
Let o(a) be the third derivative of 0*a + 3/280*a**7 + 0 - 2*a**2 + 1/240*a**6 + 1/192*a**8 + 0*a**5 + 0*a**4 + 0*a**3. Suppose o(c) = 0. Calculate c.
-1, -2/7, 0
Let g = 80/7 + -153/14. Factor -1/4*z + 1/4*z**3 + 1/2 - g*z**2.
(z - 2)*(z - 1)*(z + 1)/4
Let 0 - 8/7*g + 2/7*g**4 - 8/7*g**2 + 2/7*g**3 = 0. What is g?
-2, -1, 0, 2
Let a(w) be the first derivative of w**4/16 - w**3/12 + 11. Factor a(s).
s**2*(s - 1)/4
Suppose 0 = 13*m - 14*m + 4. Factor 1/2*s**5 - 1/2*s**3 - 1/2*s**m + 0*s + 1/2*s**2 + 0.
s**2*(s - 1)**2*(s + 1)/2
Solve -2/5*x**4 - 2/5*x**3 + 0 + 2/5*x**2 + 2/5*x = 0 for x.
-1, 0, 1
Let c(w) be the first derivative of 2*w**5/5 + 3*w**4/2 + 2*w**3 + w**2 + 1. Determine x so that c(x) = 0.
-1, 0
Let v(s) = 5*s**5 + 11*s**4 + s**3 + s**2 - 3*s - 3. Let w(t) = -4*t**2 + 0*t**2 + 1 + 3*t**2 + t - t**4. Let y(r) = -2*v(r) - 6*w(r). What is k in y(k) = 0?
-1, 0, 2/5
Let o(j) be the second derivative of j**6/540 - 2*j**5/45 + 4*j**4/9 + 5*j**3/6 + 5*j. Let i(v) be the second derivative of o(v). Suppose i(r) = 0. What is r?
4
Solve 4*a**3 - 6*a - 6*a**5 + 5*a**3 - 2*a**4 - 2*a**4 - 4 + 3*a**3 + 8*a**2 = 0.
-1, -2/3, 1
Let g(i) = -14*i**2 - 14*i. Let l be (-7 + 9)/(4/6). Let f(d) = -5*d**2 - 5*d. Let k(j) = l*g(j) - 8*f(j). Factor k(b).
-2*b*(b + 1)
Let w be 20*1 + 1 + -3. Solve -2*o**2 + 5 + 18 + 4 - w*o + 5*o**2 = 0.
3
Let y(g) = 3*g**2 - 9*g + 2. Let t be y(3). Find d, given that 18/11 - 12/11*d + 2/11*d**t = 0.
3
Let v = 13 + -13. Let g be 3 + (-1 - v) + -2. Find r, given that 2/3*r + 2/3*r**3 + 4/3*r**2 + g = 0.
-1, 0
Factor 0 - 2/3*l**3 + 0*l - 1/3*l**2.
-l**2*(2*l + 1)/3
Suppose -20/7*y**3 - 4/7*y**2 - 25/7*y**4 + 0 + 0*y = 0. Calculate y.
-2/5, 0
Suppose -6*v + 27 = 15. Factor 20/7*y**3 + 4/7*y + 0 - 24/7*y**v.
4*y*(y - 1)*(5*y - 1)/7
Let q(m) be the second derivative of 0*m**3 + 0 + 0*m**5 + 1/10*m**6 + 0*m**4 - 2*m + 0*m**2. Solve q(y) = 0.
0
Let f be 0 + ((1 - -2)/(-3))/(-3). Suppose 2/3 + f*d**2 - d = 0. Calculate d.
1, 2
Determine a so that -2/9*a - 2/3*a**2 + 0 = 0.
-1/3, 0
Let j(k) be the third derivative of k**5/210 + 5*k**4/84 + 4*k**3/21 - 2*k**2 - 27. Determine m, given that j(m) = 0.
-4, -1
Let l = 55/372 - 2/31. Let n(g) be the second derivative of -3*g + 0 - l*g**3 - 1/24*g**4 + 0*g**2. Find w such that n(w) = 0.
-1, 0
Let z(p) be the second derivative of p**8/7560 - p**6/540 - p**5/270 - 5*p**3/6 + 6*p. Let k(w) be the second derivative of z(w). Factor k(f).
2*f*(f - 2)*(f + 1)**2/9
Suppose x + x = 12. Let w(o) = o**4 + o**3 - o**2 - o. Let n(j) = 134*j**4 + 230*j**3 + 114*j**2 + 20*j + 2. Let u(q) = x*w(q) - n(q). Factor u(h).
-2*(h + 1)*(4*h + 1)**3
Factor -1 - 4*s - s**2 + 2*s + 0*s.
-(s + 1)**2
Factor -8 - 224*f + 8*f**2 + 220*f - 4*f**2.
4*(f - 2)*(f + 1)
Let b(f) = f + 9. Let l be b(-7). Let d = 1 + l. Factor -1 + m - 2*m**3 + m**3 + 2 + 2*m**4 - d*m**2.
(m - 1)**2*(m + 1)*(2*m + 1)
Suppose -61 = 4*x + 19. Let h be (-2)/20 + (-12)/x. Find t such that 0*t + 0 - 1/2*t**2 - t**3 - h*t**4 = 0.
-1, 0
Let o be (10/35)/((-2)/(-14)). Suppose -3*b = -3*z + 21, -z + 13 = -0*z - 4*b. Factor -4*k**4 + 2*k + 12*k**3 + o*k**5 + k**4 + z*k**4 + 8*k**2 + 6*k**4.
2*k*(k + 1)**4
Let w = 3/130 - -31/65. Factor -1/2*g**2 - w*g**3 + 0 + 0*g.
-g**2*(g + 1)/2
Suppose -2*z - 3*r - 7 = -15, -z + 4 = -3*r. Find j such that j - 3*j**4 + 12 + 10*j**2 - 5*j**5 - 5*j**z + 0*j**2 - 14 + 4*j**3 = 0.
-1, 2/5, 1
Suppose 32 = -8*o + 12*o. Suppose -2 = o*t - 9*t. Factor -i**t + i + 1/3*i**3 - 1/3.
(i - 1)**3/3
Let p(m) = -m**2 + 3*m + 23. Let c be p(6). Determine d so that 2*d**4 + 4/5*d**c + 4/5*d**3 - 2/5 - 8/5*d - 8/5*d**2 = 0.
-1, -1/2, 1
Let n be 1/((-2)/(-24)) - 1. Let c = 36 - n. Factor 11*t**3 + 20*t**3 - c*t**4 - 4*t**2 - 11*t**3.
-t**2*(5*t - 2)**2
Let k(c) be the second derivative of c**7/7560 - c**6/1080 - c**5/120 + c**4/3 + 2*c. Let m(b) be the third derivative of k(b). Factor m(n).
(n - 3)*(n + 1)/3
What is a in 9/2*a**2 + 3/2*a**4 + 3/2*a + 0 + 9/2*a**3 = 0?
-1, 0
Let f = 2 + 3. Factor -3*p - 4*p**f - 4*p**3 - 8*p**4 + 2*p + p.
-4*p**3*(p + 1)**2
Suppose 2*i + 3 = 3*i. Let n(z) be the second derivative of -2*z + 0*z**2 + 1/3*z**i + 3/10*z**5 + 0 + 1/15*z**6 + 1/2*z**4. Find t such that n(t) = 0.
-1, 0
Let z be ((-17)/((-833)/112))/(1*2). Solve -2/7*w**2 + z*w - 6/7 = 0 for w.
1, 3
Factor -1/3*l**2 + 2/3 + 1/3*l.
-(l - 2)*(l + 1)/3
Let u(h) be the first derivative of -h**7/70 - h**6/8 - 3*h**5/10 + h**4/2 + 4*h**3 - 3*h**2/2 - 4. Let m(q) be the second derivative of u(q). Factor m(g).
-3*(g - 1)*(g + 2)**3
Let c = 82 - 82. Determine p so that 1/2*p**2 - 1/2*p**4 + p**3 + c - p = 0.
-1, 0, 1, 2
Let s(h) be the third derivative of h**8/560 - h**6/100 + h**4/40 - 10*h**2. Factor s(g).
3*g*(g - 1)**2*(g + 1)**2/5
Let p(y) be the second derivative of 0 - 1/20*y**5 - 2*y + 0*y**2 + 1/6*y**4 + 1/3*y**3 + 1/180*y**6. Let q(g) be the second derivative of p(g). Factor q(n).
2*(n - 2)*(n - 1)
Let r(f) = -f**5 - f**4 - 2*f**3 - f**2 - f + 1. Let d(k) = k**5 + k**4 - 12*k**3 + 5*k**2 - k + 1. Let z(n) = -2*d(n) + 2*r(n). Factor z(l).
-4*l**2*(l - 1)**2*(l + 3)
Let z(f) be the second derivative of 0 + 1/9*f**3 + 0*f**2 - 1/36*f**4 + 3*f. Factor z(m).
-m*(m - 2)/3
Let g(i) be the second derivative of -1/6*i**3 - 4*i + 0 + 3/8*i**2 + 1/48*i**4. Factor g(z).
(z - 3)*(z - 1)/4
Let h(q) be the third derivative of 3*q**2 - 1/42*q**4 + 0*q + 0 + 0*q**3 + 1/735*q**7 + 1/1176*q**8 - 1/42*q**5 - 1/140*q**6. Factor h(u).
2*u*(u - 2)*(u + 1)**3/7
Let i(j) = -2*j**3 + 4*j - 9*j**2 - 6*j**3 - 3*j**3 + 7 + 2*j**2. Let o(m) = -5*m**3 - 3*m**2 + 2*m + 3. Let k(v) = -3*i(v) + 7*o(v). Solve k(d) = 0 for d.
-1, 0, 1
Let 5/4*o**2 + 3/4*o**3 + 1/2*o + 0 = 0. What is o?
-1, -2/3, 0
Let t(z) = -z**3 + 5*z**2 - 4*z. Let s be t(4). Factor -2/9*g**4 + 2/9*g**2 + s*g + 0 + 0*g**3.
-2*g**2*(g - 1)*(g + 1)/9
Let a = -323/5 + 65. Determine c so that 1/5*c**4 - a + 1/5*c**2 + 3/5*c**3 - 3/5*c = 0.
-2, -1, 1
Suppose 0*p**2 + 0 + 4/5*p**5 + 0*p**4 - 4/5*p**3 + 0*p = 0. Calculate p.
-1, 0, 1
Factor 3*m**2 - 55*m - 46*m + 139*m - 50*m.
3*m*(m - 4)
Let x = -10 + 6. Let k be 4/8 + (-1)/x. Factor 1/4*s**3 + 3/4*s - k*s**2 - 1/4.
(s - 1)**3/4
Let f(v) be the third derivative of -v**6/300 + v**5/75 - v**4/60 + 5*v**2. Find s such that f(s) = 0.
0, 1
Let 4/9 - 2/9*y**2 - 2/9*y = 0. Calculate y.
-2, 1
Suppose 3*j - 24 = -5*n + 2, n + j - 6 = 0. Let p = n + -2. Let -4*a**2 + 4*a**p + a**2 = 0. What is a?
0
Let v(n) = -n**2 + 12*n + 2 - 14*n - 12*n. Let s be v(-14). Let 0 + 0*g**s + 0*g + 0*g**3 + 1/4*g**4 = 0. What is g?
0
Let z(m) be the third derivative of m**7/240 - m**6/80 - m**5/120 - 26*m**2. Let z(g) = 0. What is g?
-2/7, 0, 2
Let v(b) be the third derivative of b**8/28 + 8*b**7/105 - b**6/30 - 2*b**5/15 + 8*b**2. Factor v(k).
4*k**2*(k + 1)**2*(3*k - 2)
Let r(l) be the first derivative of -2 - 1/2*l**2 + 2*l + 0*l**3 + 1/12*l**4. Let f(t) be the first derivative of r(t). Suppose f(m) = 0. Calculate m.
-1, 1
Determine j so that -3*j**5 + 1626*j**2 + 20*j**3 - 1617*j**2 - 5*j**3 + 3*j**4 = 0.
-1, 0, 3
Let w(h) be the first derivative of -h**8/840 + h**6/150 - h**4/60 + h**2 - 2. Let m(u) be the second derivative of w(u). Suppose m(t) = 0. Calculate t.
-1, 0, 1
Let y(j) be the third derivative of j**6/80 + j**5/8 + 7*j**4/16 + 3*j**3/4 - 12*j**2. Find c, given that y(c) = 0.
-3, -1
Let n(l) be the third derivative of 4*l**7/735 + 11*l**6/420 + 3*l**5/70 + l**4/84 - l**3/21 + 6*l**2. Determine w so that n(w) = 0.
-1, 1/4
Let p(h) be the first derivative of 3*h**4/4 - 7*h**3 + 33*h**2/2 - 15*h + 17. Factor p(x).
3*(x - 5)*(x - 1)**2
Let c(p) be the third derivative of -p**6/360 + p**5/36 - p**4/18 + 17*p**2. Suppose c(y) = 0. What is y?
0, 1, 4
Let t(m) = -m**3 + 3*m**2. Let r be t(2). Let f = -2/69 - -217/345. Factor 1/5*i**2 + 3/5*i**r + 1/5*i**5 + 0*i + f*i**3 + 0.
i**2*(i + 1)**3/5
Suppose -4*y - 5*r = 0, 0 = -y + 2*r - 0*r. Let i be (y - (4 + 6))/(-2). Factor 8/7*c**2 - 16/7*c**3 + 10/7*c**4 + 0 - 2/7*c**i + 0*c.
-2*c**2*(c - 2)**2*(c - 1)/7
Let d(a) = -a**3 + 5*a**2 + a - 1. Let p be d(5). Let y(m) = -m**2 + 6*m - 6. Let k be y(p). Let -1 - j**k - j**3 + 2*j**3 - j + 2*j**2 = 0. What is j?
-1, 1
Let j(p) = -3*p**3 - 13*p**2 - 5*p - 3. Let u(y) = y**3 - y - 1. Let k(s) = -j(s