- 3. Let y(h) be the second derivative of m(h). Factor y(k).
2*(k + 2)**2/5
Let u(f) = -f. Let i be u(-2). Solve -3*q**2 + 4*q**i - q**3 - 3*q**2 + 3*q**2 = 0 for q.
0, 1
Let m(n) be the third derivative of 1/300*n**5 - 4*n**2 + 0 - 1/30*n**3 + 1/120*n**4 - 1/600*n**6 + 0*n. Factor m(u).
-(u - 1)**2*(u + 1)/5
Let u be 26/10 - 15/25. Suppose 2*h - 2 = 2. Solve u*k**5 - 4*k**4 + 0*k**5 - 2*k + 8*k**2 - 4*k**h + 0*k = 0 for k.
-1, 0, 1
Let j(k) = 3*k**2 + 2*k - 4. Let v be j(-4). Suppose -3*b - h + v = 2*b, -4*b + h = -36. Suppose -2 + 3*t**2 + b*t - t**3 - 12*t - t**4 + 5*t = 0. What is t?
-2, -1, 1
Let y(a) = -a. Let o be y(-7). Let x be 19/o - (-10)/35. Factor -11/2*r**2 + 5/2*r**5 + 21/2*r**x + r - 17/2*r**4 + 0.
r*(r - 1)**3*(5*r - 2)/2
Let b be 2/(-10)*(-9 - -6). Let z = b + -7/20. Solve -i**2 + 0 - z*i**3 - i = 0.
-2, 0
Let o(g) be the third derivative of g**7/70 - g**6/40 - g**5/10 + 8*g**2. Let o(s) = 0. Calculate s.
-1, 0, 2
Factor 0 + 1217*w**2 + 12*w - 1213*w**2 + 8.
4*(w + 1)*(w + 2)
Suppose -45 = -5*w - 5*y, -2*y + 33 = 5*w - y. Let o be w/(-10) - 84/(-40). What is q in 0*q**2 + 1 + 1/2*q**3 - o*q = 0?
-2, 1
Let o(m) be the second derivative of -1/10*m**5 + 1/3*m**3 + 4/15*m**6 - 2/3*m**4 + 0*m**2 - 6*m + 0. Solve o(b) = 0.
-1, 0, 1/4, 1
Factor 0*p - p**2 + 0*p**3 + 1/2*p**4 + 1/2.
(p - 1)**2*(p + 1)**2/2
Let i(r) be the first derivative of r**4/4 + 5*r**3/3 - r**2/2 - 3*r - 2. Let k be i(-5). Factor -k*o**4 - o**3 - o**2 + 5*o**3 - o**2.
-2*o**2*(o - 1)**2
Let w(z) be the first derivative of 4*z**5 - 65*z**4/4 + 5*z**3 + 8. Factor w(m).
5*m**2*(m - 3)*(4*m - 1)
Let b(d) be the first derivative of -2/3*d**3 - 1/4*d**4 + 2/5*d**5 + 0*d + 1/2*d**2 - 3. Factor b(f).
f*(f - 1)*(f + 1)*(2*f - 1)
Let l(v) = -v**2 - 5*v + 6. Let i be l(-6). Factor -o**4 - 2*o + 5*o**2 + 3*o**3 - 4*o**2 + i*o**2 - o**5.
-o*(o - 1)**2*(o + 1)*(o + 2)
Let t(i) be the first derivative of 3/2*i**2 + 3/4*i**4 + 0*i - 3 - 2*i**3. Suppose t(n) = 0. What is n?
0, 1
Determine f, given that 2/3*f**4 - 2*f**2 - 1/3*f - 1/3*f**3 + 2/3 = 0.
-1, 1/2, 2
Let b(i) = 2*i + 12. Let p be b(-8). Let r be (2 + (-3)/1)*p. Determine k so that -3/2*k**2 + k - 1/4 - 1/4*k**r + k**3 = 0.
1
Suppose 3*m + 18 = -0*m. Let y be 2 + m/(-1 + 4). Solve -1/3*v - 2/3*v**2 + y - 1/3*v**3 = 0 for v.
-1, 0
Let z(f) be the second derivative of 6*f + 0*f**2 + 2/3*f**4 + 3/5*f**5 + 1/21*f**7 + 4/15*f**6 + 0 + 1/3*f**3. Factor z(r).
2*r*(r + 1)**4
Let d(m) = -2*m**2 - 3*m. Let w(c) be the second derivative of -5*c**4/12 - 7*c**3/6 - c. Let z(v) = -14*d(v) + 6*w(v). Determine b so that z(b) = 0.
0
Let t(k) = k**2 + 5*k - 2. Let j be t(-6). Let i be 1 + -5 - (-120)/28. Factor 0 - 4/7*r**3 + 0*r**j + 0*r**2 + 2/7*r + i*r**5.
2*r*(r - 1)**2*(r + 1)**2/7
Let h be 2/6 - (-10923)/63. Let l = 174 - h. Let 4/7*u**2 - 2/7 - 2/7*u + 4/7*u**3 - 2/7*u**5 - l*u**4 = 0. What is u?
-1, 1
Factor -c + 4*c - 3*c**2 - 4*c + 7*c.
-3*c*(c - 2)
Let c(t) = -20*t**2 - 56*t - 40. Let r be -2*2/(-4) - -4. Let b(y) = -13*y**2 - 37*y - 27. Let p(g) = r*c(g) - 8*b(g). Factor p(q).
4*(q + 2)**2
Suppose m = -m + 10. Let 4/5*o**4 - 2/5*o**3 - 2/5*o**m + 0*o**2 + 0 + 0*o = 0. Calculate o.
0, 1
Let b(w) = w**3 - 5*w**2 - 6*w + 2. Let u be b(6). Suppose u*m = -l + 3 - 1, -3*m = 0. Factor -1/2 - 1/2*k**l - k.
-(k + 1)**2/2
Factor 10*o - 5*o**2 + 0*o**3 - 4*o**3 + 3*o**4 + 2*o**4 - 6*o**3.
5*o*(o - 2)*(o - 1)*(o + 1)
Let q(l) = -2*l - 6. Suppose 6 = -x + 2. Let w be q(x). Factor -2*i + 6*i**2 + i**2 + i**w.
2*i*(4*i - 1)
Let q(a) be the first derivative of a**6/120 + a**5/30 + a**4/24 + 4*a**2 - 9. Let x(j) be the second derivative of q(j). Find k such that x(k) = 0.
-1, 0
Let k(f) be the second derivative of 0 - 1/15*f**3 + 2*f + 2/5*f**2 - 1/30*f**4. Factor k(g).
-2*(g - 1)*(g + 2)/5
Factor 2/11*z**3 - 26/11*z + 0*z**2 - 24/11.
2*(z - 4)*(z + 1)*(z + 3)/11
Let p(v) be the third derivative of v**9/151200 + v**8/50400 - v**7/2520 + v**6/600 + 3*v**5/20 + 5*v**2. Let k(h) be the third derivative of p(h). Factor k(z).
2*(z - 1)**2*(z + 3)/5
Let j(s) = 2*s - 2. Let b = 6 + -4. Let g be j(b). Factor 2*k + k**2 + k**2 + 2*k**2 + g*k**3.
2*k*(k + 1)**2
Let l(v) = 15*v**2 + 30*v + 32. Let p(m) = 5*m**2 + 10*m + 11. Let s(a) = -6*l(a) + 17*p(a). Solve s(c) = 0 for c.
-1
Let n be 2 - (-11478)/(-5040) - (-4)/14. Let w(r) be the third derivative of 0*r + 1/48*r**4 + 0 + 1/6*r**3 - n*r**5 - r**2. Factor w(i).
-(i - 2)*(i + 1)/2
Let t(y) = -y**2 - 9*y - 4. Let k be t(-8). Let r = 57/2 + -28. Find l such that 0 - r*l**3 - 1/2*l**2 - 1/6*l - 1/6*l**k = 0.
-1, 0
Let d(b) = -b**3 - 3*b**2 + 4*b + 3. Let u be d(-4). Let c(o) = o**2 - o - 2. Let k be c(2). Factor 0*y + k + 0*y**2 + 2/5*y**5 - 2/5*y**u + 0*y**4.
2*y**3*(y - 1)*(y + 1)/5
Let i(h) be the third derivative of 1/12*h**4 - 13/210*h**7 - 3/40*h**6 + 1/60*h**5 - 2*h**2 + 0*h + 0 - 5/336*h**8 + 0*h**3. What is n in i(n) = 0?
-1, 0, 2/5
Suppose 2*x = x. Let o(l) be the first derivative of 1/3*l - 1/6*l**4 + 1/3*l**2 - 1/15*l**5 - 3 + x*l**3. Factor o(v).
-(v - 1)*(v + 1)**3/3
Let i(n) be the second derivative of 16/11*n**2 - 8/33*n**3 + 0 + 1/66*n**4 + 3*n. Determine d so that i(d) = 0.
4
Determine k, given that 9*k - 3*k**2 - 3*k**2 - 3*k**5 + 15*k**3 - 21*k**3 + 9*k**4 - 3 = 0.
-1, 1
Let v(b) = b**2. Let m(k) = -15*k + 1. Let x(u) = -m(u) - 2*v(u). Let j(l) = l**2 - 7*l + 1. Let c(o) = -7*j(o) - 3*x(o). Factor c(q).
-(q - 2)**2
Let i(m) be the first derivative of m**7/168 - m**5/40 + m**3/24 + 4*m - 3. Let u(x) be the first derivative of i(x). What is l in u(l) = 0?
-1, 0, 1
Let p(f) = -3*f**3 - 13*f**2 + 3*f + 9. Let x(w) = -3*w**3 - 12*w**2 + 3*w + 9. Let h(s) = 3*p(s) - 4*x(s). Factor h(u).
3*(u - 1)*(u + 1)*(u + 3)
Let x(t) = -5*t + 12*t + 0*t**3 + t**3 - 7. Let n(u) = -5 + 2*u + 0 + u**3 + 3*u. Let d(h) = 7*n(h) - 5*x(h). Factor d(v).
2*v**3
Suppose -w + 6 = 2*w. Let v(m) be the third derivative of 1/12*m**3 - 1/32*m**4 + 0 + 1/240*m**5 + 0*m + w*m**2. Factor v(u).
(u - 2)*(u - 1)/4
Let y = 70 - 67. Let q be 0 - (-1 - 2 - -1). Let 0 + 2/5*d + 2/5*d**y - 4/5*d**q = 0. Calculate d.
0, 1
Solve 0 + 1/3*d**3 + 2/3*d - d**2 = 0 for d.
0, 1, 2
Suppose -3*d + 8*d - 90 = 0. Let p be (24/d)/((-14)/(-3)). Factor 0 - p*r**4 + 0*r + 0*r**2 + 0*r**3.
-2*r**4/7
Let r(u) = 7*u**3 + u**2 + 5*u - 7. Let m(l) = -8*l**3 - l**2 - 6*l + 8. Let j(k) = 6*m(k) + 7*r(k). Find s, given that j(s) = 0.
-1, 1
Let y be 0/4 + (-11)/(-33). Solve 4/3*l - 4/3 - y*l**2 = 0 for l.
2
Let f be 1/6 - 17/(-6). Determine m so that 5*m**2 - m**2 - f*m - 3*m**2 + 2 = 0.
1, 2
Let d(t) be the first derivative of 2*t**3/3 - 2*t**2 + 2*t + 1. Suppose d(n) = 0. Calculate n.
1
Let l(c) = 2*c - 26. Let d be l(0). Let g = 28 + d. Let 2/7*h + 4/7*h**g + 2/7*h**3 + 0 = 0. What is h?
-1, 0
Let h(q) = q**3 - q**2 + 1. Let c(f) = -9*f**3 + 4*f**2 + 5*f - 4. Let v(g) = c(g) + 4*h(g). Find a, given that v(a) = 0.
-1, 0, 1
Let d be (4/(-12)*1)/(1/(-6)). Factor 1/5 + 1/5*x**4 - 4/5*x + 6/5*x**d - 4/5*x**3.
(x - 1)**4/5
Let m(p) be the third derivative of -p**8/2184 + p**7/1365 + p**6/260 - p**5/78 + p**4/78 + 12*p**2. Find g, given that m(g) = 0.
-2, 0, 1
Let t(c) be the first derivative of 3*c**5/20 + 9*c**4/16 + 3*c**3/4 + 3*c**2/8 - 3. Determine j so that t(j) = 0.
-1, 0
Let a(u) = u**4 - 21*u**3 - 11*u**2 + 5. Let c(m) = -20*m**3 - 12*m**2 + 4. Let o be (6/2)/3*5. Let b(l) = o*c(l) - 4*a(l). Factor b(i).
-4*i**2*(i + 2)**2
Factor 1/3*h**2 + 0 - 1/3*h.
h*(h - 1)/3
Let k be 92/115*(-2)/(-12). Solve 0*w + 0 - 2/5*w**3 - 2/15*w**2 - k*w**5 - 2/5*w**4 = 0 for w.
-1, 0
Let y(u) be the third derivative of u**7/2520 - u**6/180 + u**5/30 + u**4/6 + u**2. Let l(x) be the second derivative of y(x). Let l(t) = 0. Calculate t.
2
Determine q so that 0 - 3*q - 1 + 3*q**2 - 5 = 0.
-1, 2
Factor -1/8*c**2 + 1/4 - 1/8*c.
-(c - 1)*(c + 2)/8
Let v be (1/7)/((-8)/(-16)). Find t such that 0 + 0*t**2 + 0*t + 0*t**3 + 2/7*t**4 + v*t**5 = 0.
-1, 0
Let x(a) be the first derivative of -a**4/6 + a**2 + a - 3. Let z(c) be the first derivative of x(c). Factor z(i).
-2*(i - 1)*(i + 1)
Let 1/3 - 10/3*y**3 - 1/3*y**5 + 10/3*y**2 - 5/3*y + 5/3*y**4 = 0. What is y?
1
Let g(f) be the second derivative of -2*f**6/15 - 8*f**5/5 + 10*f**4/3 + 16*f**3/3 - 18*f**2 - 5*f - 1. Find q, gi