7728. Let l(g) be the third derivative of -g**2 + 0 + 0*g**3 + c*g**8 + 1/240*g**6 + 0*g**4 - 1/210*g**7 + 0*g + 0*g**5. Factor l(n).
n**3*(n - 1)**2/2
Let a = -7 + 3. Let p = -1 - a. Factor s**2 - 3*s**2 - 2*s**2 + 3*s**2 - s**p.
-s**2*(s + 1)
Let r = 19 + -14. Let c(j) be the second derivative of -1/15*j**3 + 0*j**4 + 0*j**2 + 0 - 2*j + 1/50*j**r. Factor c(q).
2*q*(q - 1)*(q + 1)/5
Let a be (0 - 1) + 3/3*1. Let g(y) be the second derivative of 1/15*y**3 - 1/30*y**4 + 0*y**2 + a + 2*y. Solve g(p) = 0 for p.
0, 1
Let n = -71/2 + 36. Let s(h) be the first derivative of 4/15*h**3 - 1 + n*h**2 + 1/5*h. What is v in s(v) = 0?
-1, -1/4
Let p(q) be the third derivative of q**5/120 + 5*q**4/48 - q**3/2 - q**2. Factor p(u).
(u - 1)*(u + 6)/2
Suppose 0 + 2/9*y**4 - 2/9*y**2 - 2/9*y**3 + 2/9*y = 0. What is y?
-1, 0, 1
Let a(x) be the third derivative of x**7/210 + x**6/40 + x**5/60 - x**4/8 - x**3/3 + 12*x**2. Find h such that a(h) = 0.
-2, -1, 1
Let u be (-32)/10 - 2/(-10). Let m(g) = g**5 + g**4 + 2*g**2 + 2*g - 3. Let p(q) = -q**4 - q + 1. Let x(j) = u*p(j) - m(j). Let x(v) = 0. What is v?
-1, 0, 1
Let k be 11/(-55) - (-2045)/100. Factor 1/4*q**4 + 27*q + 3*q**3 + 27/2*q**2 + k.
(q + 3)**4/4
Let f(o) be the second derivative of 27*o**5/20 - 15*o**4/2 + 14*o**3 - 12*o**2 + 2*o. Factor f(t).
3*(t - 2)*(3*t - 2)**2
Suppose -q + 3 = n, -4*q = -2*n - 2*n + 4. Let m(g) = 2*g - 2 - 2*g**3 - 3*g**2 + 3*g**2 - 6*g**n. Let v(h) = -h. Let s(p) = -m(p) - 8*v(p). Factor s(d).
2*(d + 1)**3
Let j(n) = -n**2 + n - 1. Let m(f) = -9*f**2 + 5*f - 9. Let o(g) = 4*j(g) - m(g). Let l(i) = -i**2 - 1. Let x(q) = 9*l(q) + 2*o(q). Factor x(c).
(c - 1)**2
Let f(b) be the third derivative of -1/20*b**5 + 0*b**3 + 0*b + 0*b**4 - b**2 + 0. Factor f(z).
-3*z**2
Let i(d) be the second derivative of d**5/40 - 2*d. Factor i(l).
l**3/2
Let j(f) = -f**2 + 23*f + 29. Let d be j(24). Factor -2/3 - 10/3*i**4 + 10/3*i - 20/3*i**2 + 2/3*i**d + 20/3*i**3.
2*(i - 1)**5/3
Let m be 2 + 65/(-15) + 4 + 0. Determine r, given that -m*r**2 + 3 - r - 1/3*r**3 = 0.
-3, 1
Suppose v - 105 = -5*w, -4*w + 0 + 84 = -3*v. Suppose -4*i = -i - w. Find d, given that i*d - d - 4*d - 2*d**2 = 0.
0, 1
Let h(o) = -2*o**2 - 9*o + 8. Let y be h(-5). Solve -3*d**2 - 1/2 - 2*d**y - 2*d - 1/2*d**4 = 0.
-1
Let a(l) be the third derivative of l**10/680400 + l**5/60 + 2*l**2. Let s(k) be the third derivative of a(k). Determine x so that s(x) = 0.
0
Let s(r) be the second derivative of r**8/16800 - r**7/6300 + r**4/12 + 3*r. Let o(v) be the third derivative of s(v). Factor o(z).
2*z**2*(z - 1)/5
Let q(i) be the third derivative of i**7/840 - i**6/120 + i**5/40 - i**4/24 - i**3/2 - i**2. Let o(a) be the first derivative of q(a). Factor o(g).
(g - 1)**3
Suppose 2*q = -q. Let y(l) be the second derivative of 1/126*l**7 - 2*l + 0*l**2 + 0*l**4 + 0*l**5 + 1/90*l**6 + 0*l**3 + q. Factor y(j).
j**4*(j + 1)/3
Suppose -4*y + 40 = y - 3*i, 2*y - 4*i - 16 = 0. Let j = 19/2 - y. Find b, given that -j*b**3 + 1/2 - 1/2*b**2 + 3/2*b = 0.
-1, -1/3, 1
Let o be (-2)/(2 - 3) - -1. Suppose -2*t - o = -3*t. Factor 0*j - 2/9*j**4 + 4/9*j**2 - 2/9 + 0*j**t.
-2*(j - 1)**2*(j + 1)**2/9
Let s(c) be the third derivative of -c**7/1680 + c**5/240 - c**3/3 - 3*c**2. Let u(f) be the first derivative of s(f). Solve u(z) = 0 for z.
-1, 0, 1
Let c(k) be the third derivative of -k**8/1176 + k**7/735 + k**6/420 - k**5/210 + k**2. Solve c(m) = 0.
-1, 0, 1
Let c(h) be the third derivative of -h**5/20 + 17*h**4/8 - 8*h**3 + 65*h**2. Factor c(y).
-3*(y - 16)*(y - 1)
Let v be 24/20*12/9. Determine i so that -18/5*i**3 + v*i**4 + 12/5*i**2 - 2/5*i + 0 = 0.
0, 1/4, 1
Factor -12 + 273*q**2 + 6*q - 269*q**2 + 2*q.
4*(q - 1)*(q + 3)
Suppose -21 = 2*i - 9*i. Suppose -p**2 + 3*p**4 + 2*p**i - 2*p + 6*p**4 - 8*p**4 = 0. What is p?
-2, -1, 0, 1
Let g(o) = o**2 + 4*o + 3. Let l be g(-3). Let w = 0 + 2. Factor l*m - 1/3*m**w + 2/3*m**3 + 0 - 1/3*m**4.
-m**2*(m - 1)**2/3
Let y(s) be the third derivative of s**9/151200 - s**8/16800 + s**7/4200 - s**6/1800 - s**5/60 - 7*s**2. Let b(q) be the third derivative of y(q). Factor b(n).
2*(n - 1)**3/5
Let l(z) be the second derivative of z**4/6 - 5*z**3/3 + 6*z**2 + 11*z. Factor l(a).
2*(a - 3)*(a - 2)
Solve 1/7*w**2 - 8/7*w + 16/7 = 0.
4
Let i = 24/19 + -130/133. Factor -i - 8/7*x**2 - 10/7*x.
-2*(x + 1)*(4*x + 1)/7
Let k(h) = -4*h + 27 - h - 11 + 3*h. Let z be k(7). Solve -1/3*n**z + 0*n**3 + 0 + 0*n + 1/3*n**4 = 0 for n.
-1, 0, 1
Let k = -3 - -5. Suppose 98 = 3*g - 2*o, -k*g + 180 = 3*g + 5*o. Factor 12 - 24*w**3 + 4 + g*w**3 + 44*w**2 + 56*w.
2*(w + 2)**2*(5*w + 2)
Let j(n) be the first derivative of -n**5/45 + n**4/18 + n**3/27 - n**2/9 + 5. Factor j(t).
-t*(t - 2)*(t - 1)*(t + 1)/9
Let s(y) = -y**2 + 6*y + 8. Let j be s(6). Factor -4*f**5 - 12*f**3 - j*f**4 + 3*f - 8*f**2 - 5*f + 2*f**5.
-2*f*(f + 1)**4
Let r(c) = -c**2 - 9*c - 8. Let q be r(-11). Let z be 40/q - 64/(-30). Factor -z*t**2 + 0*t + 0*t**3 + 2/5 + 2/5*t**4.
2*(t - 1)**2*(t + 1)**2/5
Suppose 4 = -5*m - 1. Let z(y) = y. Let i(w) = w**2 - 3*w. Let k(r) = m*i(r) - z(r). Factor k(b).
-b*(b - 2)
Factor 3/2*r**5 + 0*r - 3*r**2 + 0 + 0*r**4 - 9/2*r**3.
3*r**2*(r - 2)*(r + 1)**2/2
Let w = 1959 - 5827/3. Factor 8/3*v - 40/3*v**2 + 0 + w*v**3.
2*v*(5*v - 2)**2/3
Let y be 0 - ((-44)/10 - -4). What is m in 0 + y*m - 1/5*m**2 = 0?
0, 2
Let j = -4 - -9. Suppose 5*k - 16 = 2*s, j*k - 3*k - 6 = s. Factor 0*q**s - q + 2*q**2 + 3*q.
2*q*(q + 1)
Let d(n) be the first derivative of 3*n**6/10 - 4*n**5/5 + 5*n**4/12 + n**3/3 - n - 2. Let j(h) be the first derivative of d(h). Factor j(u).
u*(u - 1)**2*(9*u + 2)
Let i(f) be the second derivative of -f**5/90 - f**4/27 - f**3/27 + f. Factor i(o).
-2*o*(o + 1)**2/9
Determine r so that 45*r**2 + 144*r - 11*r**3 + 6*r**3 + 8*r**3 - 192 = 0.
-8, 1
Let n(y) = -y + 21. Let l be n(14). Suppose -3*q + 5 + l = 0. Find m such that -22*m**3 + 5/2*m - q*m**2 + 1/2 + 16*m**4 + 32*m**5 = 0.
-1, -1/4, 1/2
Find j such that 5*j**2 + 82*j + 127*j + 1620 - 29*j = 0.
-18
Let j be 1*-2*15/(-225). Let f(i) be the first derivative of 2/3*i**3 + 0*i - 1/2*i**4 - 1 + j*i**5 - 1/3*i**2. Solve f(p) = 0.
0, 1
Let t be 3795/414 - 1/(-6). Solve t*x - 8/3*x**4 + 8/3 - 4/3*x**5 + 32/3*x**2 + 8/3*x**3 = 0.
-1, 2
Let s(j) = -3*j**3 - 6*j**2 - 6*j. Let p(m) = -m. Let y(u) = -3*p(u) + s(u). What is g in y(g) = 0?
-1, 0
Let r = 2 - 0. Factor r - 4 + a**2 + a**2 + a - a**2.
(a - 1)*(a + 2)
Solve -2/9*m**2 + 0 - 2/9*m = 0.
-1, 0
Let z = 84 - 84. Factor 2/3*r**4 + z + 0*r**2 + 0*r - 2/3*r**3.
2*r**3*(r - 1)/3
Let x(q) be the second derivative of -q**5/4 + 5*q**3/6 + 2*q. Factor x(m).
-5*m*(m - 1)*(m + 1)
Let l(w) be the second derivative of 2/3*w**3 + 0 + 5/6*w**4 + 2/5*w**5 + 1/15*w**6 + 0*w**2 - 2*w. Determine d, given that l(d) = 0.
-2, -1, 0
Let g(k) be the third derivative of -1/270*k**6 + 1/108*k**4 + 0*k**3 + 1/1512*k**8 + 0*k**7 + 0 - k**2 + 0*k + 0*k**5. What is h in g(h) = 0?
-1, 0, 1
Suppose -7/2*l + 4*l**4 - 10*l**3 + 9*l**2 + 1/2 = 0. Calculate l.
1/2, 1
Suppose 2 = -2*t + 8. Factor -2*p + 2*p + 4 + p - t*p - 2*p**2.
-2*(p - 1)*(p + 2)
Suppose -v + h + 0 - 1 = 0, 5*v + 3*h = 3. Suppose 0*d + d - 3 = v. Factor -2/5*i + 2/5*i**d + 2/5*i**4 - 2/5*i**2 + 0.
2*i*(i - 1)*(i + 1)**2/5
Let a(r) = -r**3 + 8*r**2 + 9*r + 18. Let k be a(9). Let h = k + -18. Determine d so that 2/9*d**3 - 2/9*d**5 + 0*d**4 + 0*d**2 + 0 + h*d = 0.
-1, 0, 1
Let z(x) be the third derivative of 1/30*x**5 - 1/210*x**7 - 1/6*x**3 + 0*x + 0*x**6 + 0 + 0*x**4 + x**2. Factor z(i).
-(i - 1)**2*(i + 1)**2
Determine m so that 0 + 0*m**2 + 1/5*m - 1/5*m**3 = 0.
-1, 0, 1
Let r(l) be the first derivative of 2/5*l**4 + 2/25*l**5 + 2/5*l**2 + 1 + 2/3*l**3 + 0*l. Factor r(p).
2*p*(p + 1)**2*(p + 2)/5
Suppose 4*r - 3*a = r + 9, 4*r + 3*a - 12 = 0. Let k be (-4)/r + (-10)/(-3). Factor 0 - 2/5*z**k + 0*z + 2/5*z**3.
2*z**2*(z - 1)/5
Suppose -7 = 5*z - 27. Factor 5*q**3 + q**3 - q**2 - q**z + 0*q**3 - 4*q**3.
-q**2*(q - 1)**2
Let q(h) = h**3 + 5*h**2 + h + 7. Let w be -2 + (-2)/(8/12). Let l be q(w). Factor 3/4*t**l - 3/4*t + 0.
3*t*(t - 1)/4
Let v(b) = -b**2 + 3*b + 2. Let r be v(5). Let p = -6 - r. Factor f**2 + f**p - f**2 + f**2 - 4*f.
2*f*(f - 2)
Let k(v) = -v**3 + 7*v**2 - 6*v + 3. Let o be k(6). Let j(i) b