derivative of 0*m**4 + 0*m - 2/5*m**5 + 0*m**c + 2/3*m**3 - 3. Factor q(g).
-2*g**2*(g - 1)*(g + 1)
Let k(q) be the third derivative of 0*q**3 + 0 + q**2 + 0*q - 1/4*q**4 + 1/20*q**5. Factor k(p).
3*p*(p - 2)
Solve 0*a + 9/2*a**5 - 33/2*a**2 + 21/2*a**4 + 6 - 9/2*a**3 = 0 for a.
-2, -1, 2/3, 1
Suppose p - 4*z = 26 - 4, -p - 13 = 3*z. Factor -6*y - 2*y - y - 3*y**p - 6.
-3*(y + 1)*(y + 2)
Let i be 6 - (2 - (-20)/6). What is b in -8/3*b - i*b**4 - 10/3*b**3 + 0 - 16/3*b**2 = 0?
-2, -1, 0
Suppose 0 - r**2 + 1/3*r + r**3 - 1/3*r**4 = 0. What is r?
0, 1
Let a(b) be the second derivative of 4*b**2 - 3*b + 0 + 3/5*b**5 - 2*b**3 - 2/15*b**6 - 1/3*b**4. Factor a(h).
-4*(h - 2)*(h - 1)**2*(h + 1)
Factor -12/5*d**2 + 4/5*d**4 + 8/5*d + 0 + 0*d**3.
4*d*(d - 1)**2*(d + 2)/5
Let u(c) = -c**2 + 6*c - 3. Let o be u(5). Solve -8*y + y**o + 5*y**2 - 4*y + 12 - 3*y**2 = 0.
2
Let s(l) be the second derivative of -4*l**6/45 + l**5/10 + 7*l**4/6 + 17*l**3/9 + l**2 - 29*l. What is w in s(w) = 0?
-1, -1/4, 3
Let w be (171/114)/((-3)/(-4)). Factor -2*a - 14/3*a**3 - 8*a**w + 4/3.
-2*(a + 1)**2*(7*a - 2)/3
Let l(a) = -a**2 + 2*a + 3. Let j be l(3). Suppose 3*o - 9 = j, 2 + 12 = i + 4*o. What is f in -4*f**2 + i - 2*f**2 + f + 4*f**2 - f**3 = 0?
-2, -1, 1
Let k = 397/2 + -198. Factor -k + t - t**3 + 1/2*t**4 + 0*t**2.
(t - 1)**3*(t + 1)/2
Let o(i) = -3*i - 8*i**2 + 2*i + 12*i**2. Let p be o(-1). Determine v so that 4*v**2 + 6*v**p - 1 - 1 - 4*v**3 + 2*v - 4*v**5 - 2*v**4 = 0.
-1, 1
Let d(o) be the second derivative of o**7/252 + o**6/120 - o**5/30 + o**4/3 + o. Let v(q) be the third derivative of d(q). Factor v(p).
2*(p + 1)*(5*p - 2)
Suppose -d + 24 = -5*d - 4*s, -3*d - 2*s - 17 = 0. Let p be d/(-7) + 6/21. Solve 4*j**2 - 2*j - 2*j**2 - p - 3*j**2 = 0.
-1
Let m(p) be the first derivative of p**6/180 - p**5/45 + p**4/36 + p**2 - 1. Let a(u) be the second derivative of m(u). Factor a(w).
2*w*(w - 1)**2/3
Let z(a) be the first derivative of a**5/15 + a**4/6 - a**2/3 - a/3 - 6. Let z(d) = 0. Calculate d.
-1, 1
Let r = -10 + 12. Let t = r + 1. Factor 0 + 0*m**t - m**2 + 1/2*m + m**4 - 1/2*m**5.
-m*(m - 1)**3*(m + 1)/2
Let k(r) be the third derivative of r**6/480 + r**5/60 + 5*r**4/96 + r**3/12 + 2*r**2 - 11*r. What is j in k(j) = 0?
-2, -1
Let w(m) be the third derivative of m**8/22176 - m**7/2310 + m**6/990 - m**5/12 + 3*m**2. Let z(s) be the third derivative of w(s). Factor z(n).
2*(n - 2)*(5*n - 2)/11
Let h(x) = -x**2 + 3*x. Let s(i) = 2*i**2 - 5*i. Suppose 7 = -3*o - r - r, 2*r + 1 = -o. Let q(k) = o*s(k) - 5*h(k). Factor q(w).
-w**2
Let u(l) be the first derivative of 1/18*l**3 - 2 - 2/3*l + 1/4*l**2. Factor u(d).
(d - 1)*(d + 4)/6
Let b(h) = h**2 + 10*h. Let z be b(-10). Let t(k) be the first derivative of 3/2*k**4 + 4/5*k**5 + 1/2*k**2 + 1 + 4/3*k**3 + z*k + 1/6*k**6. Factor t(j).
j*(j + 1)**4
What is d in -11/2*d**3 + 30*d**4 + 50*d**5 + 1/2*d + 0 - 3*d**2 = 0?
-1/2, 0, 1/5
Let f(w) be the second derivative of -w**4/24 + w**3/3 - w**2 + w. Factor f(u).
-(u - 2)**2/2
Let y(q) = 3*q - 4. Let z be y(3). Let o be (-2)/(-1)*1/z. Factor 0 + 2/5*l**5 - o*l + 4/5*l**4 + 0*l**3 - 4/5*l**2.
2*l*(l - 1)*(l + 1)**3/5
Factor -1 + 1 + 2*b**2 - b**2.
b**2
Let f(r) be the second derivative of -r**2 + 1/3*r**4 - 1/15*r**6 - 9*r + 0 + 0*r**5 + 0*r**3. Solve f(g) = 0.
-1, 1
Let q(p) be the first derivative of -p**5/20 + p**3/6 + 2*p + 2. Let v(u) be the first derivative of q(u). Factor v(f).
-f*(f - 1)*(f + 1)
Suppose 2*h - 6 = 2. Suppose -5*m = h*s - m - 24, -2*s = -4*m + 6. Determine v so that -v - v + v + s*v**2 = 0.
0, 1/3
Suppose -11*y**2 - 2*y**3 + 2*y**4 + 2*y + 3 + 1 + 5*y**2 = 0. Calculate y.
-1, 1, 2
Let i(l) be the second derivative of l**7/36 + 23*l**6/180 + 9*l**5/40 + 13*l**4/72 + l**3/18 + 3*l. Factor i(d).
d*(d + 1)**3*(7*d + 2)/6
Let v be (-3496)/(-672) + 4/(-14). Let s = v + -14/3. Suppose 1/2*m - s - 1/4*m**2 = 0. Calculate m.
1
Let l(z) be the second derivative of 0 + 0*z**2 + 2*z + 1/18*z**4 + 0*z**3 + 1/30*z**5. Let l(v) = 0. What is v?
-1, 0
Let l = 104/155 - 2/465. Factor 0*z**2 - l*z + 2/9*z**3 + 4/9.
2*(z - 1)**2*(z + 2)/9
Suppose 0 = -4*z + 5 + 3. Factor -2*n**2 + n - 2*n**3 - 2*n**3 + z + 3*n**3.
-(n - 1)*(n + 1)*(n + 2)
Suppose -10 = -14*m + 9*m. Suppose m = -7*t + 8*t. Factor 1/2 - a + 1/2*a**t.
(a - 1)**2/2
Let l(a) be the second derivative of -a**4/24 + 9*a. Factor l(p).
-p**2/2
Factor 6/5*u**2 - 78/5 + 72/5*u.
6*(u - 1)*(u + 13)/5
Let d(u) = -u + 3. Let v be d(0). Solve -14*x + 3*x**2 + 14*x - 3*x**v = 0.
0, 1
Let k(q) be the second derivative of 4*q - 1/4*q**4 + 1/2*q**3 + 0 + 3/2*q**2 - 3/20*q**5. Let k(l) = 0. Calculate l.
-1, 1
Let c(a) be the third derivative of -1/40*a**6 - 1/4*a**3 + 3*a**2 + 3/16*a**4 - 1/224*a**8 + 0 + 3/140*a**7 + 0*a - 1/20*a**5. Solve c(g) = 0.
-1, 1
Let c = 1249/16 + -78. Let a(x) be the second derivative of 0*x**3 - c*x**5 - 2*x + 0 + 0*x**2 + 1/24*x**4. Let a(k) = 0. What is k?
0, 2/5
Let x be (-5)/((-40)/(-12))*-2. Let h be (-5 + 5)/(1 - 0). Find g, given that 2/5*g**5 - 2/5*g + 4/5*g**2 - 4/5*g**4 + h*g**x + 0 = 0.
-1, 0, 1
Let z(n) = 2*n**4 - n**3 - n + 2. Let h(w) = -4*w**4 + 2*w**3 + w**2 + 2*w - 4. Let x(t) = -6*h(t) - 11*z(t). What is c in x(c) = 0?
-1, 1/2, 2
Let x(w) be the third derivative of -w**7/42 + w**6/24 + w**5/3 - 5*w**4/6 - w**2 + 20*w. Factor x(m).
-5*m*(m - 2)*(m - 1)*(m + 2)
Let h be ((-4)/10)/((-2)/10). Factor -3*w + 2*w - 3*w - w**h + w.
-w*(w + 3)
Let y(l) = 4*l**2 - 7*l - 4. Let v(r) = 3*r**2 - 5*r - 3. Let s(q) = 7*v(q) - 5*y(q). Let s(m) = 0. Calculate m.
-1, 1
Let u = 89222433935/2674 + -33366653. Let x = u - -1/382. Factor -22/7*v**2 + 8/7*v**3 + 4/7 + x*v.
2*(v - 2)*(v - 1)*(4*v + 1)/7
Let b(z) be the second derivative of 7*z**4/12 + 5*z**3/6 - z**2 + 5*z. Factor b(a).
(a + 1)*(7*a - 2)
Let v(s) be the third derivative of -1/40*s**6 + 0*s**3 + 0*s**5 + 0 + s**2 + 0*s + 0*s**4. Factor v(x).
-3*x**3
Factor 3*z - 9/5*z**2 + 3/5*z**4 - 6/5 - 3/5*z**3.
3*(z - 1)**3*(z + 2)/5
Suppose -3*s = -5*p + 11, s + 10 = -4*p + 29. Let m(q) be the first derivative of -q**2 + 0*q**3 + q**p - 1 + 0*q + 0*q**5 - 1/3*q**6. Factor m(r).
-2*r*(r - 1)**2*(r + 1)**2
Let r(i) = 5*i**5 - 28*i**4 + 18*i**3 + 48*i**2. Let m(v) = -65*v**5 + 365*v**4 - 235*v**3 - 625*v**2. Let g(q) = 3*m(q) + 40*r(q). Factor g(y).
5*y**2*(y - 3)**2*(y + 1)
Let 6*w**3 - 9*w**2 - 5*w**2 + 6*w**2 - 10*w**3 = 0. What is w?
-2, 0
Let s(t) be the third derivative of -t**7/168 + t**6/48 + t**5/16 + 7*t**2. Determine r, given that s(r) = 0.
-1, 0, 3
Let f(o) be the second derivative of 0*o**6 + 9*o + 0*o**3 + 0*o**4 + 0*o**2 + 1/10*o**5 - 1/21*o**7 + 0. What is l in f(l) = 0?
-1, 0, 1
Let h(l) be the first derivative of -l**5/60 - l**4/36 + l**3/9 - l + 3. Let c(b) be the first derivative of h(b). Find a such that c(a) = 0.
-2, 0, 1
Let p be (8/300)/(((-8)/6)/(-4)). Let s(n) be the first derivative of 4/5*n**3 + 4 - 4/5*n**2 - 2/5*n**4 + 2/5*n + p*n**5. Find g, given that s(g) = 0.
1
Let -9/7*g**3 + 0 + 12/7*g + 3/7*g**5 - 12/7*g**2 + 6/7*g**4 = 0. What is g?
-2, 0, 1
Factor -2*i**2 - 102*i**3 + i**2 + 127*i**3 - 4*i**2.
5*i**2*(5*i - 1)
Let p be 2 - -1 - (2 - 2). Let q(a) = 95*a**4 + 56*a**3 - 87*a**2 - 53*a - 11. Let m(t) = t**4 - t**2 - t + 1. Let o(f) = p*m(f) + q(f). Factor o(k).
2*(k - 1)*(k + 1)*(7*k + 2)**2
Suppose 3*x = -x + 4. Let w(z) be the first derivative of -x + 1/6*z**3 - 1/2*z + 0*z**2. Factor w(m).
(m - 1)*(m + 1)/2
Let i(y) = -y**2 - 5*y - 3. Let l(z) = -z**2 + z + 1. Suppose 0 = 3*g - 1 + 4. Let n(r) = g*i(r) - l(r). Solve n(p) = 0.
-1
Let p(t) be the first derivative of -4*t**6/315 + 2*t**5/105 - t**4/84 + 4*t**3/3 + 2. Let c(n) be the third derivative of p(n). Factor c(d).
-2*(4*d - 1)**2/7
Suppose 3*w = i + 6, -2*i + 5*w - 7*w + 12 = 0. Find z such that 0 + 2/3*z**5 + 2/3*z**2 - 2/3*z**4 + 4/3*z - 2*z**i = 0.
-1, 0, 1, 2
Let g = -60 + 62. Factor 2*y - g - 1/2*y**2.
-(y - 2)**2/2
Let g(z) = z**2 - 2*z + 1. Let q(h) = 4*h**2 - 8*h + 3. Let c(m) = -3*g(m) + q(m). Factor c(r).
r*(r - 2)
Let n(w) be the third derivative of 0 + 0*w**3 + 0*w**5 + 0*w + 2/35*w**7 - w**2 + 13/120*w**6 - 1/24*w**4. Factor n(x).
x*(x + 1)*(3*x + 1)*(4*x - 1)
Factor 1/4*a**3 - 1/4*a - 1/2 + 1/2*a**2.
(a - 1)*(a + 1)*(a + 2)/4
Suppose 2*g - 6*g + 