w**4 + 21*w**3 - 21*w**2 + 6*w. Let s(j) = 8*j**5 + 45*j**4 - 64*j**3 + 63*j**2 - 18*j. Let x(a) = 6*s(a) + 17*z(a). Factor x(n).
-3*n*(n - 2)*(n - 1)**3
Let o(j) be the third derivative of j**6/900 - j**5/300 + j**3/3 + 2*j**2. Let c(f) be the first derivative of o(f). Find q, given that c(q) = 0.
0, 1
Let u be 12/(-8)*2 - -5. Let v(h) be the first derivative of 1/6*h**3 + 0*h + 0*h**2 + u + 3/10*h**5 + 1/12*h**6 + 3/8*h**4. Factor v(i).
i**2*(i + 1)**3/2
Suppose 0 = 3*d - 4*l - 20, 0 = 3*d + 5*l + 45 - 20. Solve d - 12/7*o**5 - 3/7*o + 15/7*o**3 + 9/7*o**4 - 9/7*o**2 = 0 for o.
-1, -1/4, 0, 1
Suppose 5*n = 4*n. Suppose m - 1 = n, 5*h + 4*m - 3 = 11. Suppose 6/5*l**4 + 0 + 2*l**5 + 0*l**h + 0*l - 4/5*l**3 = 0. What is l?
-1, 0, 2/5
Let u = -118 + 828/7. Find h, given that 0*h + u*h**3 + 0 + 2/7*h**2 = 0.
-1, 0
Suppose 3*o - 3*w - 31 - 104 = 0, 3*w + 215 = 5*o. Determine r so that -44*r**4 + 27*r**3 + 16*r**2 - 51*r**3 + 36*r**5 - o*r**3 = 0.
-1, 0, 2/9, 2
Find i, given that 49 - 77*i**2 + 24*i**2 + 26*i**2 - 14*i + 28*i**2 = 0.
7
Let d(n) be the third derivative of -2*n**5/285 + 7*n**4/228 - n**3/19 + 26*n**2. Suppose d(w) = 0. Calculate w.
3/4, 1
Let q(f) be the second derivative of f**8/3360 + f**7/1260 - f**6/360 - f**5/60 - f**4/2 + 2*f. Let r(g) be the third derivative of q(g). Factor r(v).
2*(v - 1)*(v + 1)**2
Factor a**2 - 2*a + a**2 - a**2 - 3*a + 6.
(a - 3)*(a - 2)
Suppose -8 + 1 = 7*o. Let x(v) = 0 + 4 - 5. Let t(a) = 2*a**2 + 4*a - 5. Let l(b) = o*t(b) + 5*x(b). Let l(i) = 0. Calculate i.
-2, 0
Let n(b) be the third derivative of -b**6/160 + b**4/8 + 14*b**2. Find h such that n(h) = 0.
-2, 0, 2
Let z(r) be the second derivative of r**5/30 - r**4/9 - r**3/9 + 2*r**2/3 + 25*r. Find k, given that z(k) = 0.
-1, 1, 2
Let f = -7 + 169/24. Let g(y) be the second derivative of 5/48*y**4 - 2*y + 0 - f*y**3 - 1/20*y**5 + 0*y**2. Determine t so that g(t) = 0.
0, 1/4, 1
Suppose 3*f**5 - 8*f**5 + 19*f + 10*f**2 - 14*f - 10*f**4 = 0. What is f?
-1, 0, 1
Let d(f) be the first derivative of -2 + 18/5*f + 2/15*f**3 - 6/5*f**2. Factor d(z).
2*(z - 3)**2/5
Let x(s) be the first derivative of -s + 1/4*s**4 - 1/2*s**2 + 1/3*s**3 + 8. Suppose x(g) = 0. What is g?
-1, 1
Let p(j) = -10*j**2 + 15*j - 6. Let s(l) = -50*l**2 + 76*l - 31. Let b(n) = -22*p(n) + 4*s(n). Suppose b(q) = 0. Calculate q.
1/2, 4/5
Let f(g) be the first derivative of 0*g + 1/8*g**2 + 2 + 1/12*g**3. Find p, given that f(p) = 0.
-1, 0
Let a(n) be the first derivative of 6*n**3 + 2*n**2 + 22. Determine d, given that a(d) = 0.
-2/9, 0
Let o be ((-4)/(1 + -2))/2. Factor 0 - 8/3*v**o - 8/3*v - 2/3*v**3.
-2*v*(v + 2)**2/3
Let w(n) be the first derivative of 1/4*n**2 + 0*n**3 + 1/20*n**5 - 1/8*n**4 - 1/4*n + 1. Determine h, given that w(h) = 0.
-1, 1
Let i(p) be the second derivative of 0 + 0*p**3 + 0*p**5 + 0*p**2 - 1/90*p**6 + 9*p + 0*p**4 - 1/252*p**7. Factor i(n).
-n**4*(n + 2)/6
Let u = 33 + -25. Let i be u*((-435)/(-100) + -4). Factor i*t**3 - 14/5*t + 4/5*t**2 - 4/5.
2*(t - 1)*(t + 1)*(7*t + 2)/5
Let a(o) = -5*o**5 + 6*o**4 - 2*o**3 - 6*o**2 + 7*o. Let f(r) = r**5 - r**4 + r**2 - r. Let s(k) = a(k) + 6*f(k). Factor s(v).
v*(v - 1)**2*(v + 1)**2
Let d(w) be the second derivative of -w**5/70 + w**4/14 - w**3/7 + w**2/7 - 5*w. Factor d(n).
-2*(n - 1)**3/7
Let g(n) be the second derivative of -n**6/150 - n**5/100 + n**4/60 + n**3/30 - 8*n. Find i such that g(i) = 0.
-1, 0, 1
Let o(n) be the third derivative of 0*n + 0 - 1/16*n**4 - 1/240*n**5 - 5*n**2 - 3/8*n**3. Let o(p) = 0. Calculate p.
-3
Suppose -3*s - 4*i - 1 + 11 = 0, -3*s + 7 = i. What is w in -16*w + s*w**3 - 2*w**4 + 8 - w**2 - 2*w**5 - 4*w**3 + 12*w**3 + 3*w**2 = 0?
-2, 1
Let q(b) be the third derivative of -b**6/180 + b**5/45 - b**4/36 - 6*b**2. Solve q(f) = 0 for f.
0, 1
Let l be 2/(-6) - 260/(-150). Solve -l*s**2 + 9/5*s - 2/5 = 0 for s.
2/7, 1
Let p(r) = 2*r**3 + 4*r**2 + 4*r - 4. Let u(h) = 3*h**3 + 5*h**2 + 5*h - 5. Let d(w) = 4*p(w) - 3*u(w). Suppose d(j) = 0. Calculate j.
-1, 1
Let g(k) = 3*k**5 - 37*k**4 - 96*k**3 - 75*k**2 - 11*k - 11. Let m(x) = -x**5 + 9*x**4 + 24*x**3 + 19*x**2 + 3*x + 3. Let i(h) = -6*g(h) - 22*m(h). Factor i(d).
4*d**2*(d + 2)**3
Let l(z) = 2*z**3 - 4*z**2 + 4*z - 3. Let p be l(2). Suppose p*w = 2*s - 24, -s - 2*w - 3 - 3 = 0. Factor 4 - 4*n**2 - 2*n + s*n**5 + 4*n**4 - 4.
2*n*(n - 1)*(n + 1)**3
Let o(a) be the second derivative of -a**5/20 + a**3/6 - 6*a. Factor o(r).
-r*(r - 1)*(r + 1)
Let p(y) be the third derivative of 0*y - 1/840*y**7 + 0 - 3*y**2 + 0*y**6 + 0*y**4 - 1/24*y**3 + 1/120*y**5. Find z such that p(z) = 0.
-1, 1
Let k(s) be the first derivative of -3*s**4/22 + 16*s**3/33 + 3*s**2/11 - 11. Find h, given that k(h) = 0.
-1/3, 0, 3
Factor 21*i**2 + 15*i + 0*i**3 + 15*i**3 - 9*i.
3*i*(i + 1)*(5*i + 2)
Let o(h) be the third derivative of -h**5/9 - 14*h**4/27 + 8*h**3/27 + 36*h**2. Factor o(z).
-4*(z + 2)*(15*z - 2)/9
Let d = 6 - 5. Let n(q) = q**3 - 1. Let i be n(d). Determine m so that -m**4 + 3*m**4 - 4*m**4 - m**5 + i*m**5 - m**3 = 0.
-1, 0
Let w = 14 + -11. Let h(u) be the third derivative of 0 + 0*u**w + 0*u + 1/50*u**5 + 1/525*u**7 - 1/100*u**6 - 1/60*u**4 + u**2. Let h(t) = 0. What is t?
0, 1
Let f(m) = 5*m**5 - 17*m**4 + 6*m**3 + 3*m + 3. Let t(z) = 6*z**5 - 16*z**4 + 6*z**3 + 2*z + 2. Let j(c) = -2*f(c) + 3*t(c). Factor j(b).
2*b**3*(b - 1)*(4*b - 3)
Let s(g) = 3*g**2 - 4*g + 5. Let q(n) = 2*n**2 - 3*n + 4. Let u be (1*6)/((-12)/8). Let w(a) = u*q(a) + 3*s(a). What is l in w(l) = 0?
-1, 1
Let x be (1/2)/((-124)/(-186)). Factor -9/4*w + x*w**2 + 9/4*w**3 + 3/4*w**4 - 3/2.
3*(w - 1)*(w + 1)**2*(w + 2)/4
Let o(m) = -m - 1. Let y be o(-3). Let c be y/10 - (-3)/10. Factor -b**2 + c*b**3 + 1/2*b + 0.
b*(b - 1)**2/2
Let s be 6*-4*(-1)/6. Let w(m) be the first derivative of -1/12*m**6 + 0*m - 1/6*m**3 + 3 - 3/8*m**s + 0*m**2 - 3/10*m**5. Let w(l) = 0. Calculate l.
-1, 0
Let y(c) be the second derivative of c**4/48 + c**3/24 - 3*c. Factor y(s).
s*(s + 1)/4
Let k(v) be the second derivative of v**6/24 + 2*v**5/15 + v**4/24 - v**3/3 + v**2 - 4*v. Let i(c) be the first derivative of k(c). Let i(m) = 0. Calculate m.
-1, 2/5
Let t(a) be the first derivative of -a**5/5 + a**4/6 + a**3/3 - a**2/3 - 7. Determine p, given that t(p) = 0.
-1, 0, 2/3, 1
Let v be 9/36*(1 + (2 - 2)). Solve -v*t**3 - 3/4*t**2 + 1 + 0*t = 0.
-2, 1
Suppose -10*u - 11 = -41. Let b(x) be the second derivative of 1/48*x**4 + 1/4*x**2 + 0 - 1/8*x**u - 2*x. Factor b(i).
(i - 2)*(i - 1)/4
Suppose -4*b = -3*a + 7*a - 20, 0 = -4*b. Suppose -2/9*q**a + 0*q - 2/3*q**3 + 2/9*q**2 + 2/3*q**4 + 0 = 0. What is q?
0, 1
Suppose 0 = -2*m - 0*m + 12. Suppose 2*s**2 - s**2 + 3*s**3 + m*s**2 - 4*s**2 = 0. Calculate s.
-1, 0
Let l(d) be the second derivative of 8*d**2 - 121/5*d**5 - 32*d**3 + 0 + 55*d**4 + 5*d. Determine f, given that l(f) = 0.
2/11, 1
Determine t, given that -7 - 4 + 12*t + 1 - 3*t**2 + 1 = 0.
1, 3
Let a(s) be the third derivative of s**7/70 - s**6/8 + 2*s**5/5 - s**4/2 - 4*s**2. Factor a(c).
3*c*(c - 2)**2*(c - 1)
Let r be (1/2)/((-7)/42). Let b be ((-4)/8 - 0)*r. Solve 3/4 + b*h - 3/4*h**4 + 0*h**2 - 3/2*h**3 = 0 for h.
-1, 1
Let v be (-2)/(-3) + -1 + (-15)/(-18). Let n be 0*(-1)/(-2)*-1. Determine k, given that -v*k**2 - 1/4*k**3 + n - 1/4*k = 0.
-1, 0
Let r(p) be the second derivative of -2*p**6/75 + 2*p**4/15 - 2*p**2/5 + 6*p. Solve r(m) = 0 for m.
-1, 1
Suppose -2*a - a = -42. Let t(d) = -84*d**3 - 90*d**2 - 20*d + 14. Let n(w) = -17*w**3 - 18*w**2 - 4*w + 3. Let y(g) = a*n(g) - 3*t(g). Factor y(r).
2*r*(r + 1)*(7*r + 2)
Let b(w) be the first derivative of -w**7/1155 - w**6/396 - w**5/660 - 4*w**3/3 + 5. Let u(s) be the third derivative of b(s). Solve u(a) = 0.
-1, -1/4, 0
Suppose -5*w + 8 = -3*l, 4*l - 14 - 2 = 0. Factor 21*t - 4*t**3 - 2*t**4 - 19*t - 2 + w*t**2 + 0*t**5 + 2*t**5 + 0.
2*(t - 1)**3*(t + 1)**2
Let d be 8*(26/8 + -2). Suppose d*j = 15*j - 10. Factor -1 + m - 1/4*m**j.
-(m - 2)**2/4
Let g(s) be the third derivative of s**9/3024 + s**8/1680 - s**3/2 + 3*s**2. Let l(t) be the first derivative of g(t). Factor l(i).
i**4*(i + 1)
Solve -2/5*m**4 + 2*m**2 + 6/5*m + 0 + 2/5*m**3 = 0.
-1, 0, 3
Suppose 10 = 4*m - 3*a + a, -5*m = -a - 5. Suppose -4*r + 9 - 1 = m. Factor 2*q**3 + r*q**5 + q**5 - 5*q**3.
3*q*