. What is x?
-2, 0
Let w = 2/3 + -1/6. Factor p**3 + 0 - w*p**2 - 1/2*p**4 + 0*p.
-p**2*(p - 1)**2/2
Let z(j) = -j**3 - 5*j**2 - 6*j - 3. Let g be z(-4). Suppose -g - 5 = -5*f. What is o in -o**5 + 0 + 0 - f*o**4 - o**3 = 0?
-1, 0
Let i be ((-168)/(-9))/(-4)*6/(-64). Let h(f) be the first derivative of -1/2*f + 7/8*f**2 + 1/6*f**3 + 3 - i*f**4. Find u, given that h(u) = 0.
-1, 2/7, 1
Let d(w) = -5*w**4 - 4*w**3 + 39*w**2 - 23*w + 7. Let o(n) = 2*n**4 + 2*n**3 - 20*n**2 + 12*n - 4. Let t(k) = 4*d(k) + 7*o(k). Factor t(s).
-2*s*(s - 1)*(s + 2)*(3*s - 2)
Factor -2*v**4 - 9*v + v**5 - 4*v**4 - 2*v**5 - 14*v**3 - 2 - 16*v**2.
-(v + 1)**4*(v + 2)
Suppose 0*b + b + 5*w = 3, 5*w = -2*b + 6. Find x such that 8/15*x**b + 4/5*x - 2/15 - 6/5*x**2 = 0.
1/4, 1
Let i(s) be the second derivative of 75*s**5/4 + 75*s**4/2 + 30*s**3 + 12*s**2 - 10*s. Factor i(v).
3*(5*v + 2)**3
Let b be (-3)/(-1) + (3 - 2). Suppose c - b + 2 = 0. Find o such that 6*o - 3*o**2 - 4*o**c - 21*o**3 - 8*o**2 = 0.
-1, 0, 2/7
Let c be (0 + -5 - -5)/(1*2). Factor -2*w**4 + 0*w + 0 + 4/5*w**3 + c*w**2.
-2*w**3*(5*w - 2)/5
Let 25/6*y**2 + 5/3 - 55/6*y = 0. What is y?
1/5, 2
Let f(t) be the second derivative of t**8/5040 + t**7/2520 - t**6/360 - t**5/360 + t**4/36 + t**3 - 5*t. Let n(b) be the second derivative of f(b). Factor n(l).
(l - 1)**2*(l + 1)*(l + 2)/3
Let b(h) be the second derivative of 0*h**4 - 1/135*h**6 - 1/189*h**7 + 0*h**2 + 3*h + 0*h**3 + 1/45*h**5 + 0. Solve b(j) = 0 for j.
-2, 0, 1
Let d(i) be the third derivative of i**7/350 + i**6/100 + i**5/100 + 4*i**2. Factor d(v).
3*v**2*(v + 1)**2/5
Let r(b) be the third derivative of -b**5/140 + b**4/56 + 28*b**2 - 2*b. Factor r(a).
-3*a*(a - 1)/7
What is k in -15/4*k**2 - 6*k - 3/4*k**3 - 3 = 0?
-2, -1
Find y such that -1/7*y**2 + 2/7*y**3 - 1/7*y**4 + 0*y + 0 = 0.
0, 1
Factor 4/5*q**3 + 0*q**2 - 6/5*q**4 + 0*q + 0 + 2/5*q**5.
2*q**3*(q - 2)*(q - 1)/5
Let g = -107/18 - -37/6. Factor 0 + g*b**4 + 4/9*b**3 + 0*b + 2/9*b**2.
2*b**2*(b + 1)**2/9
Let f(p) be the first derivative of -1/18*p**4 + 0*p**2 - 2/27*p**3 + 1/27*p**6 + 0*p + 2/45*p**5 - 3. Factor f(i).
2*i**2*(i - 1)*(i + 1)**2/9
Let h(k) be the first derivative of k**4/10 - k**2/5 - 8. Determine b, given that h(b) = 0.
-1, 0, 1
Suppose -19 = 16*t - 83. Find u such that 0*u + 0*u**2 - 1/2*u**t + 0 + 3/2*u**5 - u**3 = 0.
-2/3, 0, 1
Let r(c) = 3*c**2 - 9*c + 6. Let m(q) = -3*q**2 + q**2 - 18*q + 8*q**2 - 10 + 22. Let o(v) = 3*m(v) - 5*r(v). Factor o(l).
3*(l - 2)*(l - 1)
Let 0 - 2/5*z**4 - 26/5*z**2 - 16/5*z**3 - 12/5*z = 0. What is z?
-6, -1, 0
Factor -1/6*t**3 - 2/3 - 4/3*t - 5/6*t**2.
-(t + 1)*(t + 2)**2/6
Let s(y) = -4*y**3 - 10*y**2 - 5*y - 5. Let a(f) = -f + 1. Let m(q) = 3*a(q) + s(q). Factor m(v).
-2*(v + 1)**2*(2*v + 1)
Let i be 2*(2 - 0 - 0). Suppose 2*r = -h - i, -3*r + 1 - 14 = -2*h. Factor -2 + 4 + 0*v**2 - h*v**2.
-2*(v - 1)*(v + 1)
Let t be (-26)/(-10) + 216/(-360). Solve 2*s**4 - 2/9 - 4/3*s**3 + 4/3*s - 16/9*s**t = 0 for s.
-1, 1/3, 1
Let d(a) = -7*a**4 + 4*a**3 - 7*a**2. Let v(l) = -22*l**4 + 12*l**3 - 22*l**2. Let u(i) = 16*d(i) - 5*v(i). Factor u(o).
-2*o**2*(o - 1)**2
Let i(v) be the first derivative of 9/8*v**4 + 4 + 11/2*v**3 - 9/2*v + 15/4*v**2. Let i(j) = 0. Calculate j.
-3, -1, 1/3
Let u(n) be the second derivative of -2*n + 0 + 1/20*n**5 - 3/2*n**2 + 0*n**3 - 1/8*n**4. Let c(x) be the first derivative of u(x). Factor c(q).
3*q*(q - 1)
Let z(d) be the first derivative of -2/35*d**5 + 2 + 1/21*d**6 - 3/14*d**4 - 2/7*d**2 + 0*d + 10/21*d**3. Factor z(l).
2*l*(l - 1)**3*(l + 2)/7
Let k = -644/5 + 652/5. What is h in k + 2/5*h**2 + 8/5*h = 0?
-2
What is n in -12/5*n**2 + 24/5*n + 2/5*n**3 - 16/5 = 0?
2
Let i = -3415/7 - -489. Factor 0 + i*v**2 + 8/7*v**4 + 12/7*v**3 + 2/7*v + 2/7*v**5.
2*v*(v + 1)**4/7
Let k(u) be the third derivative of -1/12*u**4 - 1/120*u**6 + 0 - 1/20*u**5 + 0*u**3 + 0*u + 3*u**2. Determine r so that k(r) = 0.
-2, -1, 0
Let d(b) be the first derivative of -b**6/360 - b**5/60 - b**4/24 - b**3/3 - 4. Let w(j) be the third derivative of d(j). Factor w(u).
-(u + 1)**2
Suppose 10*m - 5*m = -10. Let l be -4 - m - (-1 + -5). Suppose 1/3*g**5 - 2/3*g**3 - 2/3*g**2 + 1/3*g**l + 1/3*g + 1/3 = 0. What is g?
-1, 1
Suppose 9/5*t**3 - 9/5*t + 11/5*t**2 - 1/5*t**4 - 2 = 0. What is t?
-1, 1, 10
Let z(n) be the third derivative of n**5/450 - n**4/60 - 4*n**2. Solve z(x) = 0.
0, 3
Let u(x) = 125*x**4 - 155*x**3 - 125*x**2 - 15*x - 85. Let p(n) = -9*n**4 + 11*n**3 + 9*n**2 + n + 6. Let k(t) = 85*p(t) + 6*u(t). Factor k(i).
-5*i*(i - 1)*(i + 1)*(3*i - 1)
Let t(a) = -a**5 + a**4 + a**3. Let n = 2 - 6. Let k(f) = f**5 + 3*f**4 - 12*f**3 + 10*f**2 - 5*f + 1. Let m(u) = n*t(u) - 2*k(u). Determine w so that m(w) = 0.
1
Suppose -d - 3*q = 10, -8 = -0*d + 2*d + 3*q. Solve -2*n - d*n**2 - 4 - 4*n**2 + 5*n**2 + 6*n = 0 for n.
2
Let v = 32 - 11. Suppose 13 = 5*z - 4*z + 3*m, v = 3*z + 3*m. Factor -2*l**3 - 2*l**z + 4*l**3 + 0*l**3.
-2*l**3*(l - 1)
Suppose 2*m - 4 - 2 = 0. Find t such that -t**2 + 3*t**2 + 4*t - m*t - 3*t = 0.
0, 1
Let d be (2 - 69/36)*(-4 - -8). Determine x, given that 0 + x**3 + 1/3*x + x**2 + d*x**4 = 0.
-1, 0
Suppose -68*x + 130*x = 58*x. Factor 2/7*t + x + 2/7*t**2.
2*t*(t + 1)/7
Suppose 5 + 3 = 4*p. Let m(a) = 2*a**3 + 4*a**2. Let s(g) = -g**2 - g - 1. Let o(t) = p*s(t) + m(t). Factor o(k).
2*(k - 1)*(k + 1)**2
Find y such that 3*y - 1 + 11*y**2 - 5*y - 8*y**2 = 0.
-1/3, 1
Let m(g) be the second derivative of g**7/168 - g**5/80 + 11*g - 3. Suppose m(l) = 0. What is l?
-1, 0, 1
Let d be ((-8)/10)/(6/(-15)). Factor 0*u**3 - u**2 - d*u - u**3 + u - u**2.
-u*(u + 1)**2
Let z(y) be the third derivative of y**8/504 + 2*y**7/105 + 13*y**6/180 + 2*y**5/15 + y**4/9 + 32*y**2. Factor z(l).
2*l*(l + 1)**2*(l + 2)**2/3
Let l = -3 + 6. Factor -2*u + 2*u - l*u**4 - 3*u**3 + 6*u**4.
3*u**3*(u - 1)
Let i = -2 + 4. Let g be 6 + 3/3 + -2. Factor -3 - 5*u**2 + 0*u**i - 3*u + g.
-(u + 1)*(5*u - 2)
Suppose -6 = -18*t + 12*t. Suppose t + 4*p + 9/4*p**3 + 21/4*p**2 = 0. What is p?
-1, -2/3
Let y(x) be the third derivative of -81*x**6/220 - 117*x**5/110 - 10*x**4/11 - 4*x**3/11 - 9*x**2. Suppose y(r) = 0. Calculate r.
-1, -2/9
Let m = 0 - -2. Let x(n) be the first derivative of -m + 1/12*n**4 + 2/3*n + 5/6*n**2 + 4/9*n**3. Find y such that x(y) = 0.
-2, -1
Let u(g) be the first derivative of -g**5/10 + g**4/8 + g**3/3 - 9. Factor u(o).
-o**2*(o - 2)*(o + 1)/2
Let u(w) be the third derivative of w**8/20160 + w**7/3780 + 5*w**4/24 - 6*w**2. Let p(m) be the second derivative of u(m). Factor p(b).
b**2*(b + 2)/3
Let o = 0 + -2. Let z be 0 - (-3 - (o + 1)). Factor -j**z + 0*j**2 + 1 + 2*j - j**3 - j.
-(j - 1)*(j + 1)**2
Let x(k) = -k**2 - 5*k - 4. Let h be x(-3). Let j(z) = -z**3 - 2*z**2 + z + 2. Let m(a) = a + 1. Let d(p) = h*m(p) - j(p). Factor d(s).
s*(s + 1)**2
Let b = -1893/8 + 237. Suppose -3/4 + 9/8*o - b*o**2 = 0. Calculate o.
1, 2
Let d be 12/(-3) + 6/1. Let y be 6/28*21/d. Find j, given that 6*j**2 + 3/2 - y*j**3 - 21/4*j = 0.
2/3, 1
Let w = 160 + -158. Let z(p) be the first derivative of -2/33*p**3 + 0*p**2 + 0*p - w. Factor z(d).
-2*d**2/11
Let n(g) be the second derivative of 0*g**2 - 3*g - 1/54*g**4 + 0 - 1/135*g**6 - 1/45*g**5 + 0*g**3. Suppose n(a) = 0. What is a?
-1, 0
Let x(t) be the third derivative of t**8/2856 - t**6/340 + t**5/255 - 24*t**2. Find c such that x(c) = 0.
-2, 0, 1
Factor 0*j**2 + j**3 - 4*j**2 + 3*j**2 + 0*j**3.
j**2*(j - 1)
Let p = 29 - 86/3. Factor 0 + p*a**2 + 1/3*a.
a*(a + 1)/3
Let l(c) = -2*c**2 + 3*c + 3. Let v(z) = -z**2 + 2*z + 2. Let r(f) = -2*l(f) + 3*v(f). Factor r(h).
h**2
Let i(w) be the first derivative of w**3/3 + w**2/2 + w + 5. Let h(x) = 14*x**2 + 8*x + 14. Let u(l) = -h(l) + 12*i(l). Factor u(j).
-2*(j - 1)**2
Let b(y) = -15*y - 17. Let d(h) = -7*h - 8. Let t(c) = -6*b(c) + 13*d(c). Let p be t(-5). Let -p*s**4 + 0*s**4 + 5*s**4 + s**2 + 4*s**3 + s**2 = 0. What is s?
-1, 0
Let j be 7/(-4) + 5*(-6)/(-15). Let v(i) = -i + 5. Let s be v(3). Factor j*t**s - 1/4*t + 1/4*t**3 - 1/4.
(t - 1)*(t + 1)**2/4
Let z(j) be the third derivative of -j**8/448 - j**7/120 - j**6/240 + j**5/40 + 5*j**4/96 + j**3/24 + 13*j**2. Suppose z(m) = 0. What is m?
-1, -1/3, 1
Let o(n) be the first derivative of n**6/60 + n**5/10 + n**4/4 + n**