
Let y(l) be the first derivative of l**4/18 - 2*l**3/27 - 2*l**2/9 - 4. Factor y(q).
2*q*(q - 2)*(q + 1)/9
Let m(r) = -r + 10. Let f be m(11). Let o = f - -1. Find q such that -4/9*q + 4/9*q**3 + o*q**2 - 2/9*q**4 + 2/9 = 0.
-1, 1
Let h(p) = p**2 - 7*p - 9. Let q be h(8). Let y be (0 - 3)*(q + 0). Suppose -2/3*f**y + 1/3*f + 1/3*f**4 + 1/3 + 1/3*f**5 - 2/3*f**2 = 0. What is f?
-1, 1
Let v be 4/93*(-189)/14. Let b = v + 224/279. Factor b*m**2 + 0*m + 0 + 2/9*m**3.
2*m**2*(m + 1)/9
Let j(a) be the third derivative of -a**8/1680 - 2*a**7/315 - a**6/36 - a**5/15 - a**4/24 + 3*a**2. Let l(h) be the second derivative of j(h). Factor l(m).
-4*(m + 1)**2*(m + 2)
Let h(f) = -f + 4 + 5 + 2 + 0*f. Let k be h(8). Factor -2/3*c**k + 4/3*c - 2/3*c**2 + 0.
-2*c*(c - 1)*(c + 2)/3
Suppose 5*t = 2*q + 2, -t - 5*q = -0*q + 5. Factor t*f + 2/11*f**3 + 2/11*f**4 - 2/11*f**5 + 0 - 2/11*f**2.
-2*f**2*(f - 1)**2*(f + 1)/11
Let n(f) be the second derivative of -f - 1/21*f**4 + 0*f**3 - 1/210*f**6 + 0 + 1/35*f**5 + 0*f**2. Factor n(m).
-m**2*(m - 2)**2/7
Suppose 3*n + 2 = -2*h, 14 = 5*n - 0*h - h. Suppose 7*j - 6 = 4*j. Factor -2 + 0 - q**n + 5*q - j*q.
-(q - 2)*(q - 1)
Let c = -10 - -14. Factor -4 - 4*p**2 + 3*p + c + 7*p**2.
3*p*(p + 1)
Let n(r) be the third derivative of r**8/5040 + r**7/1680 + r**6/2160 + r**3/6 + 2*r**2. Let c(v) be the first derivative of n(v). Factor c(z).
z**2*(z + 1)*(2*z + 1)/6
Let r(j) be the third derivative of -5*j**8/252 + 5*j**7/126 - j**6/72 + 26*j**2. Find q such that r(q) = 0.
0, 1/4, 1
Let j be ((-2)/(-3))/((-160)/15)*-6. Factor -j*c**2 + 0 + 1/8*c + 3/8*c**3 - 1/8*c**4.
-c*(c - 1)**3/8
Let w(a) be the first derivative of -a**6/27 + 4*a**5/45 + a**4/9 - 8*a**3/27 - a**2/9 + 4*a/9 + 46. Determine m, given that w(m) = 0.
-1, 1, 2
Let m(w) be the second derivative of w**6/60 - w**5/40 + 6*w. Determine j so that m(j) = 0.
0, 1
Let c be 30/77 + (-20)/(-110). Let k = c - 3/7. Factor -1/7 - 1/7*o + 1/7*o**2 + k*o**3.
(o - 1)*(o + 1)**2/7
Let n(y) be the first derivative of y**6/24 + y**5/40 - y**4/16 - y**3/24 + 11. Find g, given that n(g) = 0.
-1, -1/2, 0, 1
Let h be (4 - -5)/((-9)/6). Let k be h/8 + (0 - -1). Suppose 1/4*p + p**4 + 0 + k*p**5 + p**2 + 3/2*p**3 = 0. What is p?
-1, 0
Factor -27/5*f**2 + 48/5*f + 12/5.
-3*(f - 2)*(9*f + 2)/5
Factor 3*z**3 + 7*z**3 - z**3 - 6*z**2 - 11*z**3.
-2*z**2*(z + 3)
Suppose -2*w + 17*w - 4*w**3 - 5*w + 4*w**2 - 4 - 6*w = 0. What is w?
-1, 1
Let x(z) be the third derivative of z**6/240 - z**4/48 + 21*z**2. Factor x(n).
n*(n - 1)*(n + 1)/2
Let t(x) = -x**3 + 4*x**2 - x + 2. Let o be t(4). Let l be 3/12*(-4)/o. Suppose 1/2*v**5 - l*v**4 - 1/2*v**3 + 1/2*v**2 + 0 + 0*v = 0. What is v?
-1, 0, 1
Factor -36/7*u**3 - 3/7*u**5 + 30/7*u**2 + 18/7*u**4 - 9/7*u + 0.
-3*u*(u - 3)*(u - 1)**3/7
Solve -1/3*u**3 - 1/3*u + 0 - 2/3*u**2 = 0 for u.
-1, 0
Let p(c) be the third derivative of -11*c**7/350 - 61*c**6/600 - 7*c**5/100 + 3*c**4/40 + c**3/15 - 15*c**2. Let p(m) = 0. Calculate m.
-1, -2/11, 1/3
Let m be (36/(-64))/((-2)/8). Factor 0 - g - 7/4*g**4 + 3*g**2 + m*g**3.
-g*(g - 2)*(g + 1)*(7*g - 2)/4
Suppose 249*n**4 - 251*n**4 - 8*n**2 + 0*n**3 - 8*n**3 = 0. What is n?
-2, 0
Factor 4/9*a**2 - 8/9*a + 4/9.
4*(a - 1)**2/9
Let 2/13*m**4 + 2/13*m**5 - 2/13*m**2 + 0*m - 2/13*m**3 + 0 = 0. Calculate m.
-1, 0, 1
Let z(y) be the second derivative of y**6/40 - 3*y**4/16 - y**3/4 - 4*y. Factor z(d).
3*d*(d - 2)*(d + 1)**2/4
Let u(z) = -3*z**3 - 5*z**3 - 21*z - 9 - z - 2*z + 24*z**2. Let n(d) = d**3 - 3*d**2 + 3*d + 1. Let r(j) = -51*n(j) - 6*u(j). Determine v, given that r(v) = 0.
1
Let u(p) be the second derivative of -p**5/90 - p**4/27 + p**3/27 + 2*p**2/9 + 3*p. Factor u(g).
-2*(g - 1)*(g + 1)*(g + 2)/9
Find y such that -4*y**2 + y**3 - y - 13*y + y**3 - 8 = 0.
-1, 4
Determine b so that 1/7*b**2 + 3/7 - 4/7*b = 0.
1, 3
Let h(i) = -20*i**4 + 38*i**3 + 2*i**2 - 38*i + 7. Let u(b) = -7*b**4 + 13*b**3 + b**2 - 13*b + 2. Let o(p) = 4*h(p) - 11*u(p). Solve o(n) = 0 for n.
-1, 1, 2
Factor -7*b**4 - 5*b**5 + 12*b**3 - 5*b - 13*b**4 - 42*b**3 - 31*b**2 + 11*b**2.
-5*b*(b + 1)**4
Let 3*f**2 + 5*f**5 - 3*f**4 - 8*f**5 + 5*f**3 - 6*f + 4*f**3 = 0. Calculate f.
-2, -1, 0, 1
Factor -10*q**3 - 13*q**2 + q**3 + 7*q**2 + 3*q**5.
3*q**2*(q - 2)*(q + 1)**2
Factor 0 - 4/5*s**2 + 2/5*s**4 - 2/5*s**3 + 0*s.
2*s**2*(s - 2)*(s + 1)/5
Let x(o) be the second derivative of o**5/20 - o**4/6 - o**3/6 + o**2 + o. Factor x(t).
(t - 2)*(t - 1)*(t + 1)
Determine u so that -1/8*u**3 - 5/8*u**2 + 1/8*u**4 + 0 - 3/8*u = 0.
-1, 0, 3
Suppose -2*s - 6 = 3*m - m, 5*m + 3*s = -11. Let p be (-16)/(-8) + m + 1. Determine b, given that -b**p - b**3 + 0*b - 2*b**2 + 5*b**2 - b = 0.
0, 1
Let f(c) be the second derivative of -c**7/84 + c**6/15 - c**5/10 - c**4/12 + 5*c**3/12 - c**2/2 - 11*c. Let f(j) = 0. Calculate j.
-1, 1, 2
Let n(g) be the third derivative of 0 - 1/180*g**6 + 0*g**4 + 3*g**2 + 0*g + 1/630*g**7 + 1/180*g**5 + 0*g**3. Find o such that n(o) = 0.
0, 1
Let 4*p + 0*p - 12*p**2 + 8*p**2 = 0. What is p?
0, 1
Let z(i) be the second derivative of 1/3*i**4 - i - 1/20*i**5 + 0 - 5/6*i**3 + i**2. Factor z(w).
-(w - 2)*(w - 1)**2
Let s be (-2)/(12/10)*-3. Find h, given that -s*h - 19*h**2 + 9*h**2 - 1 + 6*h**2 = 0.
-1, -1/4
Let g(z) = -3*z**2 + 36*z + 45. Let m(o) = -3*o**2 + 37*o + 44. Let j(f) = 2*g(f) - 3*m(f). Factor j(c).
3*(c - 14)*(c + 1)
Let h(f) be the third derivative of f**8/952 + 11*f**7/1785 + f**6/85 + 2*f**5/255 + 5*f**2. Suppose h(y) = 0. Calculate y.
-2, -1, -2/3, 0
Let t(b) be the third derivative of -3*b**7/14 + 5*b**6/8 - 7*b**5/12 + 5*b**4/24 - 2*b**2. Suppose t(k) = 0. What is k?
0, 1/3, 1
Let c(o) = -5*o**3 + 50*o + 9 + 7*o**2 - 2*o - 16. Let w(m) = -2*m**3 + 2*m**2 + 16*m - 2. Let b(a) = -2*c(a) + 7*w(a). Find s, given that b(s) = 0.
-2, 0, 2
Factor -4/7*h**3 - 2/7*h**4 + 0*h**2 + 4/7*h + 2/7.
-2*(h - 1)*(h + 1)**3/7
Let h(s) = s - 1. Let v be h(3). Let c = -14 - -20. Solve 13*f**2 - 3 + 15*f**v - 4*f**2 - c*f = 0 for f.
-1/4, 1/2
Let x(o) = -o - 9. Let w be x(-15). Let h(q) = q**3 - q**2 - 1. Let u be h(2). Determine m so that 2*m**2 - 2*m**4 - w*m**u + 2*m**3 + 0*m**4 + 4*m + 0*m = 0.
-2, -1, 0, 1
Suppose -3*z + 2*s = -5, 5*z - 4*z - 11 = -4*s. Factor -2*n**2 - 3*n**3 + 3*n**z - 2*n**3.
-2*n**2*(n + 1)
Let v be -7 + 10 - (-38)/(-14). Let b(p) be the first derivative of 8/21*p**3 + v*p - 5/7*p**2 + 2. Factor b(o).
2*(o - 1)*(4*o - 1)/7
Let u be ((-252)/27 + 10)*(-9)/(-8). Factor 9/4*s**3 + u*s**2 + 0*s + 3/4*s**5 + 0 + 9/4*s**4.
3*s**2*(s + 1)**3/4
Suppose p + 4 = 2*p. Suppose 0*l - 4*l**2 + 2*l**2 - p - 6*l = 0. Calculate l.
-2, -1
Suppose -2*p - l = 10, p + 16 = -p - 4*l. Let x be -12*(p + 11/3). Factor 0*b + 0*b**2 - 15/2*b**x + 9/2*b**5 + 0 + 3*b**3.
3*b**3*(b - 1)*(3*b - 2)/2
Let b(j) be the first derivative of j**5/20 + j**4/8 - j**3/4 - j**2 - j + 12. Find u, given that b(u) = 0.
-2, -1, 2
Let p be (-20)/(-6) + 4/6. Suppose 2*t = -5*k + 7, -2*k - p*t - 4 = 2*k. Factor 3*w - 6*w**3 - 2*w**2 + w + 3*w**3 + w**k.
-2*w*(w - 1)*(w + 2)
Let o = -6 - -9. Suppose z + 2*z = 2*g + 10, 6 = -o*g. Let -1/2*l**z + 1/2*l**3 - 1/2*l + 1/2 = 0. What is l?
-1, 1
Let o(h) be the second derivative of h**7/2520 - h**6/720 - h**5/60 + h**4/6 - 3*h. Let x(l) be the third derivative of o(l). Determine b so that x(b) = 0.
-1, 2
Let l = 3 - 1. Suppose 0*u + 10 = l*u. Factor 0*y - y**3 + u*y - 4*y.
-y*(y - 1)*(y + 1)
Suppose -3*k = 5*n - 6, 0*k + 5*n = k + 18. Let d be 0 + (-1)/(k/9). Let 2*c**5 - 2*c**d + 0*c + 2/3*c**2 + 0 - 2/3*c**4 = 0. Calculate c.
-1, 0, 1/3, 1
Let u = 2 + -2. Let o = 1 + 7. Solve u*h**2 - 4*h + o + 2*h**2 - 4*h = 0 for h.
2
Let m(w) be the third derivative of w**8/90720 - w**7/22680 - w**5/60 - 2*w**2. Let n(u) be the third derivative of m(u). Let n(z) = 0. What is z?
0, 1
Let l be 24*(1 - 8/9). Factor -l*j - 2/3*j**2 - 8/3.
-2*(j + 2)**2/3
Let k be 1/3*3*2. Find b, given that 9*b**k + 6*b**3 + 2*b + 2*b - b = 0.
-1, -1/2, 0
Let 47*r**2 + 8*r**3 - 76*r**2 + 41*r**2 - 4*r**4 = 0. Calculate r.
-1, 0, 3
Let t(a) be the first derivative of a**4/34 + 2*a**3/51 - a**2/17 - 2*a/17 - 9. Find s, given that t(s) = 0.
-1, 1
Let j be (-5 + 10)/(-5)*0. Let b(d) be the third derivative of -1/180*d**5 + 0*d + 1/9*d**3 - 4*d**2 + j - 1/72*d**4.