h**4/4 + 2375*h**3/3 - 2205*h**2/2 - 810*h - 69. Solve m(i) = 0 for i.
-9, -2/7, 1
Let i = -1007099/540 + 1865. Let u(o) be the third derivative of 1/54*o**4 + 1/90*o**5 + 0*o - 7*o**2 + 0*o**3 + i*o**6 + 0. Find x such that u(x) = 0.
-2, -1, 0
Let u be ((-41)/6 - -9) + 0. Factor -1/3 - 10/3*v**2 - 3/2*v**3 - u*v.
-(v + 1)**2*(9*v + 2)/6
Let v = -46/205 - -128/205. Find t, given that 0 - v*t - 2/5*t**2 = 0.
-1, 0
Suppose 5*h + 18 = 53. Let k(p) = p - 9. Let i be k(h). Let r(a) = 4*a**3 - 4*a + 2. Let f(q) = 9*q**3 - 9*q + 5. Let m(w) = i*f(w) + 5*r(w). Factor m(g).
2*g*(g - 1)*(g + 1)
Solve 4119*j + 1662*j**4 + 38016*j**2 - 28*j**5 + 11369*j + 1223*j**4 - 401*j**4 - 55960*j**3 = 0 for j.
-2/7, 0, 1, 44
Let r(d) be the first derivative of -d**5/50 + d**4/5 - 32*d**2/5 + 25*d + 2. Let j(a) be the first derivative of r(a). Find u, given that j(u) = 0.
-2, 4
Suppose -2*o - 52 = -4*o + 4*t, 3*o - 100 = -5*t. Let b be (-7)/(-5) - 2/o*3. Determine f so that b*f**2 + 3/5*f**3 + 0*f + 0 = 0.
-2, 0
Let d(z) be the second derivative of 0 + 0*z**2 - 40/3*z**4 - 12*z + 518/15*z**6 - 8*z**3 + 121/5*z**5 - 140/3*z**7. Solve d(v) = 0 for v.
-2/7, 0, 1/2, 3/5
Let w(q) be the third derivative of -q**7/420 - q**6/80 + 84*q**2. Factor w(p).
-p**3*(p + 3)/2
Let c be (-1)/((3/(-27))/1). Solve -4*r**3 - 4*r + c*r**2 - 4*r + 2*r + r**3 = 0 for r.
0, 1, 2
Let x(v) be the third derivative of v**5/12 - 55*v**4/24 + 25*v**3 - 719*v**2. Determine z, given that x(z) = 0.
5, 6
Let g(i) be the first derivative of 5*i + 3/20*i**5 + 0*i**2 + 1/2*i**4 + 1/2*i**3 + 7. Let m(p) be the first derivative of g(p). Factor m(w).
3*w*(w + 1)**2
Let y(d) = d**3 + 6*d**2 - 261*d - 1076. Let i be y(-4). Solve -1/6*o**2 - 2/3*o + i = 0.
-4, 0
Suppose -68*x + 73*x = 0. Let m(d) be the second derivative of 1/48*d**4 + 0*d**3 + 0 + x*d**2 - 2*d + 1/80*d**5. Find k such that m(k) = 0.
-1, 0
Let r = 311/15 + -102/5. Let i(t) be the second derivative of 0 - 1/18*t**4 - r*t**2 - 5/18*t**3 - 6*t. Suppose i(y) = 0. Calculate y.
-2, -1/2
Let d be (1305/290)/(1 - (0 + 0)). Let k(u) be the first derivative of -u**3 + 3 - d*u**2 + 0*u. Factor k(l).
-3*l*(l + 3)
Let -3/7*c**2 + 0 - 18*c = 0. What is c?
-42, 0
Determine i, given that 32/5*i**3 + 0 - 52/5*i**2 + 4*i = 0.
0, 5/8, 1
Let p(j) be the first derivative of -3*j**4/4 - 7*j**3 + 15*j**2/2 + 9*j - 4. Let s(t) = t**2 - t. Let m(w) = p(w) + 12*s(w). Determine z so that m(z) = 0.
-3, -1, 1
Let v(b) = 0*b + 3*b + 4*b - 2. Let r be v(2). Solve -21 + 0*a**2 + 15 - 2*a**3 - r*a**2 - 15*a - a**3 = 0 for a.
-2, -1
Let z(x) = 2*x**5 + x**3. Let u(p) = -7*p**5 + 50*p**4 - 81*p**3 - 190*p**2 + 85*p + 140. Let d(a) = -u(a) - z(a). Suppose d(i) = 0. What is i?
-1, 1, 4, 7
Let t = 201 - 195. Let y(z) be the third derivative of -1/18*z**3 - 4*z**2 - 1/24*z**4 - 1/360*z**t - 1/60*z**5 + 0 + 0*z. Solve y(p) = 0.
-1
Let i(f) = 15*f**2 + 11*f + 13. Let n be 3/1 - ((-1 - -7) + 3). Let s(j) = 4 - 1 + 3 + 7*j**2 + 5*j. Let x(k) = n*i(k) + 13*s(k). Factor x(y).
y*(y - 1)
Let v(p) = -p**3 - 15*p**2 - 15*p - 21. Let o be v(-14). Let i be (o - -7 - 4/21)*-3. Factor 0 + i*h**2 - 2/7*h**3 + 0*h.
-2*h**2*(h - 2)/7
Factor -13*c**2 - 16*c - 6 - c**2 - c**2 - c**3 + 8*c**2 - 6.
-(c + 2)**2*(c + 3)
Let n(z) be the third derivative of z**7/840 + z**6/180 - z**5/120 - z**4/12 - 7*z**3/3 + 19*z**2. Let o(t) be the first derivative of n(t). Factor o(p).
(p - 1)*(p + 1)*(p + 2)
Find h, given that 159/7*h**4 + 2187/7 - 2022/7*h**3 - 2346/7*h**2 + 2025/7*h - 3/7*h**5 = 0.
-1, 1, 27
Let u be 12/(-16)*(7424/(-2880) - (-8)/18). Factor -44/5*l**2 - 16/5*l**3 - 4*l + u.
-4*(l + 1)*(l + 2)*(4*l - 1)/5
Let t(o) be the second derivative of -4*o - 1/294*o**7 + 5/42*o**3 + 0 - 2/105*o**6 + 1/7*o**2 + 1/42*o**4 - 1/35*o**5. Determine x, given that t(x) = 0.
-2, -1, 1
Let p = 6/307 - -253/2763. Let w(m) be the first derivative of -p*m**3 + 2/3*m**2 - 4/3*m + 1. Find i such that w(i) = 0.
2
Let p(g) be the second derivative of 5/96*g**4 + 0 + 25*g + 3/16*g**2 + 7/48*g**3 + 1/160*g**5. Solve p(z) = 0 for z.
-3, -1
Let w be 1*44/(-11)*(4 + -5). Factor -3 - 34/3*r**3 + 5/3*r**w + 68/3*r**2 - 10*r.
(r - 3)**2*(r - 1)*(5*r + 1)/3
Let 171 + 3*w**2 + 17*w + 116*w + 27*w + 14*w = 0. Calculate w.
-57, -1
Let u(l) be the second derivative of -l**6/40 + 9*l**5/80 - l**4/8 + 80*l. Factor u(z).
-3*z**2*(z - 2)*(z - 1)/4
Let u(q) = -7*q - 9. Let w be u(-6). Suppose -40*o + 28 = -w*o. Let 3/2*x**3 + 9/2*x**o + 1/2*x - 5/2*x**2 + 0 = 0. What is x?
-1, 0, 1/3
Factor 10*l - 2*l**3 - 11539*l**2 + 11522*l**2 + 7 + 2.
-(l - 1)*(l + 9)*(2*l + 1)
Let o(f) = 17*f**3 - 662*f**2 + 147856*f - 10941052. Let a(x) = -13*x**3 + 663*x**2 - 147855*x + 10941051. Let n(j) = 4*a(j) + 3*o(j). Solve n(r) = 0.
222
Let d be (-180)/144 - (114/(-440) - 1). Let m(n) be the second derivative of 4/11*n**2 + 8/33*n**3 + d*n**5 + 5/66*n**4 - 7*n + 0. Determine l so that m(l) = 0.
-2, -1
Let m = 230 - 230. Let z(y) be the third derivative of 0 + 1/21*y**3 - 1/42*y**4 - y**2 + m*y + 1/210*y**5. Let z(w) = 0. What is w?
1
Let o be ((-192)/54)/(26 - 28). Factor -25/9*j**2 - 1/9*j**5 - 40/9*j - o + 5/9*j**4 + 5/9*j**3.
-(j - 4)**2*(j + 1)**3/9
Let c be (-280)/(-45) + 10/(-45). Suppose 3*w - c = -0. Suppose 8/3 + 2/3*d**w + 10/3*d = 0. What is d?
-4, -1
Suppose 0 = -2*v - 0 + 24. Suppose -5*u - n + v = 0, -12 = -u - 4*n - n. Factor -24*g - 19*g**2 - 4 - 4*g**2 - 24*g**u - 30*g**3.
-(2*g + 1)*(3*g + 2)*(5*g + 2)
Suppose 2*b = -4*d + 16, -5*b + 0 = -10. Let q(c) be the third derivative of -7*c**2 + 0*c + 0*c**4 + 0*c**d + 1/330*c**5 + 0 + 1/660*c**6. Factor q(j).
2*j**2*(j + 1)/11
Let v(x) be the first derivative of x**3 + 21*x**2/2 + 36*x + 151. Find q such that v(q) = 0.
-4, -3
Let u(z) be the second derivative of z**8/2240 - z**7/140 + z**6/20 - z**5/5 + z**4/2 - 7*z**3/6 - 13*z. Let c(h) be the second derivative of u(h). Factor c(s).
3*(s - 2)**4/4
Let n = 35 + -24. Let v = n + -5. Let q(y) = y**2 - 2*y + 1. Let t(f) = -3*f**2 + 7*f - 4. Let x(b) = v*t(b) + 21*q(b). Factor x(k).
3*(k - 1)*(k + 1)
Factor -5/3*a**3 + 40/3 + 20/3*a - 10/3*a**2.
-5*(a - 2)*(a + 2)**2/3
Let b(j) = -j**3 + j**2 + j + 6. Let s be b(0). Let y be (-17)/34*(8/s + -2). Determine g, given that 2/3*g - g**2 + 0*g**3 + y*g**4 + 0 = 0.
-2, 0, 1
Suppose 0*c + 5*x = c + 10, -12 = -2*c + 2*x. Suppose l = -0*l + 3, -4*l + c = -s. Factor 1/2*i**3 - i + 1/2*i**s + 0.
i*(i - 1)*(i + 2)/2
Let n(t) be the third derivative of -t**9/20160 + t**7/1680 - t**5/160 - 7*t**4/12 - 3*t**2. Let b(f) be the second derivative of n(f). Factor b(k).
-3*(k - 1)**2*(k + 1)**2/4
Let h(x) = -x**3 + 11*x**2 + 2*x. Let a be h(8). Suppose -4*n = f - 436, n = 3*n - 2*f - a. Factor n*d - 108*d - 4*d**2 + 4*d**3.
4*d**2*(d - 1)
Let r(h) be the third derivative of h**8/5040 + h**7/945 + h**6/540 - 3*h**4/4 + 12*h**2. Let l(m) be the second derivative of r(m). Solve l(a) = 0.
-1, 0
Let p(h) = -18*h**2 - 96*h - 27. Let m be p(-5). Find b such that 0 - 6/5*b**2 + 9/5*b + 1/5*b**m = 0.
0, 3
Let q(z) = -7*z**2 + z - 1. Let m be q(-1). Let i be 0*(-2 + -1)/m. Factor i*u**2 + 0*u + 0 - 1/6*u**3.
-u**3/6
What is d in 1/6*d**4 + 11/6*d**2 + 0 + 3/2*d**3 - 7/2*d = 0?
-7, -3, 0, 1
Let q(l) be the first derivative of 10 - 9/4*l**4 - 3/2*l**2 + 0*l + 3/5*l**5 + 3*l**3. Factor q(r).
3*r*(r - 1)**3
Let m(f) be the third derivative of 0 + 0*f**3 + 0*f - 1/1260*f**7 - 1/720*f**6 + 1/360*f**5 + 4*f**2 + 0*f**4 + 1/2016*f**8. Determine i, given that m(i) = 0.
-1, 0, 1
Let v(x) = -x**3 - 8*x**2 - 5*x + 10. Let h be v(-7). Let w be (-6)/((2*h)/4). Solve -6/5 - 9/5*a + w*a**2 = 0.
-2/5, 1
Let l(w) be the second derivative of 3/50*w**5 + 0*w**2 + 4/15*w**3 + 4/15*w**4 + 0 + 8*w. Factor l(b).
2*b*(b + 2)*(3*b + 2)/5
Let o be (52/(-9) + 2)*46/(-420). Let g = o - -2/135. Factor 24/7 + g*y**3 + 36/7*y + 18/7*y**2.
3*(y + 2)**3/7
Let d(r) = -7*r - 30. Let i be d(-14). Let s be (-4)/(-5)*(5 + i/(-16)). Suppose 1/5 + 3/5*t**2 - 1/5*t**3 - s*t = 0. Calculate t.
1
Let c(s) be the third derivative of s**6/180 + s**5/90 - s**4/18 - 2*s**2 + s. Factor c(n).
2*n*(n - 1)*(n + 2)/3
Let s(m) = -5*m**4 + 260*m**3 + 2310*m**2 + 5165*m + 3610. Let g(y) = -y**4 + 37*y**3 + 330*y**2 + 738*y + 516. Let r(t) = -15*g(t) + 2*s(t). Factor r(o).
5*(o - 13)*(o +