t m(d) be the second derivative of -d**4/20 - d**3/5 - 3*d**2/10 - 5*d. Factor m(i).
-3*(i + 1)**2/5
Let j = -13/20 - -371/540. Let o(q) be the first derivative of 4/27*q**3 - 1/9*q**2 + 1/9*q**4 - 2/45*q**5 - j*q**6 - 2 - 2/9*q. Factor o(g).
-2*(g - 1)**2*(g + 1)**3/9
Factor 2/7*m**2 + 8/7 + 10/7*m.
2*(m + 1)*(m + 4)/7
Let q(t) = -t**2 + 1. Let f(v) = 1. Suppose 4*p = 10 + 2. Let a(h) = p*f(h) - 3*q(h). Determine n so that a(n) = 0.
0
Let h(t) be the first derivative of -5 - 9/2*t**2 + 6*t + t**3. What is g in h(g) = 0?
1, 2
Let t(f) = f**4 + f**3 - f. Let v(y) = -y**4 + 3*y**3 + 8*y**2 + 6*y. Let c(a) = 6*t(a) + 3*v(a). Factor c(o).
3*o*(o + 1)*(o + 2)**2
Let g(x) = 3*x**2 + 4*x. Let m(f) = -f**2 - 1. Let v(r) = -3*g(r) - 12*m(r). Suppose v(y) = 0. What is y?
2
Factor -2/11*v**2 - 20/11*v - 50/11.
-2*(v + 5)**2/11
Solve -4*n**2 + n**2 - 2 + 5 = 0.
-1, 1
Let y(u) = u**2 + 3*u + 4. Let q be y(-2). Solve 1/5*t**q - 1/5*t**4 + 1/5*t + 0 - 1/5*t**3 = 0.
-1, 0, 1
Let u be (7/3)/((-1)/(-21)). Let h be (2/7)/(7/u). Factor 0*n**3 + 0*n**2 + 6*n + 3*n**3 + h + 6*n**2 - n**3.
2*(n + 1)**3
Let h be 6/15*(-10)/(-6). Let o = -20/9 - -32/9. Suppose 0 + 2/3*b**2 + 0*b - o*b**3 + h*b**4 = 0. What is b?
0, 1
Suppose -4 = -a - 2. Determine v so that -1 - 1 + 2*v + 2 + 2*v**a = 0.
-1, 0
Let a(y) be the second derivative of -2/9*y**3 + 1/72*y**4 + 5*y + 0 + 4/3*y**2. Factor a(t).
(t - 4)**2/6
Let w = 3395/9 - 377. Let -2/9 + 2/9*x**2 + 2/9*x - w*x**3 = 0. Calculate x.
-1, 1
Suppose 0 = 2*x - 26 - 20. Let k = x + -45/2. Factor -1/4*l**5 + 0*l**2 + 0*l**4 + k*l**3 + 0 - 1/4*l.
-l*(l - 1)**2*(l + 1)**2/4
Let m(g) = 0 + 1 - 2*g - g**2 + 2*g**2 + g. Let y(s) = -5*s**2 + 10*s - 2. Let u(h) = -6*m(h) - y(h). Suppose u(l) = 0. What is l?
-2
Let m(r) be the third derivative of -1/120*r**5 + 0*r**3 - 1/96*r**4 + 1/420*r**7 + 1/1344*r**8 + 0*r + 0 + 0*r**6 - 4*r**2. Factor m(c).
c*(c - 1)*(c + 1)**3/4
Let k(x) = 2*x - 1. Let p be 2*2 - (3 - 1). Let i be k(p). Factor -5 + 5 - 2*r + 2*r**i.
2*r*(r - 1)*(r + 1)
Let j be (-2)/(-3 - 15/(-6)). Factor -3*y**2 + 3*y - 3*y - 5*y - 6 - j*y.
-3*(y + 1)*(y + 2)
Let a(y) = -2*y**2 - 10*y + 18. Let j(w) = -w**2 - 1. Let l(s) = -a(s) - 3*j(s). Factor l(n).
5*(n - 1)*(n + 3)
Let p(f) be the second derivative of f**10/15120 - f**8/1680 + f**6/360 + f**4/12 - f. Let h(m) be the third derivative of p(m). Let h(v) = 0. Calculate v.
-1, 0, 1
Let r(z) be the second derivative of -z**7/84 + z**5/20 - z**3/12 + 12*z. Factor r(d).
-d*(d - 1)**2*(d + 1)**2/2
Suppose 2 = 2*r - 6. Suppose -1/5 + 2/5*i**3 - 1/5*i**5 + 2/5*i**2 - 1/5*i**r - 1/5*i = 0. What is i?
-1, 1
Let d(i) be the third derivative of i**10/151200 - i**9/60480 - i**5/15 - 4*i**2. Let j(t) be the third derivative of d(t). Determine l, given that j(l) = 0.
0, 1
What is f in 5 - f**3 + f**3 + 38*f**2 + 5 + 42*f + 6*f**3 = 0?
-5, -1, -1/3
Let u(v) be the third derivative of v**6/40 + v**5/4 + 3*v**4/8 - 9*v**3/2 + 2*v**2 - 24*v. Solve u(k) = 0 for k.
-3, 1
Let q(j) be the second derivative of -7*j**5/20 + j**4 - j**3/2 - j**2 - 11*j. Factor q(v).
-(v - 1)**2*(7*v + 2)
Let y = 2686/5 - 537. Find g such that -y*g**2 + 6/5*g - 9/5 = 0.
3
Let z be 14/4*(-4)/(-8). Let x(k) be the first derivative of -2 - 13/4*k**2 - 25/6*k**3 - k - z*k**4. Factor x(f).
-(f + 1)*(2*f + 1)*(7*f + 2)/2
Let s(c) = c**2 + 7*c + 3. Let a be s(-7). Let i be (1*a/(-2))/(-3). Factor -i - z**3 - 5/2*z**2 - 2*z.
-(z + 1)**2*(2*z + 1)/2
Let p(m) be the third derivative of 0 + 0*m**5 + 0*m + 1/24*m**4 - 1/360*m**6 + m**2 + 1/9*m**3. Factor p(d).
-(d - 2)*(d + 1)**2/3
Find a, given that 0*a**4 + 0 + 0*a**3 + 0*a + 2/7*a**5 + 0*a**2 = 0.
0
Factor -17*q**4 + 5*q**4 - 6*q**3 - q**4 + 12*q**4 - 5*q**2.
-q**2*(q + 1)*(q + 5)
Let b(f) be the first derivative of 2*f**3/45 + 3. Factor b(s).
2*s**2/15
Let w(q) be the second derivative of -q**6/60 + q**4/12 + q**2/2 + 2*q. Let o(a) be the first derivative of w(a). Find m such that o(m) = 0.
-1, 0, 1
Let s = -24 - -12. Let n be (-53)/s - 1/(-4). Determine q so that 4/3*q**2 + 0*q + 6*q**3 + n*q**4 + 0 = 0.
-1, -2/7, 0
Let q(x) be the third derivative of -x**7/1680 - x**6/120 - 3*x**5/80 - x**4/12 - 5*x**3/48 + 48*x**2. Factor q(h).
-(h + 1)**3*(h + 5)/8
Let y = -16 + 769/48. Let c(m) be the third derivative of 0*m + 0 + 1/60*m**5 + 0*m**3 + y*m**4 - 2*m**2 + 1/240*m**6. Find z such that c(z) = 0.
-1, 0
Let o = -15 - -17. Determine q, given that 2/7*q**o + 2/7*q + 0 = 0.
-1, 0
Factor 3/5*y**3 - 48/5*y + 3/5*y**2 + 12.
3*(y - 2)**2*(y + 5)/5
Factor 0*o**4 + 0*o**2 + 2/5*o**3 - 1/5*o**5 + 0 - 1/5*o.
-o*(o - 1)**2*(o + 1)**2/5
Suppose -3 + 3/2*d**2 + 3/2*d = 0. Calculate d.
-2, 1
Let w(c) = -2*c**3 - 6*c**2 + 2*c + 4. Let r(p) be the second derivative of p**4/12 + 2*p. Let m(v) = -2*r(v) - w(v). Solve m(k) = 0.
-2, -1, 1
Let b = 84 + -82. Let f(c) be the third derivative of 1/240*c**5 - 2*c**b + 1/32*c**4 + 0 + 1/12*c**3 + 0*c. Factor f(g).
(g + 1)*(g + 2)/4
Suppose 0 = w - 4*w - 42. Let q be 4/w + (-92)/(-28). Factor c**3 - 2*c**2 + 2 - 3*c**q - 2*c + 4*c**3.
2*(c - 1)**2*(c + 1)
Let h be 1/4*3 + (-3)/6. What is o in 1/4*o**2 + 0*o + h*o**4 + 1/2*o**3 + 0 = 0?
-1, 0
Let s = 4697/5 + -939. Find r, given that -4/5 - 6/5*r - s*r**2 = 0.
-2, -1
Let y = 5 - 2. Let v = 2 - 0. Factor -4*o**3 - v*o**y + 4*o**3.
-2*o**3
Suppose 11 = 3*k - 1. Suppose -n + 10 = -4*s, 0 = n + k*n + 2*s - 6. What is a in n + 2*a**4 - 2*a**5 + 6*a**3 - 4*a**2 - a**3 - a**3 - 2*a = 0?
-1, 1
Let b(o) = -o**5 + o**4 + o**2 + o. Let r(i) = -4*i**5 + 6*i**4 + 2*i**2 + 2*i. Let y(t) = -2*b(t) + r(t). Factor y(j).
-2*j**4*(j - 2)
Factor -2 + o + 4*o**2 - o**4 + 6*o**5 - 4*o**5 + o - o**4 - 4*o**3.
2*(o - 1)**3*(o + 1)**2
Let d(l) be the second derivative of -1/36*l**4 + 1/18*l**3 + 0*l**2 + 0 + 3*l. Find i such that d(i) = 0.
0, 1
Let m be ((-8)/6)/((-8)/12). Let k be ((-5)/(-10))/(m/8). Find x such that x**3 - k*x**2 + 4*x**2 + 0*x**2 = 0.
-2, 0
Suppose -3 = -j - 0*j. Solve 1/2*i**j + 0*i + 0*i**2 + 0 - 1/2*i**5 + 0*i**4 = 0.
-1, 0, 1
Let a(z) be the first derivative of z**6/18 + z**5/3 + 5*z**4/6 + 10*z**3/9 + 5*z**2/6 + z/3 - 5. Find k, given that a(k) = 0.
-1
Let p = -18 - -20. Suppose -3*d = 4*w - 32, 2*d + p*d + 2*w = 26. Factor -3/2*k**2 + 1 - 1/2*k**3 + 1/2*k + 1/2*k**d.
(k - 2)*(k - 1)*(k + 1)**2/2
Let u(o) = -o**2 + 8*o - 8. Suppose -3*m + 1 + 17 = 0. Let s be u(m). Factor 4*l**3 + 2*l**2 + 0*l**2 + 2*l**4 + 0*l**s.
2*l**2*(l + 1)**2
Factor -1/2*l**5 - 3/2*l**3 + 1/2*l**2 + 0*l + 3/2*l**4 + 0.
-l**2*(l - 1)**3/2
Suppose 4*y - 8 = -0*y. Let g(d) = 0 - 1 - y*d**3 + d**3 - d - d**4. Let l(c) = c**5 - 8*c**4 - 3*c**3 - 5*c - 5. Let r(b) = 5*g(b) - l(b). Factor r(i).
-i**3*(i - 2)*(i - 1)
Let v = -31 + 32. Let f be v/((-3)/((-12)/16)). Let 1/2*m**4 - f*m**2 + 0*m + 1/4*m**3 + 0 = 0. What is m?
-1, 0, 1/2
Let k be 19/(-5) + (-8)/40. Let i = -10/3 - k. Solve -2*w**3 + i*w**4 - 2/3*w + 0 + 2*w**2 = 0.
0, 1
Suppose 5 + 22 = 9*f. Factor -1/4*i**f - 3/4*i**2 - 3/4*i - 1/4.
-(i + 1)**3/4
Let l(i) be the second derivative of 3/40*i**5 + 5/16*i**4 + 3*i + 1/2*i**3 + 3/8*i**2 + 0. Determine s, given that l(s) = 0.
-1, -1/2
Let l be 0/(-2 - (0 + 0)). Suppose -3*s - 4*s + 21 = l. Factor 9 + 45*u + 75*u**2 + 125/3*u**s.
(5*u + 3)**3/3
Solve 5*v**2 - 16*v**4 - v**2 - 4*v**3 + 16*v**3 = 0.
-1/4, 0, 1
Suppose -3 = 2*h - 7. Find v such that 0 + v + 1/2*v**h = 0.
-2, 0
Let u be 9*(-1 + (-8)/(-6)). Suppose 0 = 2*b - 4*b. Determine w, given that -2/3*w**u + 2/3*w**2 + 0*w + b = 0.
0, 1
Suppose 2*t - 5*f = 20, -t + 0*t + 2*f = -9. Let s = -3 + t. Factor -5*y**4 - 5*y - 1 - 8*y**2 - y**2 - 10*y**3 - y**s - y**5.
-(y + 1)**5
Let j(g) be the first derivative of g**4/16 + g**3/12 - g**2/8 - g/4 - 9. Suppose j(r) = 0. Calculate r.
-1, 1
Let m(c) be the first derivative of c**7/140 + c**6/60 - c**5/120 - c**4/24 + c**2 + 3. Let r(u) be the second derivative of m(u). Let r(v) = 0. Calculate v.
-1, 0, 2/3
Let v(i) = 10*i**3 + 15*i**2 + 30*i - 10. Let f(u) = -u**3 - u**2 - u. Let x(j) = -15*f(j) - v(j). Let x(m) = 0. What is m?
-2, 1
Factor 2*s + 4*s + 0*s - 5*s + s**2.
s*(s + 1)
Let z(o) be the third derivative of o**8/168 - 2*o**7/105 + o**5/15 - o**4/12 - 7*o**2. Let z(f) = 0. Calculate f.
-1, 0, 1
Let k(z) be the second derivative of -3*z*