 j such that n(j) = 0.
1
Let p = 178857/5 + -35632. Let b = p - 139. Find h, given that -b*h**2 + 0 + 0*h = 0.
0
Let w(i) be the second derivative of -i**4/4 + 8*i**3 - 96*i**2 + i - 22. Determine o, given that w(o) = 0.
8
Let f be 5 + (6/8 - (-246)/(-48)). Factor 3/8*g**5 - 1/4*g**3 + 3/4*g**2 - f*g**4 - 1/8*g - 1/8.
(g - 1)**3*(g + 1)*(3*g + 1)/8
Let o(v) be the first derivative of 2*v + 7/6*v**4 + 4/7*v**2 + 1 + 4/3*v**3. Let f(d) be the first derivative of o(d). Find g such that f(g) = 0.
-2/7
Let m be (6/(-4))/(-2 + 2 - 3). Find q such that 1/2*q**4 + 0 + q**3 + m*q**2 + 0*q = 0.
-1, 0
Let k(j) be the third derivative of 0*j + 0 - 5*j**2 + 1/80*j**6 - 1/8*j**4 + 0*j**3 - 1/40*j**5. Suppose k(z) = 0. What is z?
-1, 0, 2
Let v be 128/156 + (-4)/26. What is g in 0 + 2/3*g**2 + v*g**4 + 0*g - 4/3*g**3 = 0?
0, 1
Let j(z) = z**4 + z**3 - 4*z + 2. Let d(r) = 2*r**4 - 4*r + 2. Let v(a) = -3*d(a) + 4*j(a). Find t such that v(t) = 0.
-1, 1
Solve 72/7*d - 4/7*d**2 - 324/7 = 0 for d.
9
Suppose 0 = -4*s + 14 - 6. Factor -s*g + 0*g + 4*g - 2*g**3.
-2*g*(g - 1)*(g + 1)
Let r be (2/5)/((-7)/(-70)). Let j(o) be the third derivative of 3/20*o**5 - r*o**2 + 0 + 3/8*o**4 + 1/40*o**6 + 0*o + 1/2*o**3. Let j(a) = 0. What is a?
-1
Let 1/9 - 2/9*n**3 - 4/9*n + 5/9*n**2 = 0. What is n?
1/2, 1
Let k = -8 + 12. Let g(z) be the third derivative of 2*z**2 - 1/12*z**k + 0*z**3 - 1/60*z**6 + 0*z + 1/15*z**5 + 0. What is o in g(o) = 0?
0, 1
Find w, given that 8/7*w - 8/7 - 2/7*w**2 = 0.
2
Let z(n) be the first derivative of -n**6/3 - 2*n**5/5 + 3*n**4/8 + 2*n**3/3 + n**2/4 + 6. Find v such that z(v) = 0.
-1, -1/2, 0, 1
Let q(m) be the second derivative of 0 - 1/48*m**4 + 2*m + 1/24*m**3 + 0*m**2. Factor q(c).
-c*(c - 1)/4
Let l(i) = -7*i**4 + 2*i**2 + 2*i + 2. Let n(a) = -190*a**4 + 55*a**2 + 55*a + 55. Let k(m) = 55*l(m) - 2*n(m). Factor k(s).
-5*s**4
Let b(x) be the second derivative of -x**6/150 + x**4/20 + x**3/15 - 50*x. Factor b(q).
-q*(q - 2)*(q + 1)**2/5
Let r(c) = 6*c**2 - 12*c + 12. Let q(a) be the third derivative of -a**5/60 + a**2. Let k(t) = 3*q(t) + r(t). Factor k(y).
3*(y - 2)**2
Let l(z) be the third derivative of z**5/20 + 11*z**2. Factor l(k).
3*k**2
Let m be ((36/8)/9)/((-6)/(-4)). Let f(s) be the second derivative of s - 1/45*s**6 + 0*s**4 + 2/9*s**3 - 1/15*s**5 + m*s**2 + 0. Factor f(t).
-2*(t - 1)*(t + 1)**3/3
Let q(s) = 2*s**2 + 10*s + 2. Let x be q(-5). Let 0 - 2/3*b**4 - 2/3*b - 2*b**3 - x*b**2 = 0. What is b?
-1, 0
Suppose 12 - 6 = 2*w. Let b(x) be the second derivative of 4*x**2 - x + 0 + 1/6*x**4 - 4/3*x**w. Factor b(f).
2*(f - 2)**2
Let t(d) be the first derivative of d**7/63 - d**6/45 - d**5/30 + d**4/18 - 2*d - 1. Let o(u) be the first derivative of t(u). Suppose o(q) = 0. What is q?
-1, 0, 1
Suppose 3*n + 1 = -4*a, 3*n - 2*n + a = 0. Let b(r) = -r**3 + r - 1. Let h(k) = 2*k**3 + k**2 - 2*k + 2. Let i(m) = n*h(m) + 3*b(m). Let i(x) = 0. Calculate x.
-1, 1
Suppose -w = -7*w. Factor -2/3*d**3 - 2/3*d**2 + w + 0*d.
-2*d**2*(d + 1)/3
Factor -4/7 - 6/7*d - 2/7*d**2.
-2*(d + 1)*(d + 2)/7
Factor 0 - 24/5*w + 4/5*w**2.
4*w*(w - 6)/5
Let r(n) be the second derivative of 0*n**3 + 0 - 1/135*n**6 + 0*n**5 + 2*n - 1/9*n**2 + 1/27*n**4. Solve r(d) = 0.
-1, 1
Factor 1/3*n**3 - 1/3*n + 2/3 - n**2 + 1/3*n**4.
(n - 1)**2*(n + 1)*(n + 2)/3
Let u(b) be the third derivative of -b**6/108 - 4*b**5/135 - b**4/108 + 2*b**3/27 - 7*b**2. Factor u(p).
-2*(p + 1)**2*(5*p - 2)/9
Let i be (-9)/(-5) + 5/25. Let d**3 - i - 2*d**4 - d**5 + 2 - d**2 + 3*d**4 = 0. Calculate d.
-1, 0, 1
Let n(v) = -v**3 + 3*v**2 - v - 2. Let z be n(2). Suppose z*y - 3*y = -9. Factor -q**2 + 3*q + q**y + 0*q**2 + q**4 - 4*q.
q*(q - 1)*(q + 1)**2
Let w(x) be the second derivative of 0 - 1/63*x**7 - 1/15*x**5 + 1/3*x**3 - 1/9*x**4 + 1/15*x**6 - 1/3*x**2 - x. What is u in w(u) = 0?
-1, 1
Factor 0 - 2/9*g - 2/9*g**4 + 2/9*g**3 + 2/9*g**2.
-2*g*(g - 1)**2*(g + 1)/9
Let q be 0/(4*(-3)/(-4)*-1). Determine s so that q - 1/3*s + 1/3*s**3 + 2/3*s**2 - 2/3*s**4 = 0.
-1, 0, 1/2, 1
Let n be 3/(-5)*(-2)/3. Let i be (18/21)/((-180)/(-126)). Factor -i*l + 1/5*l**2 + n.
(l - 2)*(l - 1)/5
Let c be 360/(-8) + -1*1. Let g be 0 - (c/14 + 3). Let -2/7*j**4 + 2/7*j**3 + g*j**2 + 0 + 0*j - 2/7*j**5 = 0. Calculate j.
-1, 0, 1
Let b(g) be the second derivative of -g**5/10 - 5*g**4/8 - g**3 + g**2 - 7*g. Suppose b(x) = 0. Calculate x.
-2, 1/4
Factor 0*v + 0 + 4/5*v**2.
4*v**2/5
Factor 2 - 4/3*i**2 - 1/3*i**3 - 1/3*i.
-(i - 1)*(i + 2)*(i + 3)/3
Let v(u) be the third derivative of 0 + 1/6*u**4 + 0*u**3 + 0*u - 1/60*u**5 - 3*u**2. Let y(z) = 2*z**2 - 10*z. Let g(x) = 12*v(x) + 5*y(x). Factor g(c).
-2*c*(c + 1)
Let s(i) be the first derivative of 1/8*i**6 + 3 - 3/10*i**5 + 0*i**2 + 1/2*i**3 + 0*i - 3/16*i**4. Solve s(q) = 0 for q.
-1, 0, 1, 2
Let g(y) be the second derivative of y**6/15 - y**5/10 - y**4/2 + y**3/3 + 2*y**2 + 3*y. Find s such that g(s) = 0.
-1, 1, 2
Let w(d) be the first derivative of -d**5/10 - d**4/3 - d**3/3 + 2*d - 1. Let s(x) be the first derivative of w(x). Find z, given that s(z) = 0.
-1, 0
Let t = 853/3 - 284. Let g be (0 + 6)*2/6. Factor -t*k**g - 1/3 - 2/3*k.
-(k + 1)**2/3
Let r(p) be the first derivative of -2/5*p**2 + 0*p + 0*p**4 - 2/25*p**5 + 2/5*p**3 - 2. What is u in r(u) = 0?
-2, 0, 1
Let p(w) be the second derivative of -w**5/210 - w**2 + 5*w. Let a(i) be the first derivative of p(i). Factor a(f).
-2*f**2/7
Let a(w) = -7*w**5 - 9*w**4 + 21*w**3 - 5*w**2 - 11. Let p(h) = 4*h**5 + 4*h**4 - 10*h**3 + 2*h**2 + 6. Let j(l) = -6*a(l) - 11*p(l). Find z such that j(z) = 0.
0, 1, 2
Suppose 0 + 12 = 3*g. Suppose b = -g*b. Solve b + 1/2*r + 1/2*r**2 = 0 for r.
-1, 0
Let 40/13*z**2 + 8/13*z + 18/13*z**3 + 0 = 0. What is z?
-2, -2/9, 0
Let n(t) be the second derivative of -t**7/168 + t**5/40 - t**3/24 - t. What is v in n(v) = 0?
-1, 0, 1
Let f(j) be the second derivative of 3*j**5/140 + 3*j**4/7 - j**3/14 - 18*j**2/7 + 17*j. Determine z, given that f(z) = 0.
-12, -1, 1
Let t(r) be the second derivative of r**6/420 - r**4/84 + 3*r**2/2 + 3*r. Let z(k) be the first derivative of t(k). Factor z(c).
2*c*(c - 1)*(c + 1)/7
Solve -11*l**4 + 0*l**4 + 5*l**5 - 44*l**3 + 30*l**2 - 19*l**4 - 25*l + 64*l**3 = 0.
-1, 0, 1, 5
Let p = 91 - 40. Determine g so that 63*g**4 - 58*g + 219*g**3 - 12 - 147*g**5 - p*g**2 + 15*g - 40*g + 11*g = 0.
-1, -2/7, 1
Let o(d) be the second derivative of d**5/120 + d**4/16 + d**3/6 - 3*d**2/2 - d. Let y(a) be the first derivative of o(a). Factor y(n).
(n + 1)*(n + 2)/2
Let d(b) be the first derivative of b**4 + 4*b**3 - 16*b + 8. Let d(c) = 0. Calculate c.
-2, 1
Let h(k) be the third derivative of k**6/240 + k**5/40 + k**4/24 + 4*k**2. Factor h(c).
c*(c + 1)*(c + 2)/2
Let g = 234 + -933/4. Let o = 49/6 - 20/3. Factor 0*h**3 + 3/2*h**4 - 3/4*h + g*h**5 + 0 - o*h**2.
3*h*(h - 1)*(h + 1)**3/4
Let j be (-6)/(-8) - 37/50. Let u(a) be the third derivative of -a**2 + j*a**5 + 1/30*a**3 + 0*a + 1/40*a**4 + 1/600*a**6 + 0. Suppose u(m) = 0. What is m?
-1
Suppose 5*a = -5*c, 4*c = -7*a + 5*a - 4. Find k such that -3/5*k**4 - 3/5*k + 0 - 9/5*k**a - 9/5*k**3 = 0.
-1, 0
Suppose -13 - 3 = -4*z. Let h(f) be the third derivative of -2*f**2 + 1/24*f**3 + 0*f**z + 0*f + 0 - 1/240*f**5. Suppose h(s) = 0. What is s?
-1, 1
Factor 9/8 - 3*m + 15/8*m**2.
3*(m - 1)*(5*m - 3)/8
Let l(f) = -f**2 - 3. Let t(c) = -6*c**2 - c - 15. Let a(m) = 33*l(m) - 6*t(m). Suppose a(s) = 0. Calculate s.
-3, 1
Let r be (-4)/6 + 121/132. Let u(b) be the first derivative of 1/12*b**6 + 2 + 1/2*b - 1/3*b**3 + r*b**2 + 1/10*b**5 - 1/4*b**4. Factor u(g).
(g - 1)**2*(g + 1)**3/2
Factor 4/5*w**2 + 0 - 8/5*w.
4*w*(w - 2)/5
Let t(b) = 10*b + 92. Let k be t(-9). Determine f so that 1/7*f**k - 1/7 + 0*f = 0.
-1, 1
Let r(x) be the third derivative of -x**9/5760 - x**8/6720 + x**7/480 + x**6/240 - x**5/20 + 3*x**2. Let a(g) be the third derivative of r(g). Factor a(l).
-3*(l - 1)*(l + 1)*(7*l + 2)/2
Let d = -14 - -10. Let i be 3/(-63)*(d - 2). Factor -4/7*w**2 - i*w + 2/7*w**5 + 4/7*w**4 + 0*w**3 + 0.
2*w*(w - 1)*(w + 1)**3/7
Let r be (-32)/(-36) + 18/(-81). Factor -r*b**2 + 2*b - 4/3.
-2*(b - 2)*(b - 1)/3
Let b = -227/3 - -77. Let t(v) = v**3 + 5*v**2 - 6*v + 2. Let n be t(-6). Solve -14/3*y + n*y**2 + b = 0.
1/3, 2
Let d be ((-54)/9