 19*b**6/600 + b**5/12 + 2*b**4/15 + 2*b**3/15 + 28*b**2. Factor a(w).
(w + 1)**3*(w + 2)**2/5
Factor -12/5 + 2*j + 2/5*j**2.
2*(j - 1)*(j + 6)/5
Let y(z) be the first derivative of -4 - 2/9*z**3 + 2/45*z**5 - 4/9*z + 1/18*z**4 - 5/9*z**2. Determine q, given that y(q) = 0.
-1, 2
Let y be ((60/8)/(-3))/(-5). Let k = 4 - 2. Determine x so that -1/2*x**3 - 1/2*x**k + 1/2*x + y = 0.
-1, 1
Let f(l) be the first derivative of l**4/4 + l**3/3 - l**2/2 - l - 5. Factor f(m).
(m - 1)*(m + 1)**2
Let k(t) be the third derivative of t**5/30 - t**4/12 - 2*t**3/3 + 18*t**2. Factor k(s).
2*(s - 2)*(s + 1)
Let a(c) be the third derivative of c**7/350 - c**6/200 - c**5/100 + c**4/40 - 2*c**2. Factor a(w).
3*w*(w - 1)**2*(w + 1)/5
Let h = 205/27 + 20/27. Factor 8*p**3 + 16/3*p - 80/3*p**4 + 0 + 64/3*p**2 + h*p**5.
p*(p - 2)**2*(5*p + 2)**2/3
Let h(f) be the first derivative of -f**5/45 - f**4/36 + f**3/9 + f**2/2 + 2. Let q(z) be the second derivative of h(z). Factor q(c).
-2*(c + 1)*(2*c - 1)/3
Let i be (-3)/(-6) - (-10)/4. Let r(d) be the first derivative of 2 + 1/3*d**i + d**2 + d. Solve r(c) = 0.
-1
Let r(c) = c**2 + 1. Let x(l) = 1 - 11*l + 11*l + 2*l**2. Let q(o) = -3*r(o) + 2*x(o). Factor q(y).
(y - 1)*(y + 1)
What is n in -826*n - n**3 + 4*n**2 - 3*n**2 + 828*n = 0?
-1, 0, 2
Let a(m) be the third derivative of 0*m**3 + 1/72*m**4 + 0 + m**2 + 1/180*m**5 + 0*m. Factor a(o).
o*(o + 1)/3
Suppose 5*f = -14 + 4. Let m be (4 - (-114)/9) + f. Factor -4/3 - 121/3*p**2 - m*p.
-(11*p + 2)**2/3
Suppose 2*t + 2*o = 216, t + o + 114 = 2*t. Let i be 2/(-11) + t/66. Suppose 2*r + i*r**2 + 1/2 = 0. Calculate r.
-1, -1/3
Suppose d = k - 3, -4*k + 4 = -0. Let f be 2/(-7) + d/(-7). Factor 2/7*j**3 - 2/7*j**2 + f + 0*j.
2*j**2*(j - 1)/7
Let g be (0 + 4)*4/8. What is o in -274*o - 10 + 280*o - o**g - 2 + 3 = 0?
3
Let r(v) be the third derivative of -1/105*v**7 - 4/3*v**3 - 3*v**2 + 1/10*v**6 + v**4 + 0 + 0*v - 13/30*v**5. Determine x so that r(x) = 0.
1, 2
Let j be -2 + 9 + (3 - 7). Determine i so that -2/7*i**2 + 8/7*i + 2/7 - 8/7*i**j = 0.
-1, -1/4, 1
Let c be (-273)/560 + 1/2. Let p(t) be the third derivative of 0 + 1/96*t**4 + c*t**5 - 2*t**2 + 0*t**3 + 0*t + 1/240*t**6. Factor p(d).
d*(d + 1)*(2*d + 1)/4
Let g(s) be the second derivative of -s**5/20 + s**4/12 + 7*s. Solve g(p) = 0.
0, 1
Let y(w) be the second derivative of -w**7/1260 + w**6/720 - 3*w**2/2 + 4*w. Let m(l) be the first derivative of y(l). Factor m(d).
-d**3*(d - 1)/6
Let m be (-8 + 198/24)/((-6)/(-8)). Let -2/3*l**2 + 0 + m*l**3 + 0*l = 0. Calculate l.
0, 2
Factor 3 + i**2 - 3 - 2*i - 3*i**2.
-2*i*(i + 1)
Let h = -46 + 231/5. Let w(z) be the second derivative of 0 - 1/10*z**4 - 1/5*z**3 - 1/50*z**5 - h*z**2 + z. Factor w(b).
-2*(b + 1)**3/5
Determine w, given that 0*w**2 - 2/17*w**3 + 0 + 0*w = 0.
0
Let w(d) = 2*d + 1. Let j be w(2). Let k(h) be the second derivative of -3/70*h**j - 1/105*h**6 - 1/14*h**4 + 0*h**2 + 0 - 1/21*h**3 - h. Factor k(y).
-2*y*(y + 1)**3/7
Solve 13*t**2 + 4 - 18*t + 45/2*t**3 - 25/2*t**4 = 0.
-1, 2/5, 2
Determine p so that 2/5 + 3/5*p + 1/5*p**2 = 0.
-2, -1
Let z be (-7)/((-42)/12) + 1. Solve 0*b**4 - b**z + 0 + 0*b - 1/3*b**2 + 4/3*b**5 = 0 for b.
-1/2, 0, 1
Let o = -509 + 511. Let 2/9*a**o + 0*a - 2/9 = 0. What is a?
-1, 1
Suppose -3*g + 8 = -g. Suppose 0 = 2*o + g*y - 15 - 5, -2*y + 8 = 0. Factor 1/3*j**o - 2/3*j + 1/3.
(j - 1)**2/3
Find b, given that 3/2*b**3 - 1/2*b**5 - 1/2*b**4 + b + 0 + 5/2*b**2 = 0.
-1, 0, 2
Let h(x) be the first derivative of -4/7*x**3 + 6/7*x - 1/7*x**4 + 6/35*x**5 + 1/21*x**6 + 1/7*x**2 - 10. Suppose h(v) = 0. What is v?
-3, -1, 1
Let m be (-2)/3 - (-1)/(-3). Let o be 5 - 3 - (-2)/m. Determine c so that o - 4/3*c + 14/3*c**2 = 0.
0, 2/7
Let -k**3 + 0 - 1/3*k**4 + 1/3*k**2 + k = 0. What is k?
-3, -1, 0, 1
Let f = 6 + -5. Suppose -g - 6 = -4*g. What is s in 1 + 2*s + s**g - f = 0?
-2, 0
Let o(q) be the second derivative of 5/3*q**4 - 2*q - 1/3*q**3 + 8/3*q**6 - 16/21*q**7 - 33/10*q**5 + 0 + 0*q**2. Solve o(k) = 0 for k.
0, 1/4, 1
Let j(k) be the first derivative of -k**5/5 + 3*k**4/4 - 2*k**2 - 9. Factor j(b).
-b*(b - 2)**2*(b + 1)
Suppose w + w + 10 = r, -w - 5 = 4*r. Factor -8*x**5 + r*x**3 + 8*x**5 + 6*x**2 + 3*x**5 - 3*x**3 - 6*x**4.
3*x**2*(x - 2)*(x - 1)*(x + 1)
Let n(o) be the first derivative of o**5/330 + o**4/132 + 2*o**2 - 1. Let m(l) be the second derivative of n(l). Factor m(y).
2*y*(y + 1)/11
Let p(h) be the second derivative of -h**5/210 + 3*h**2/2 - 3*h. Let n(k) be the first derivative of p(k). Factor n(o).
-2*o**2/7
Suppose 0*x + 9 = 3*x. Suppose 0 = 5*q - 2 - x. Factor -3*y**2 + 3 + q - 1.
-3*(y - 1)*(y + 1)
Suppose 0*n + 3 = 3*n. Let t(b) be the first derivative of 1/8*b**4 - 1/6*b**3 - n - 1/4*b**2 + 1/10*b**5 + 0*b. Find g, given that t(g) = 0.
-1, 0, 1
Let b = 585 - 585. Factor 0*j**3 + b*j + 0 - 2/7*j**4 + 2/7*j**2.
-2*j**2*(j - 1)*(j + 1)/7
Let r(i) be the third derivative of -i**8/336 + i**6/60 - i**4/24 + 2*i**2. Factor r(v).
-v*(v - 1)**2*(v + 1)**2
Solve 0*w**2 + 0 + 8*w**4 + 26/3*w**3 - 2/3*w = 0 for w.
-1, -1/3, 0, 1/4
Let p(m) be the third derivative of 5*m**2 + 0 + 1/120*m**6 + 5/24*m**4 - 1/15*m**5 - 1/3*m**3 + 0*m. Determine g, given that p(g) = 0.
1, 2
Let a be (24/(-16))/(2/(-20)). Suppose 3 = -3*q + a. What is r in 8/5*r - 2/5*r**q - 16/5*r**2 + 0 + 2*r**3 = 0?
0, 1, 2
Let m be -2 + (-54)/(-15) - (-10)/25. Factor -2*u**5 - 16/5*u**m - 36/5*u**4 + 6/5*u - 44/5*u**3 + 4/5.
-2*(u + 1)**4*(5*u - 2)/5
Let q = -66 + 92. Let t be (q/7)/(-1) - -4. Factor -6/7*y**2 + t*y + 0.
-2*y*(3*y - 1)/7
Let x(m) be the second derivative of 1/15*m**6 - 1/6*m**4 - 1/10*m**5 + 0 + 0*m**2 + 1/3*m**3 + 5*m. Determine s, given that x(s) = 0.
-1, 0, 1
Let u = -1 + 0. Let h(w) = w**3 + w**2 - w. Let b(f) = -13*f**3 - 16*f**2. Let v(o) = u*b(o) - 4*h(o). Factor v(r).
r*(3*r + 2)**2
Let q(c) be the third derivative of 2/105*c**5 + 0*c**4 - 2/735*c**7 + 0*c**3 + 0 - 8*c**2 + 0*c + 1/210*c**6. Find m such that q(m) = 0.
-1, 0, 2
Factor 2/7 + 2/7*k**4 + 0*k**3 + 0*k - 4/7*k**2.
2*(k - 1)**2*(k + 1)**2/7
Determine j so that -3/4*j**2 + 3/4 + 0*j = 0.
-1, 1
Let r(p) = -66*p**3 + 129*p**2 - 117*p + 27. Let o(n) = -5*n**3 + 10*n**2 - 9*n + 2. Let y(d) = 27*o(d) - 2*r(d). Factor y(l).
-3*l*(l - 3)*(l - 1)
Let p be 6/(-27) - ((-8)/(-18) + -1). Let 1/3*z**2 - 2/3*z + p = 0. What is z?
1
Factor -1/3*x**3 - 5*x**2 - 125/3 - 25*x.
-(x + 5)**3/3
Let u be (-3 - (1 - 1))/(-1). Let o = -423 - -427. Suppose 2/9*j**o - 2/9*j**2 + 0 + 2/9*j - 2/9*j**u = 0. What is j?
-1, 0, 1
Let r = 31/24 + -5/8. Let u(a) be the first derivative of -3*a**2 - 4*a + 2 - r*a**3. Find c such that u(c) = 0.
-2, -1
Let v(b) be the second derivative of -b**10/60480 + b**9/30240 + b**8/13440 - b**7/5040 - b**4/4 + 3*b. Let z(f) be the third derivative of v(f). Factor z(r).
-r**2*(r - 1)**2*(r + 1)/2
Suppose 0 = 7*u - u. Let s(z) be the second derivative of -1/6*z**4 - 2/3*z**3 - z**2 - 3*z + u. Suppose s(i) = 0. What is i?
-1
Let b(t) = 29*t**2 + 37*t - 5. Let w(l) = -14*l**2 - 18*l + 2. Let g(v) = 6*b(v) + 13*w(v). Factor g(y).
-4*(y + 1)*(2*y + 1)
Let v(r) = -r**2 + 5*r + 2. Let g be v(5). Let d(m)