.
-1, 0, 1
Determine j, given that 2*j**3 + 10*j**2 - 14*j**2 + 6*j**2 = 0.
-1, 0
Let k be (-10)/6*1158/15. Let n = k + 130. Determine z so that 2/3*z**2 + n*z + 0 = 0.
-2, 0
Let g be (9 + -8)*0/(-2). Let w(u) be the second derivative of 0*u**2 + 1/15*u**6 + 3*u - 1/6*u**4 + g*u**3 + 0*u**5 + 0. Factor w(j).
2*j**2*(j - 1)*(j + 1)
Determine c, given that 0 - 4/5*c + 2/5*c**2 = 0.
0, 2
Let l be 0*(-3)/15 - 1. Let a be l - -5*(-2)/(-6). Factor -a*q + 1/3*q**2 + 1/3.
(q - 1)**2/3
Suppose -3*v = t + 10, 3*t - 2*v = -7*v - 14. Suppose -t*w + 0 = -14. Solve -16*s**4 - 11*s**3 - 2*s**2 - 7*s - w*s**5 + 7*s = 0 for s.
-1, -2/7, 0
Suppose -174*b + 166*b = 0. Suppose 3/2*c**4 + b - c + 4*c**3 + 3/2*c**2 = 0. Calculate c.
-2, -1, 0, 1/3
Let i(d) be the second derivative of -d**4/78 - 8*d**3/39 - 16*d**2/13 - 28*d. Factor i(o).
-2*(o + 4)**2/13
Let o(l) = l**2 - 2*l - 12. Let i be o(-3). Factor -1/4*t**i - 5/4*t - 1/2 - t**2.
-(t + 1)**2*(t + 2)/4
Suppose 3*l = -2*l - 3*h + 26, 2*h + 34 = 4*l. Let z be (6/l)/3 - 0. Factor z*d**5 + 0*d**3 + 0*d + 0*d**2 + 2/7*d**4 + 0.
2*d**4*(d + 1)/7
Let l be (-1)/((-13)/3 - -4). Let k(j) be the first derivative of -1/3*j**l - 2 + 3/2*j**2 - 2*j. Find p such that k(p) = 0.
1, 2
Let q(w) = -w - 3. Let t be q(0). Let b be 2/t*(-3 + 0). Find v, given that -v + b + 2*v**2 - 4 + 3*v - 2*v**3 = 0.
-1, 1
Factor 6*a + 9*a**4 - 2*a**5 - 24*a**3 + 16*a**2 - 6*a + 3*a**4.
-2*a**2*(a - 2)**3
Let d(h) be the second derivative of -h**5/10 - 13*h**4/6 - 16*h**3 - 36*h**2 + 18*h. Find y such that d(y) = 0.
-6, -1
Suppose -4*f = 4*w - 0*w - 4, 3*f - 17 = 4*w. Let q(o) be the first derivative of o**4 - 1 + 0*o**2 + 0*o + 2/5*o**5 + 2/3*o**f. Find s such that q(s) = 0.
-1, 0
Let f(m) be the third derivative of m**8/1680 - 2*m**7/525 + m**6/200 + m**5/75 - m**4/30 - 9*m**2. Solve f(t) = 0.
-1, 0, 1, 2
Suppose 3*t = 6 - 3. Let h be 14/21*t/2. Factor 1/3*k - 1/3 - h*k**3 + 1/3*k**2.
-(k - 1)**2*(k + 1)/3
Let o = 7/22 + 2/11. Find p such that 0 + o*p**2 + 1/2*p = 0.
-1, 0
Suppose -3*j + 5 = m - 1, -j + 2 = -2*m. Factor -5*n + 2*n + 12*n**j - 35*n**4 + 47*n**4 - 3*n**5 - 18*n**3.
-3*n*(n - 1)**4
Let y(c) be the first derivative of -2/5*c**2 + 2/5*c - 3 + 2/15*c**3. Find m, given that y(m) = 0.
1
Let n(h) be the first derivative of -h**3/9 - h**2/3 - h/3 + 12. Let n(c) = 0. What is c?
-1
Let z(b) be the first derivative of -b**4/10 - 2*b**3/5 - 2*b**2/5 - 3. Find m such that z(m) = 0.
-2, -1, 0
Suppose -10 = 5*q + 4*n, n + 28 = 4*q - 3*n. Let l be ((-90)/35 + q)*-1. Determine j so that -l - 2/7*j + 2/7*j**2 = 0.
-1, 2
Let s(w) be the third derivative of 1/480*w**6 + 0*w + 0*w**4 + 0*w**5 + 3*w**2 + 0*w**3 + 0. Factor s(m).
m**3/4
Find u, given that 10*u + 0*u**2 - u**2 - 8*u + 3*u**2 = 0.
-1, 0
Let m(c) = -c**3 + 6*c**2 - 5*c + 2. Let h be m(5). Factor -2*t**h - 2*t**2 + t**3 + t + 2*t**2.
t*(t - 1)**2
Let m(a) = -a**3 - a**2 + 3*a - 1. Let z be m(2). Let j(q) = q**2 - q + 4. Let g(y) = 2*y**2 - y + 8. Let k(h) = z*j(h) + 3*g(h). Factor k(v).
-(v - 2)**2
Let o(r) be the third derivative of 0*r + 3*r**2 + 1/4*r**4 + 0 + 0*r**3 + 3/20*r**5 + 1/40*r**6. Factor o(t).
3*t*(t + 1)*(t + 2)
Suppose -13*f = -14*f. Let i(r) be the first derivative of 1/4*r**2 + f*r**3 + 0*r - 1/8*r**4 + 2. Determine y, given that i(y) = 0.
-1, 0, 1
Let g(r) = r**3 - 3*r**2 + 3*r - 2. Let w be g(2). Suppose w*s = 5*s - 10. Suppose -2*k**3 + 3*k**3 - k**3 + 4*k**s - 2*k**5 + 2*k - 4*k**4 = 0. What is k?
-1, 0, 1
Factor 4/5*x**3 - 4/5*x**2 + 4/5*x**4 - 4/5*x + 0.
4*x*(x - 1)*(x + 1)**2/5
Let k be ((-6)/9)/(4/(-6)). Let h be -4 + k + 25/5. Factor -3/2 - 3/2*z + 3/2*z**h + 3/2*z**3.
3*(z - 1)*(z + 1)**2/2
Let m = -68 - -206/3. Let c(d) be the third derivative of -m*d**3 + 0*d + 0 - 1/60*d**5 - 1/6*d**4 - 3*d**2. Suppose c(g) = 0. Calculate g.
-2
Let m be 2 + 2 + 1/(-1). Suppose -13*c + 18*c - 20 = 0. Factor f**5 + 14*f**4 + 4*f**m - 18*f**3 - c*f**3 - 5*f**5 + 10*f**2 - 2*f.
-2*f*(f - 1)**3*(2*f - 1)
Let a(i) be the second derivative of -i**6/210 - 3*i**5/140 - i**4/28 - i**3/42 + 8*i. Factor a(n).
-n*(n + 1)**3/7
Let k(f) be the third derivative of 0*f**7 - 7/780*f**6 + 1/390*f**5 + 0 - 1/39*f**3 + 1/52*f**4 - 3*f**2 + 1/546*f**8 + 0*f. Find l, given that k(l) = 0.
-1, 1/2, 1
Let r(i) be the third derivative of i**2 + 1/12*i**3 + 1/120*i**5 + 1/24*i**4 + 0*i + 0. Factor r(o).
(o + 1)**2/2
Determine k so that -4/5*k**3 - 4/5*k**5 + 0*k**2 + 0 + 0*k + 8/5*k**4 = 0.
0, 1
Let f be (46/(-69))/(1 + (1 - 3)). What is w in 0 + 5/3*w**3 - 2/3*w**2 - f*w**4 + 0*w = 0?
0, 1/2, 2
What is b in -2/5*b**4 + 0*b**2 + 0*b**3 + 0 + 0*b = 0?
0
Let u(f) be the first derivative of f**2/2 - f + 3. Let r(h) = 2*h**3 + 4*h - 6. Let d(z) = -r(z) + 6*u(z). Solve d(l) = 0.
-1, 0, 1
Let x(g) be the third derivative of 1/12*g**4 - 1/6*g**3 + 0 - 1/60*g**5 + 2*g**2 + 0*g. Factor x(o).
-(o - 1)**2
Let d be (0/(-2))/(1 - 0). Let h be 34/14 + 27/(-63). Find i such that d - 1/2*i + 1/2*i**h = 0.
0, 1
Suppose 5*z = -16 + 26. Determine s so that 4 - 4*s**z + 3 - 3 = 0.
-1, 1
Let v be 72/(-81)*-3*1/2. Find b such that -8/9*b**3 - 2/9 - 2*b**2 - v*b = 0.
-1, -1/4
Let w = 224/9 - 421/18. Factor 0 - 3*j**2 + 3/2*j**3 + w*j.
3*j*(j - 1)**2/2
Let c(m) be the first derivative of 0*m**2 + 1/3*m**3 + 1/12*m**4 - 3 - m. Let x(y) be the first derivative of c(y). Factor x(p).
p*(p + 2)
Suppose 5*m + 2*x = 4*x, 0 = m - 4*x + 18. Factor 0 + 2/3*t + 2/3*t**m.
2*t*(t + 1)/3
Let x(s) = -8*s**3 - 20*s**2 - 17. Let m(a) be the third derivative of a**6/40 + 7*a**5/60 + a**3 + a**2. Let o(n) = 17*m(n) + 6*x(n). Factor o(z).
z**2*(3*z - 1)
Let c(n) be the second derivative of -n**5/10 + n**4/3 + n**3 + 5*n. Factor c(f).
-2*f*(f - 3)*(f + 1)
Let f = 85/2 + -42. Find h such that 1/4*h**2 + 1/4*h - f = 0.
-2, 1
Let n = 1469/16 - 92. Let d = 41/48 + n. Let -d*b**2 + 4/3 - 2/3*b = 0. What is b?
-2, 1
Let a = 5961 + -506679/85. Let j = 26/17 + a. Factor -2/5*g**2 - 8/5 + j*g.
-2*(g - 2)**2/5
Let i be -2 + (4 - 4/2). Let b(g) be the first derivative of 2 + 1/2*g**2 + 9/4*g**4 - 4/5*g**5 - 2*g**3 + i*g. Let b(h) = 0. Calculate h.
0, 1/4, 1
Let w(h) be the first derivative of -4 - 2/5*h**2 - 2/5*h - 2/15*h**3. Factor w(z).
-2*(z + 1)**2/5
Factor -6075/2*t**2 - 6 - 270*t.
-3*(45*t + 2)**2/2
Let v(l) be the second derivative of 16*l**7/147 - 8*l**6/105 - 23*l**5/70 + l**4/6 + l**3/3 + l**2/7 - 2*l. Find u such that v(u) = 0.
-1, -1/4, 1
Suppose 10*r - 8*r + 20 = 0. Let h be (-3)/(-6)*(-2 - r). Suppose -2/3*l + l**2 - l**h + 2/3*l**3 + 0 = 0. What is l?
-1, 0, 2/3, 1
Suppose -2*u + 82 = -148. Determine s so that -2*s**4 - u*s + 4*s**3 + 115*s - 2*s**2 = 0.
0, 1
Suppose -2*o + 6 = 2. Factor -9*w**2 - w - 5*w - 2*w - 3*w**3 + o*w.
-3*w*(w + 1)*(w + 2)
Let c(v) = 6*v**4 + 2*v**3 - 7*v + 4. Let i(j) = -8*j + 2*j**4 + 2*j**3 + 5*j**4 + 5 + j**4 - j**4. Let w(m) = -6*c(m) + 5*i(m). Let w(h) = 0. What is h?
-1, 1
Let q(v) = -3*v**3 - 11*v**2 + 3*v + 11. Let c(r) = r**3 + 4*r**2 - r - 4. Let w(k) = 11*c(k) + 4*q(k). Factor w(y).
-y*(y - 1)*(y + 1)
Let c(o) = -1 - 28*o**3 + 2*o + 4*o + 24*o**3. Let h(t) = t**3 - t + 1. Let q(g) = g**2 + 2*g + 2. Let d be q(-2). Let w(v) = d*c(v) + 6*h(v). Factor w(y).
-2*(y - 2)*(y + 1)**2
Let s be (-12)/(-2)*(0 - (-4)/8). Let n(i) be the first derivative of -2*i + 1/3*i**s - 3 - 1/2*i**2. Let n(b) = 0. What is b?
-1, 2
Let f(s) = -7*s**3 - s**2 + 15*s + 5. Let c(i) = 13*i**3 + i**2 - 30*i - 11. Let y(t) = -4*c(t) - 7*f(t). Find o such that y(o) = 0.
-1, 3
Let c = -13 - -16. Let -1/6*a**c + 0*a + 1/6*a**2 + 0 = 0. What is a?
0, 1
Let h(k) = k**3 - 4*k**2 + 2. Let m be h(4). Suppose 0 = -m*o + 2 + 2. Factor -5*s**2 - 2 + 3*s + 4*s**o + 0*s.
-(s - 2)*(s - 1)
Suppose -3*l + f = 2*l - 6, -3*l + 3*f = 6. Suppose -w**l + 1/3*w + 0 = 0. Calculate w.
0, 1/3
Solve 0 - 2/3*z + 1/3*z**4 - 1/3*z**2 + 2/3*z**3 = 0 for z.
-2, -1, 0, 1
Let l be (-11)/3 - (-4)/6. Let v = l + 7. What is g in -v + 5 + g - 1 - g**3 = 0?
-1, 0, 1
Let j(o) be the first derivative of 1/4*o**2 - o + 1/6*o**3 - 6. Factor j(k).
(k - 1)*(k + 2)/2
Determine j so that -4 + 114*j**3 + 1 - 19*j - 66*j**2 + 138*j**3 - 147*j**4 - 17*j = 0.
-1/7, 1
Let m(x) be the third derivative of -3*x**7/70 - x**6/4 - 3*x**5/20 + 45*x**2. Factor m(q).
-3*q**2*(q + 3)*(3*q + 1)