3. Find m, given that q(m) = 0.
-3
Let n(h) be the third derivative of -1/48*h**4 + 0 - 3*h**2 + 0*h**3 + 0*h + 1/80*h**5. Factor n(q).
q*(3*q - 2)/4
Let d(w) be the second derivative of w**5/20 - w**3/2 + 4*w**2 + 7*w. Let s(m) be the first derivative of d(m). Determine g, given that s(g) = 0.
-1, 1
Let k(i) = -i**4 - i**3 + 1. Let a(x) = 44*x**4 - 36*x**3 + 2*x**2 + 12*x - 10. Let t(u) = -a(u) - 12*k(u). Factor t(c).
-2*(c - 1)**2*(4*c + 1)**2
Let g be 11/4 - (-3)/12. Suppose -o - 9 = -4*o. What is a in -a**5 - 2*a**o + g*a**3 + 2*a**4 - 2*a**3 = 0?
0, 1
Let n(f) be the first derivative of -3/5*f**5 - 3/2*f**2 + 2 - 3*f**3 - 9/4*f**4 + 0*f. Find k, given that n(k) = 0.
-1, 0
Suppose -3 + 6 = -3*d. Let i(q) = 9*q**4 + 6*q**3 - 6*q + 3. Let a(r) = -r**4 - 1. Let k(f) = d*i(f) - 6*a(f). Let k(v) = 0. What is v?
-1, 1
Let r(c) be the second derivative of 1/66*c**4 + 4/11*c**2 + 0 - 2*c - 4/33*c**3. Determine v, given that r(v) = 0.
2
Let m(s) be the second derivative of 5*s**4/6 + s**3/6 + 3*s**2/2 - 3*s. Let c(d) = 10*d**2 + 2*d + 2. Let r(a) = -3*c(a) + 2*m(a). Solve r(w) = 0.
-2/5, 0
Factor 10/9*i**3 + 2/3*i + 14/9*i**2 + 2/9*i**4 + 0.
2*i*(i + 1)**2*(i + 3)/9
Let t be 4 - (0 + 2 - 1). Let i(o) be the first derivative of -o**4 + 3 + 0*o**t + 0*o**2 + 0*o + 14/5*o**5. Find f, given that i(f) = 0.
0, 2/7
Let b(j) = -j**3 + 4*j**2 - 4*j + 3. Let m be b(3). Let x(f) be the first derivative of m*f + 0*f**2 - 1/12*f**3 + 0*f**4 + 1/20*f**5 - 1. Factor x(h).
h**2*(h - 1)*(h + 1)/4
Let x(r) be the third derivative of 1/180*r**6 + 0 + 0*r + 0*r**5 - 1/36*r**4 + 0*r**3 - 3*r**2. Solve x(a) = 0 for a.
-1, 0, 1
Let b(a) be the first derivative of 4*a**5/25 + 2*a**4/5 + 4*a**3/15 - 8. Find m such that b(m) = 0.
-1, 0
Let g(n) = n**2 + 5*n + 3. Let y = 5 - 11. Let t be g(y). Solve -4*k - 10*k**4 - 18*k**3 - t*k**2 + 0*k**5 - 2*k**5 - 5*k**2 = 0 for k.
-2, -1, 0
Let i(p) be the second derivative of p**6/135 - p**5/90 - 5*p**4/54 - p**3/9 - 5*p. Find b such that i(b) = 0.
-1, 0, 3
Let r(n) = -n**3 + 5*n**2 + n - 5. Let f(u) = u**3 - 3*u**2 - u + 3. Let i(q) = 5*f(q) + 3*r(q). Determine v so that i(v) = 0.
-1, 0, 1
Let l(o) = 5*o**4 - 25*o**3 + 40*o**2 - 22*o + 2. Let h(i) = 5*i**4 - 25*i**3 + 40*i**2 - 23*i + 3. Let j(v) = 2*h(v) - 3*l(v). Suppose j(m) = 0. Calculate m.
0, 1, 2
Let p(d) be the first derivative of 2*d**3/21 - d**2/7 - 1. Suppose p(r) = 0. Calculate r.
0, 1
Let p(a) be the second derivative of a**5/80 - a**4/24 - a**3/8 - 16*a. Factor p(i).
i*(i - 3)*(i + 1)/4
Let y(p) = 4*p**3 + 10*p**2 - 16*p - 2. Let x(o) = o**4 + 20*o**3 + 51*o**2 - 80*o - 11. Let l(q) = 4*x(q) - 22*y(q). Determine u so that l(u) = 0.
-2, 0, 2
Suppose 3*o = -o + 12. Factor 23*g**o - g**4 - 7*g**3 + 33*g**4 + 2*g**2.
2*g**2*(4*g + 1)**2
Let z(u) be the third derivative of -u**5/600 + 11*u**4/240 + u**3/5 + 48*u**2. Find w, given that z(w) = 0.
-1, 12
Let b be 168/20 - 4/10. Let m = -6 + b. Find a such that -2*a**3 + m - 2*a**2 + 5*a - 3*a - 4*a + 4*a**3 = 0.
-1, 1
Let n(y) be the first derivative of 0*y + 1/108*y**4 - 1/3*y**3 + 0*y**2 + 1/1620*y**6 - 1/270*y**5 + 3. Let i(v) be the third derivative of n(v). Factor i(u).
2*(u - 1)**2/9
Suppose 0 = -5*b, -14 - 2 = -4*v + 5*b. Suppose 2 + 3*p + p**4 + 0*p**4 - v - 3*p**3 + p**2 = 0. What is p?
-1, 1, 2
Let c be ((-2)/(-2)*-1)/(-1). Suppose 2*l - 6 - 5 = -d, -4*d = -2*l - 4. Factor -2*y**2 + 2*y**d - c - 1 + 2.
2*y**2*(y - 1)
Let r(l) = -l**2 + l. Let p(o) = -3*o**3 + 2*o**2 - 2*o + 5. Let n(t) = p(t) + 5*r(t). Let v(q) be the first derivative of n(q). Factor v(x).
-3*(x + 1)*(3*x - 1)
Let k be (16/(-15))/((-6)/9). Let v(h) be the first derivative of -3 + k*h + 4/5*h**2 + 2/15*h**3. Factor v(a).
2*(a + 2)**2/5
Find y such that 1/4*y**3 + 3/4*y + 1/4 + 3/4*y**2 = 0.
-1
Let u(b) be the third derivative of -1/120*b**5 - 1/240*b**6 + 1/420*b**7 + 1/672*b**8 + 0 + 0*b + 0*b**3 + 0*b**4 - b**2. Let u(j) = 0. Calculate j.
-1, 0, 1
Let q = -69 - -72. Let g(p) be the first derivative of -1/3*p**q + 0*p**4 + 1/5*p**5 + 1 + 0*p + 0*p**2. Factor g(o).
o**2*(o - 1)*(o + 1)
Let h = 142/5 - 553/20. Let h*m**2 - 3/4*m**3 - 3/4 + 3/4*m = 0. Calculate m.
-1, 1
Let -98/3 - 1/3*p**3 - 7*p + 4*p**2 = 0. Calculate p.
-2, 7
Let j = 434 - 867/2. Factor -1/2*a**4 + 0 + a**3 + j*a**2 - a.
-a*(a - 2)*(a - 1)*(a + 1)/2
Factor 0 - 5/4*r**3 - 5/4*r + 5/2*r**2.
-5*r*(r - 1)**2/4
Let t be (-8)/(-16)*4/3. Determine q so that t*q**2 + 2/3*q + 0 = 0.
-1, 0
Suppose 8*f - 4*f - 20 = 0. Let w(z) = -z**5 + z**4 - 12*z**3 + 15*z**2 - 13*z. Let j(l) = -6*l**3 + 8*l**2 - 6*l. Let y(c) = f*j(c) - 2*w(c). Factor y(x).
2*x*(x - 1)**3*(x + 2)
Suppose -4*d + 5*b = -2*d + 5, 3*d + 4*b = 4. Let u(v) be the third derivative of v**2 - 1/6*v**4 + 0*v + d + 1/30*v**5 + 1/20*v**6 + 0*v**3. Factor u(n).
2*n*(n + 1)*(3*n - 2)
Suppose -2*w = 5*d - 2 + 19, 4*w - 11 = -d. Suppose 0*g**3 - 2*g**4 + w*g**4 + 2*g**3 = 0. Calculate g.
-1, 0
Let a(h) be the third derivative of -h**6/120 + 3*h**5/40 - h**4/4 + h**3 - 5*h**2. Let b(q) be the first derivative of a(q). Factor b(r).
-3*(r - 2)*(r - 1)
Solve 25*r**2 - 6*r**3 - 30*r + 8*r - 8*r + r**3 = 0 for r.
0, 2, 3
Let p(f) be the first derivative of -2*f**5/15 - 3*f**4/2 - 10*f**3/3 + 25*f**2/3 + 33. Factor p(r).
-2*r*(r - 1)*(r + 5)**2/3
Let u be 1 - (-2 - (3 - 6)). Let i(c) be the second derivative of 0 - 1/30*c**6 + c + 1/10*c**5 + 0*c**2 + u*c**3 - 1/12*c**4. Factor i(l).
-l**2*(l - 1)**2
Solve -65*f - 23*f**2 + 16*f**2 - 4 - 48*f**2 - 6 = 0 for f.
-1, -2/11
Let r(j) be the second derivative of j**4/18 - j**3/3 + 2*j**2/3 + 7*j. Factor r(k).
2*(k - 2)*(k - 1)/3
Let b(w) = w**3 + 7*w**2 + 6*w. Let l(z) = 3*z**2 + 3*z. Let d(q) = 3*b(q) - 7*l(q). Suppose d(p) = 0. What is p?
-1, 0, 1
Suppose -2*w + 1 = -5. Factor 4*g**2 + 2*g**2 - 8 - 2*g**3 + 0*g**w.
-2*(g - 2)**2*(g + 1)
Let j be 64/(-4)*(-2)/4. Let w(d) be the third derivative of 0*d**3 - 1/420*d**7 + 0*d**4 - 1/672*d**j + 0 + 0*d + 1/240*d**6 + d**2 + 1/120*d**5. Factor w(v).
-v**2*(v - 1)*(v + 1)**2/2
Let d = 1037/3 + -343. Find f, given that -d - 46/3*f**2 - 12*f - 5*f**3 = 0.
-2, -2/3, -2/5
Factor g**2 - 10*g - 3*g**4 - 2*g**2 + 6*g**3 + 4*g**2 + 4*g.
-3*g*(g - 2)*(g - 1)*(g + 1)
Let i(x) = -x**4 - 17*x**3 + x**2 + x. Let g(l) = -6*l**3. Let c(a) = 8*g(a) - 3*i(a). Factor c(d).
3*d*(d - 1)*(d + 1)**2
Let p(y) = -5*y**4 - 7*y**3 + 3*y**2 - y + 6. Let w(f) = f**4 + 21 - 26 - 2*f**2 + 6*f**3 + 3*f**4. Let x(r) = 3*p(r) + 4*w(r). What is n in x(n) = 0?
-2, -1, 1
Suppose 0 = -20*h + 21*h. Let a(r) be the first derivative of h*r + 4/35*r**5 - 1/7*r**2 - 4/21*r**3 + 1/21*r**6 + 0*r**4 + 2. Find u such that a(u) = 0.
-1, 0, 1
Let c(s) be the first derivative of s**8/2240 - s**7/560 - 4*s**3/3 + 3. Let d(a) be the third derivative of c(a). Factor d(j).
3*j**3*(j - 2)/4
Let x = 1 - 2. Let l be (1 - x)*(9 - 7). Factor -14/11*b**3 + 0 + 10/11*b**2 - 2/11*b + 6/11*b**l.
2*b*(b - 1)**2*(3*b - 1)/11
Let n = 1 + 4. Suppose -5*i + i + u = -13, u - 5 = -n*i. Factor 0 + 16/5*o**3 + 4/5*o**i + 0*o + 21/5*o**4 + 9/5*o**5.
o**2*(o + 1)*(3*o + 2)**2/5
Let x(f) = -f - 11. Suppose 3*t + 21 = -4*c, -t + 6*c - c = 26. Let p be x(t). What is b in 1/4*b**3 - 3/4*b + p*b**2 - 1/2 = 0?
-1, 2
Let g = -6 - -20. Let s(j) = j**2 - 14*j + 2. Let r be s(g). Find x such that 10*x**3 + 4 - 5*x**4 - x**4 + 2*x**2 - 5*x - 3*x - r*x = 0.
-1, 2/3, 1
Let w(g) be the first derivative of -3*g**4/16 - g**3/2 - 3*g**2/8 + 5. Suppose w(n) = 0. Calculate n.
-1, 0
Let k be 42/(-216)*6/(-28). Let f(j) be the third derivative of 2*j**2 - k*j**4 + 0 + 0*j - 1/60*j**5 + 1/3*j**3. Find w, given that f(w) = 0.
-2, 1
Let q = -8 + 10. Let u be 12/(-8) - -3*1. Find z, given that 1 - 3*z + 13/4*z**q - u*z**3 + 1/4*z**4 = 0.
1, 2
Suppose 36 = 5*g - 14. Let a be 3 + (-2)/(8/g). Find v, given that 0*v**2 + a*v**3 + v**5 + 3/2*v**4 + 0 + 0*v = 0.
-1, -1/2, 0
Let z(r) be the third derivative of -1/12*r**4 - 3*r**2 + 0 + 1/60*r**5 + 0*r + 1/6*r**3. Factor z(p).
(p - 1)**2
Let w = -8/59 - -83/177. Determine t so that -w*t**3 + 0*t**2 - 1/3*t**4 + 0 + 0*t = 0.
-1, 0
Suppose -13 + 1 = -4*r. Let n(i) be the first derivative of -i + 3 - 1/5*i**5 + 2*i**2 - 2*i**r + i**4. Let n(u) = 0. Calculate u.
1
Let n(t) = 3*t**4 - 18*t**3 + 12*t**2 - 6*t + 6.